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الكترونيات صناعيه وتحكم electronic circuits &control

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					                       ‫א‬‫א‬‫א‬
                    ã¹]<gè…‚jÖ]æ<ËÖ]<Üé×Ãj×Ö<íÚ^ÃÖ]<퉉ö¹]
                        ‫א‬‫א‬‫א‬‫א‬





     ‫א‬

       ‫א‬١٤٧
        ‫א‬                              ‫٧٤١ א‬                                    ‫א‬
                                           ‫א‬                          



                W،،‫א‬‫א‬،‫א‬
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‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
  ‫א‬ ‫א‬  ،‫א‬   ‫א‬ ‫א‬ ‫א‬ ‫א‬ ‫א‬ 
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                 
                                                              K‫א‬‫א‬‫א‬
                                                                                                     
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
  ‫א‬        ،‫א‬ ‫א‬‫א‬  
‫א‬  ‫א‬ ‫א‬ ‫א‬ ‫א‬ ‫א‬   ‫א‬    ،  
‫א‬،‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
     ‫א‬  ‫א‬   ،‫א‬   
                                     K‫א‬‫א‬،‫א‬‫א‬
                                                                                                     
?    ?  ?  ‫א‬ ? ‫א‬ ‫א‬  
             K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                                                     
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
،‫א‬،‫א‬‫א‬‫א‬‫א‬
                           K‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                                                     
،‫א‬‫א‬‫א‬‫א‬
                                                                                               K‫א‬
                                                                                                      
             ‫א‬‫א‬‫א‬‫א‬                                             
                                              ‫٧٤١ א‬                                          ‫א‬
                                                 ‫א‬                                



               ،KKK‫א‬‫א‬‫א‬‫א‬
 
‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                      K‫א‬‫א‬‫א‬
                        
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬،‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                              
‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬
،‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬
،‫א‬‫א‬‫א‬
                                                               
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                 
‫א‬‫א‬‫א‬‫א‬‫א‬ K‫א‬‫א‬‫א‬‫א‬
                                   K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                          
‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬
                                K‫א‬‫א‬،‫א‬،‫א‬‫א‬
،‫א‬‫א‬‫א‬‫א‬،
                                                                                            
‫א‬،‫א‬‫א‬‫א‬‫א‬
                                                                                          K‫א‬‫א‬
                                           KKKKKK،‫א‬
                                                                                                          
                                   ‫א‬‫א‬‫א‬
                                ã¹]<gè…‚jÖ]æ<ËÖ]<Üé×Ãj×Ö<íÚ^ÃÖ]<퉉ö¹]
                                    ‫א‬‫א‬‫א‬‫א‬




               ‫א‬
                ‫א‬‫א‬
 ‫א‬‫א‬




١
           ‫א‬‫א‬‫א‬
                    
                         W‫א‬‫א‬
                                      K‫א‬‫א‬‫א‬ •
                                  K‫א‬‫א‬ •
K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫• א‬
                          K‫א‬‫א‬‫א‬‫א‬‫• א‬
                   K‫א‬‫א‬‫א‬‫א‬‫א‬ •
                                                                                          Introduction١J ١
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       ‫א‬
      (Binary Number System)‫א‬‫א‬‫א‬‫א‬‫א‬ K‫א‬
    K(Digital Electronic Circuits) ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                     
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     ‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬
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     ‫א‬‫א‬‫א‬K‫א‬(Decimal Number System)
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                      
    K(Hexadecimal Numbering System)‫א‬‫א‬‫א‬(Octal Number System)
     ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                    
     ‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
               
     K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                          W‫א‬‫א‬‫א‬‫א‬‫א‬
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                                                                                                   K‫א‬K١
                                                                                  K‫א‬‫א‬‫א‬K٢
                                                         K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K٣
                                                                   K‫א‬‫א‬‫א‬‫א‬K٤
                                                               K‫א‬‫א‬‫א‬‫א‬‫א‬K٥
                                                                                                                       
     (Digit)‫א‬‫א‬‫א‬‫א‬
     ‫א‬‫א‬‫א‬‫א‬‫א‬(Symbol)،(Number)‫א‬
     ‫א‬‫א‬‫א‬(٠{١{٢{٣{٤, ... , ٨{٩)،‫א‬
     ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬
     ،‫א‬(١٢٣)‫א‬‫א‬‫א‬(١٤)‫א‬‫א‬‫א‬،‫א‬
     ‫א‬‫א‬‫א‬‫א‬(١،٤)(١٤)‫א‬‫א‬‫א‬‫א‬
     ‫א‬(٦)(١،٢،٣)(١٢٣)
                                                                                    K‫א‬
                                             Decimal Numbering System‫א‬‫א‬‫א‬٢J ١
                                    
    ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                           
    (١٠)‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬
     (١٠)١٠‫א‬
                                                                                           K٠{١{٢{٣{٤{٥{٦{٧{٨{٩ 
    (١٢٨)‫א‬‫א‬(Positional Weight)‫א‬‫א‬
                                                             
                                                   
    ،‫א‬E‫א‬F‫א‬‫א‬(٨)‫א‬‫א‬
    (٢)‫א‬‫א‬،(٨ × ١ = ٨) ١‫א‬‫א‬‫א‬
                                                                               
‫א‬‫א‬‫א‬E‫א‬‫א‬F‫א‬‫א‬
                               
    E‫א‬F‫א‬‫א‬E١F‫א‬‫א‬،(٢ × ١٠ = ٢٠)١٠
    ‫א‬K(١ × ١٠٠ = ١٠٠) ١٠٠‫א‬‫א‬‫א‬
                                            W،‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                                                          
                (١ × ١٠٠) + (٢ × ١٠) + (٨ × ١) = ١٠٠ + ٢٠ + ٨ = ١٢٨

    ‫א‬‫א‬E١٠F‫א‬‫א‬‫א‬
                             W١٠٠ = ١١٠ ‫א‬‫א‬‫א‬‫א‬
                                                                                                          
                ........ ١٠٥ ١٠٤ ١٠٣       ١٠٢   ١٠١ ١٠٠

                                                     W١٢٨‫א‬


                                       ١               ٢               ٨
                             ‫א‬‫א‬‫א‬‫א‬                       
                          ١٠٢             ١٠١           ١٠٠
                        ١ × ١٠٢     +    ٢ × ١٠١ +     ٨ × ١٠٠
               (١٢٨)١٠ =    ١٠٠        +     ٢٠       +     ٨

    ‫א‬١٠‫א‬‫א‬(١٢٨)‫א‬‫א‬
                                     K‫א‬‫א‬‫א‬‫א‬(Subscript)‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                                                     W١٠ ١‫א‬
                                                                                                                         
              ١٠٢   ١٠١         ١٠٠ • ١٠         ١
                                                         ١٠     ٢
                                                                          ١٠    ٣
                                                                                    ........
                                                                ‫א‬‫א‬
                                                                                                                               
                                                              (Decimal Point)
                                                                                                                               
                                           Binary Numbering System‫א‬‫א‬‫א‬٣J ١
(٢)(٢) ‫א‬‫א‬‫א‬‫א‬‫א‬
                                               
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ .(١،٠)‫א‬
                                                                                 
                                                                                                                      W(٢)
                ..... ٢٤        ٢٣       ٢٢          ٢١             ٢٠
                                                                                W‫א‬‫א‬‫א‬‫א‬
                ..... ١٦        ٨        ٤           ٢          ١
                                                                           W(١١٠٠١)‫א‬‫א‬
                                                                                                                               
                           ٢٤       ٢٣       ٢٢          ٢١         ٢٠
                           ١        ١        ٠           ٠          ١
                = (١ × ٢٤) + (١ × ٢٣) + (٠ × ٢٢) + (٠ × ٢١) + (١ × ٢٠)
                = ١٦ + ٨ + ٠ + ٠ + ١ = (٢٥)١٠

‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬
       
‫א‬‫א‬(٢)‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                                                   K(١١٠٠١)٢‫א‬‫א‬
                                                                                                                         
                                                      W‫א‬‫א‬‫א‬‫א‬‫א‬
                                     
‫א‬‫א‬ (Binary Digit)‫א‬(Bit)‫א‬‫ א‬W(Bit)‫א‬‫א‬■
                                                                             
‫א‬E‫א‬F‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬
(١١٠١١٠١)٢‫א‬(٤-bits)(١٠٠١)٢‫א‬،‫א‬‫א‬
                                                                                 K‫א‬(٧-bits)
‫א‬‫א‬ W(Number of Binary Combinations)‫א‬‫א‬■
K(bits)‫א‬‫א‬‫א‬‫א‬
                                                                                         
                                              W‫א‬‫א‬‫א‬
                N = 2 n
                                                              ‫א‬‫א‬‫א‬= N W
                                                                             (bits)‫א‬= n
                         W‫א‬‫א‬(٢)‫א‬‫א‬
                        ٢
                N=٢ =٤
                                   W‫א‬‫א‬(٣)‫א‬‫א‬
                N = ٢٣ = ٨
                                   W‫א‬‫א‬(٤)‫א‬‫א‬
                        ٤
                N = ٢ = ١٦
                         K‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬W(Bit)‫א‬‫א‬■
‫א‬(١)(١)٢٠‫א‬‫א‬‫א‬‫א‬
٢٢‫א‬(٢)٢١‫א‬‫א‬‫א‬
                                                                                    
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬(٤)
‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬،‫א‬‫א‬
                                                   
‫א‬‫א‬‫א‬(LSB)‫א‬‫א‬(Least Significant Bit)
        K(MSB)‫א‬‫א‬ (Most Significant Bit) ‫א‬‫א‬‫א‬‫א‬
                                                                                
‫א‬‫א‬‫א‬(Bit)‫א‬‫א‬WEByte) ‫א‬ ■
(٠)‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬
                                          
‫א‬‫א‬‫א‬EF‫א‬‫א‬(١)‫א‬‫א‬
                                                                              
‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬
‫א‬
                                                                        K
(Byte)‫א‬
‫א‬‫א‬‫א‬‫א‬
                                                     W‫א‬‫א‬‫א‬K
                         ١ byte = ٨ bits
                     Decimal-to-Binary Conversion ‫א‬‫א‬‫א‬‫א‬‫א‬٤J ١
  ‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬
(٢)‫א‬‫א‬‫א‬‫א‬(Sum of Weights Method)
   ‫א‬‫א‬‫א‬ (Repeated Division–by–٢ Method)
                                                                              K‫א‬‫א‬‫א‬
                                              ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬١J ٤J ١
                                             
   ‫א‬،٢١٤‫א‬،‫א‬(١٤)١٠‫א‬‫א‬
    .(٠)‫א‬٢‫א‬
                         
   ‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
   ‫א‬‫א‬،(MSB)‫א‬‫א‬‫א‬‫א‬(LSB)
                                                                                         W
                                                                                                    
                                      ‫ א‬                                                 
                  ١٤ ÷ ٢ = ٧             ٠
                  ٧ ÷٢=٣                 ١
                  ٣ ÷٢=١                 ١
                  ١ ÷٢=٠                 ١

                                               ١ ١ ١ ٠
                                 (MSB)                         (LSB)
                                                                                             W
                  (١٤)١٠ = (١١١٠)٢
                                                                                                             
                                              K‫א‬(٢٥)١٠‫א‬‫א‬WE١J ١F
                                                                                                         W‫א‬
                                      ‫א‬                                                                    

                 ٢٥ ÷ ٢ = ١٢             ١     (LSB)
                 ١٢ ÷ ٢ = ٦              ٠
                 ٦ ÷٢=٣                  ٠
                 ٣ ÷٢=١                  ١
                 ١ ÷٢=٠                  ١     (MSB)
                                                                             W‫א‬
                 (١٤)١٠ = (١١١٠)٢
                                              K‫א‬(٨٧)١٠‫א‬‫א‬WE٢J ١F 
                                                                                                             W‫א‬
                                      ‫א‬
                 ٨٧ ÷ ٢ = ٤٣             ١     (LSB)
                 ٤٣ ÷ ٢ = ٢١             ١
                 ٢١ ÷ ٢ = ١٠             ١
                 ١٠ ÷ ٢ = ٥              ٠
                 ٥ ÷٢=٢                  ١
                 ٢ ÷٢=١                  ٠
                 ١ ÷٢=٠                  ١     (MSB)
                                                                                                 W‫א‬
                 (٨٧)١٠ = (١٠١٠١١١)٢

                                                     ‫א‬‫א‬‫א‬‫א‬‫א‬٢J ٤J ١
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬ (Decimal Fractions)‫א‬‫א‬‫א‬K(٢)‫א‬‫א‬
                                                                          K(٢)‫א‬‫א‬
                                           
٠٫٣١٢٥‫א‬‫א‬‫א‬‫א‬(٠٫٣١٢٥)‫א‬‫א‬
‫א‬‫א‬‫א‬(٢)‫א‬‫א‬‫א‬،(٢)
                                      
(Carried Digits)‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬(٠)
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬K(LSB)‫א‬‫א‬‫א‬(MSB)‫א‬‫א‬‫א‬K‫א‬
                                                                                              W
                                                                                                
                                                                                                        
                                               ‫א‬
                 ٠٫٣١٢٥ × ٢ = ٠٫٦٢٥                      ٠
                       ٠٫٦٢٥ × ٢ = ١٫٢٥            ١

                       ٠٫٢٥ × ٢ = ٠٫٥              ٠

                       ٠٫٥     × ٢ = ١٫٠٠          ١
    
                                                 (LSB) ١ ٠ ١ ٠ (MSB)
                                                                            
                                                                                                                 
                                                                                                                 
                                              K‫א‬(٣٩٫٢٥)١٠‫א‬‫א‬WE٣J ١F
                    W(٢)‫א‬‫א‬‫א‬‫א‬‫א‬W‫א‬
                                                                                                                  
                                        ‫א‬
                       ٣٩ ÷ ٢ = ١٩           ١   (LSB)
                       ١٩ ÷ ٢ = ٩            ١
                       ٩ ÷٢=٤                ١
                       ٤ ÷٢=٢                ٠
                       ٢ ÷٢=١                ٠
                       ١ ÷٢=٠                ١   (MSB)
                                                                                               W‫א‬
                        (٣٩)١٠ = (١٠٠١١١)                     
                                      W(٢)‫א‬‫א‬‫א‬‫א‬
                                                                                                        
                                                 ‫א‬
                       ٠٫٢٥ × ٢ = ٠٫٥              ٠

                       ٠٫٥ × ٢ = ١٫٠٠              ١
                                                                                          W
                       (٠٫٢٥)١٠ = (٠٫٠١)٢
                                                                  W‫א‬‫א‬‫א‬
                       (٣٩٫٢٥)١٠ = (١٠٠١١١٫٠١)٢

                     Binary-to-Decimal Conversion ‫א‬‫א‬‫א‬‫א‬‫א‬٥J ١
                                                                        
    (٢)‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
    ‫א‬‫א‬‫א‬K‫א‬١٦, ٨, ٤, ٢, ١‫א‬‫א‬‫א‬‫א‬
                                  
(١)‫א‬‫א‬(Bit)‫א‬‫א‬
         
K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                     W‫א‬‫א‬‫א‬
                                               K‫א‬١١٠١٠٠١‫א‬‫א‬WE٤J ١F 
‫א‬‫א‬‫א‬‫א‬(١)W‫א‬
                                                                                                            W
              ٢٦   ٢٥      ٢٤       ٢٣ ٢٢               ٢١    ٢٠ : ‫א‬
              ١    ١       ٠        ١         ٠         ٠      ١ : ‫א‬‫א‬
           = ١ × ٢٦ + ١ × ٢٥ + ٠ × ٢٤ + ١ × ٢٣ + ٠ × ٢٢ + ٠ × ٢١ + ١ × ٢٠
           = ٦٤ + ٣٢ + ٨ + ١ = (١٠٥)١٠

(Bits ) ‫ﺧﺎﻧ ﺎت‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬ (Binary Point)‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬(Decimal Point)‫א‬‫א‬
                                                                                                  W
              ……٢٤         ٢٣           ٢٢        ٢١         ٢٠ • ٢-١      ٢-٢   ٢-٣    ٢-٤…….
                                                                         ‫א‬‫א‬
                                                                                                               
                          K‫א‬(٠٫١٠١١)٢‫א‬‫א‬‫א‬WE٥J ١F 
                                                                                                          W‫א‬
                    -١         -٢        -٣            -٤
               • ٢         ٢            ٢         ٢
              ٠• ١         ٠            ١         ١

       ∴(٠٫١٠١١)٢ = ١ × ٢-١ + ١ × ٢-٣ + ١ × ٢-٤ = ٠٫٥ + ٠٫١٢٥ + ٠٫٠٦٢٥ = (٠٫٦٨٧٥)١٠
                                        Binary Arithmetic ‫א‬‫א‬‫א‬‫א‬٦J ١
         
   ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                          K‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬
                                                                     Binary Addition ‫א‬‫א‬١J ٦J ١
 ‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬
                                                                                               W(Binary Digits)
                     ٠    +   ٠   =   ٠
                     ٠    +   ١   =   ١
                     ١    +   ٠   =   ١
                     ١    +   ١   =   ٠ carry E‫א‬F ١ ⇒ = ١٠
‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬
   ‫א‬‫א‬‫א‬‫א‬‫א‬(١)‫א‬‫א‬،(٢)١ + ١ = ١٠
                          W‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬
                                                                K٠١١, ١١٠‫א‬‫א‬WE٦J ١F 
                          W‫א‬‫א‬‫א‬‫א‬W‫א‬
                                                                                                                           
                                       ١       ١
                 ٦                             ١       ١        ٠
                +٣                      +      ٠       ١        ١
          EF ٩                      ١      ٠       ٠        ١
                                                               K٠١١, ١٠٠‫א‬‫א‬‫א‬WE٧J ١F 
                                                                                                                         W‫א‬
                 ٤                            ١        ٠        ٠
                +٣                            ٠        ١        ١
          EF ٧                            ١        ١        ١
                                                                 Binary Subtraction ‫א‬‫א‬٢J ٦J ١
                                                                     W‫א‬‫א‬
                                                    K‫א‬‫א‬‫א‬J ١
                                                                                                 K‫א‬‫א‬J ٢
             
   ‫א‬K‫א‬‫א‬،‫א‬‫א‬
   ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E‫א‬F‫א‬‫א‬
                                                              W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                     ٠–٠=٠
               ١–٠=١
               ١–١=٠
               ٠–١=١                    (١) ‫א‬ (١)‫א‬
                                              W‫א‬‫א‬‫א‬
                         K‫א‬‫א‬ •
                W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫• א‬
                                      K(٠)‫א‬(١)(١)(٠)(٠)
                                                           K(١)‫א‬(١)(٠)
‫א‬F‫א‬‫א‬(٠)(١)‫א‬(٠)(١)
                                          K(٠)(١)(١)E
                                     K‫א‬‫א‬‫א‬‫א‬‫א‬
                                                         K(٠١١)‫א‬‫א‬(١٠١)‫א‬‫א‬‫א‬WE٨J ١F 
                                                                                                     W‫א‬
         (٠)‫א‬(١)‫א‬                   ٠                                 
                                                                       ١
                                                                 ١      ٠      ١ ‫א‬          
         ‫א‬‫א‬(١)‫א‬
                                                             –٠    ١ ١      ‫א‬
         (١)(١٠)‫א‬
                                                                  ٠     ١       ٠                   
                                    (١)‫א‬
                                                                                                           
                                                                                                           
                                                                  ‫א‬‫א‬‫א‬‫א‬‫א‬٧J ١
 One's and Two's Complements of Binary Numbers
‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                 
K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬(١)(٠)(٠)(١)‫א‬‫א‬
                                                                     
                                                                                             W‫א‬
                                                       ١ ٠ ١ ١ ٠ ٠ ١ ١           ‫א‬‫א‬
                                                       ٠ ١ ٠ ٠ ١ ١ ٠ ٠          ‫א‬‫א‬          
                                   W‫א‬‫א‬‫א‬‫א‬
‫א‬ (١)‫א‬K‫א‬‫א‬W‫א‬‫א‬
                                                                                        
                                       W‫א‬‫א‬‫א‬‫א‬
                                                         ١ +‫א‬‫א‬Z‫א‬‫א‬
K١٠١١٠٠١١‫א‬‫א‬‫א‬‫א‬
                        K‫א‬‫א‬(١)‫א‬‫א‬‫א‬
                                                       ١ ٠ ١ ١ ٠ ٠ ١ ١           ‫א‬‫א‬        
                                                       ٠ ١ ٠ ٠ ١ ١ ٠ ٠          ‫א‬‫א‬          
                                                                     + ١            (١)            
                                                       ٠ ١ ٠ ٠ ١ ١ ١ ٠           ‫א‬‫א‬        
                                                                                        
‫א‬‫א‬(LSB)‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬
‫א‬‫א‬(٠)
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                       
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬F‫א‬
                                                         
،E‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                     W‫א‬‫א‬(١٠١٠١١٠١)٢‫א‬‫א‬
                                                                                                             
                                     ‫א‬‫א‬     ١ ٠ ١ ٠ ١ ١ ٠ ١            ‫א‬‫א‬        
                                                      ٠ ١ ٠ ١ ٠ ٠ ١ ١            ‫א‬‫א‬        
                                                                                                             
                                   Representation of Signed Numbers‫א‬‫א‬‫א‬‫א‬٨J ١
                                                                               
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                              
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
(١)،‫א‬(٠)‫א‬،‫א‬‫א‬‫א‬
                                    
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬
‫א‬‫א‬ (Sign Bit)‫א‬‫א‬‫א‬‫א‬
                                                                             .(Magnitude)
                         
‫א‬‫א‬W ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
            .(٢'s Complement)‫א‬‫א‬ (١'s Complement) ‫א‬‫א‬(Sign-Magnitude)
                                                     (Sign-Magnitude System) ‫א‬‫א‬١J ٨J ١
 ‫א‬‫א‬‫א‬(Bit)‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬
                    
 ‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
 (+٢٣)‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬
                                               
                                                                             W‫א‬‫א‬‫א‬
                                                                                                                                   
                                                                          ٠ ٠ ٠ ١ ٠ ١ ١ ١                                   
                                                 ‫א‬
                                                                                                      ‫א‬‫א‬                
                                                  (Sign Bit)
                                                                                                     (Magnitude Bits)              
                                                       W ‫)٣٢-( ﻓﺈﻧﻨﺎ‬‫א‬‫א‬
                                                  ١ ٠ ٠ ١ ٠ ٠ ١ ١ ١                       
                         K‫א‬(–٢٣) ، (+٢٣)‫א‬‫א‬‫א‬
                                                   (١'s Complement System) ‫א‬‫א‬٢J ٨J ١
 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬
 ‫א‬‫א‬‫א‬ (–٢٣) ‫א‬‫א‬K‫א‬
                                                            
                                                                                                                       W
                                                               ٠٠٠١٠١١١                           (+٢٣)‫א‬                 
                                                         ١ ١ ١ ٠ ١ ٠ ٠ ٠                (–٢٣)‫א‬
                                                                                                                                   
 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                                                                        K‫א‬
                                                                                                                                   
                                                                (٢'s Complement)‫א‬‫א‬٣J ٨J ١
                                                              
 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                                    
K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬
          W(+٢٣)‫א‬‫א‬‫א‬(-٢٣)‫א‬‫א‬
                                                    ٠٠٠١٠١١١                      (+٢٣)‫א‬        
                                               ١ ١ ١ ٠ ١ ٠ ٠ ١         (-٢٣)‫א‬
                                                                              
       K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ 
      Arithmetic Operations with Signed Numbers‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬٩J ١
،‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬KE٦J ١F‫א‬‫א‬،
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                   
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬
                                                                       W‫א‬
      K‫א‬‫א‬‫א‬‫א‬١١١١١٠١٠‫א‬‫א‬٠٠٠٠١١١٠‫א‬‫א‬‫א‬WE٩J ١F 
                                                                                 W‫א‬W‫א‬
       ١٤ – (– ٦) = ١٤ + ٦ = ٢٠
                                                           W‫א‬
                                       ٠٠٠٠١١١٠               ‫א‬(H١٤)
                                   + ٠٠٠٠٠١١٠                 ‫א‬‫א‬(H٦)
                                       ٠٠٠١٠١٠٠               ‫א‬(H٢٠)
                                W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬WE١٠J ١F 
                (٠٠٠٠١٠٠٠)٢ – (٠٠٠٠٠١٠٠)٢
                                                                                 W‫א‬W‫א‬
        ٨ – ٤ = ٨ + (-٤) = ٤
                                                                                           W
                                                                                                          
                                                                                                          
                                      ٠٠٠٠١٠٠٠                ‫א‬(H٨)
                                    +١١١١١١٠٠                 ‫א‬‫א‬( ٤)
                                 ١٠٠٠٠٠١٠٠                    ‫א‬(H٤)
                         ‫א‬
                         (Discard carry)                                                                  
                                       K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬WE١١J ١F 
                (١١١٠٠١١١)٢ – (٠٠٠٠١٠٠١)٢
                                                                                 W‫א‬W‫א‬
             – ٢٥ – (+٩) = – ٢٥ – ٩ = -٣٤
                                                                                                          W
                                             ١١١٠٠١١١                 ‫א‬( ٢٥)
                                          +١١١١٠١١١                   ‫א‬‫א‬( ٩)
                                       ١١١٠١١١١٠                      ‫)٤٣ ( א‬
                               ‫א‬
                              (Discard carry)                                                                         
                                       The Octal Numbering System‫א‬‫א‬‫א‬١٠J ١
    (٨)(٨)‫א‬‫א‬‫א‬‫א‬
      
    ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ (٠،١،٢،٣،٤،٥،٦،٧)
    ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬
             K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                     Octal-to-Decimal Conversion ‫א‬‫א‬‫א‬‫א‬١J ١٠J ١
    (٨)‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                 
‫א‬‫א‬‫א‬‫א‬،‫א‬(……٨٣        ٨٢       ٨١       ٨٠ )
    ‫א‬‫א‬‫א‬‫א‬‫א‬K،‫א‬(…... ٥١٢ ٦٤ ٨ ١)
    ‫א‬‫א‬(٢٢٧٥)٨‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬
                                                                                
                                                                                     W
                            ‫א‬‫א‬: ٨٣ ٨٢ ٨١ ٨٠
                      ‫א‬‫٢ : א‬      ٢     ٧ ٥
             ∴ (٢٢٧٥)٨ = (٢ × ٨٣) + (٢ × ٨٢) + (٧ × ٨١) + (٥ × ٨٠)
                      = (٢ × ٥١٢) + (٢ × ٦٤) + (٧ × ٨) + (٥ × ١)
                      = ١٠٢٤ + ١٢٨ + ٥٦ + ٥ = (١٢١٣)١٠
                 Decimal–to–Octal Conversion ‫א‬‫א‬‫א‬‫א‬٢J ١٠J ١
                                                  
    ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
    ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،(٨)‫א‬
                                                                                            K(٢)(٨)
                                       ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬١J ٢J ١٠J ١
                                                               
    (٨)١٥٠‫א‬‫א‬‫א‬(١٥٠)١٠‫א‬‫א‬
    ‫א‬(٨)‫א‬‫א‬
    ‫א‬‫א‬‫א‬‫א‬‫א‬.(٠)
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬
 {Most Significant Digit} ‫א‬‫א‬‫א‬‫א‬{Least Significant Digit} (LSD)
                                                                       W‫א‬‫א‬(MSD)
                                        
                                      ‫א‬
                 ١٥٠ ÷ ٨ = ١٨                     ٦      (LSD)
                 ١٨ ÷ ٨ = ٢              ٢
                 ٢ ÷٨=٠                  ٢     (MSD)
                                                                                  W‫א‬
         (١٥٠)١٠ = (٢٢٦)٨
                                K‫א‬‫א‬(٦٢٤)١٠‫א‬‫א‬WE١٢J ١F 
                               
                                    ‫א‬                                                                               W‫א‬

                 ٦٢٤ ÷ ٨ = ٧٨                     ٠      (LSD)
                 ٧٨ ÷ ٨ = ٩              ٦
                 ٩ ÷٨=١                  ١
                 ١ ÷٨=٠                  ١     (MSD)
                                                                                  W‫א‬
         (٦٢٤)١٠ = (٦١١)٨
                                              ‫א‬‫א‬‫א‬‫א‬‫א‬٢J ٢J ١٠J ١
                                                                        
 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
         
 ‫א‬‫א‬(٠٫٢٦٥)‫א‬‫א‬K(٨)‫א‬‫א‬
 ‫א‬‫א‬‫א‬ ،(٨)٠٫٢٦٥‫א‬‫א‬
 ‫א‬‫א‬‫א‬(٠)‫א‬‫א‬‫א‬(٨)
   
K‫א‬‫א‬‫א‬‫א‬‫( א‬Carried Digits)‫א‬‫א‬K‫א‬
                                                    
 ‫א‬(MSD)‫א‬‫א‬(LSD)‫א‬‫א‬‫א‬
                                                                                                                 W
                                                                                                                 
                                               ‫اﻟﺤﺎﻣﻞ‬
                 ٠٫٢٦٥ × ٨ = ٢٫١٢        ٢        (MSD)
                 ٠٫١٢ × ٨ = ٠٫٩٦         ٠
                 ٠٫٩٦ × ٨ = ٧٫٦٨         ٧
                 ٠٫٦٨ × ٨ = ٥٫٤٤         ٥
                 ٠٫٤٤ × ٨ = ٣٫٥٢         ٣
                 ٠٫٥٢ × ٨ = ٤٫١٦         ٤        (LSD)
 W‫א‬‫א‬(٦)‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
         (٠٫٦٢٥)١٠ = (٠٫٢٠٧٥٣٤)٨
           K‫א‬‫א‬(٤٤٫٥٦٢٥)١٠‫א‬‫א‬WE١٣J ١F 
                    K(٨)‫א‬‫א‬‫א‬‫א‬‫א‬ W‫א‬
                    
                         ‫א‬
      ٤٤ ÷ ٨ = ٥              ٤        (LSD)
      ٥ ÷٨=٠                  ٥        (MSD)
                                                                        W‫א‬
      (٤٤)١٠ = (٥٤)٨
             W(٨)‫א‬‫א‬‫א‬‫א‬
                                                                                                     
                                    ‫اﻟﺤﺎﻣﻞ‬
      ٠٫٥٦٢٥ × ٨ = ٤٫٥                 ٤
      ٠٫٥    × ٨ = ٤٫٠٠                ٤
                                                                                        W
(٠٫٥٦٢٥)١٠ = (٠٫٤٤)٨
                                                             W‫א‬‫א‬‫א‬
(٤٤٫٥٦٢٥)١٠ = (٥٤٫٤٤)٨
      Octal-to-Decimal Conversion                 ‫א‬‫א‬‫א‬‫א‬‫א‬ ٣J ١٠J ١
(٨)‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬K‫א‬٤٠٩٦, ٥١٢, ٦٤, ٨, ١‫א‬‫א‬‫א‬‫א‬
‫א‬(Digit)‫א‬‫א‬‫א‬
                             
K‫א‬‫א‬‫א‬‫א‬
                                                                                          K‫א‬‫א‬
                                   K‫א‬‫א‬(٣٢٤)٨‫א‬‫א‬WE١٤J ١F 
                                                                                                        W‫א‬
                     ‫א‬‫א‬: ٨٢ ٨١ ٨٠
               ‫א‬‫א‬: ٣ ٢ ٤

       ∴ (٣٢٤)٨ = (٣ × ٨٢) + (٢ × ٨١) + (٤ × ٨٠)
                = (٣ × ٦٤) + (٢ × ٨) + (٤ × ١)
                = ١٩٢ + ١٦ + ٤ = (٢١٢)١٠
‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                         
‫א‬‫א‬ (Octal Point) ‫א‬‫א‬‫א‬
                                                 
                                                            W‫א‬‫א‬‫א‬‫א‬
                     ٤        ٣        ٢       ١   ٠       -١
              ……٨         ٨        ٨       ٨       ٨ • ٨           ٨-٢   ٨-٣    ٨-٤…….
                                                                 ‫א‬‫א‬
                          K‫א‬‫א‬(٥٦٧٫١٤)٨‫א‬‫א‬WE١٥J ١F 
                                                                                                        W‫א‬
                     ‫א‬‫א‬: ٨٢ ٨١ ٨٠ • ٨-١ ٨-٢
               ‫א‬‫א‬: ٥ ٦ ٧ • ١ ٤

       ∴ (٥٦٧٫١٤)٨ = (٥ × ٨٢) + (٦ × ٨١) + (٧ × ٨٠) + (١ × ٨-١) + (٤ × ٨-٢)
                   = (٥ × ٦٤) + (٦ × ٨) + (٧ × ١) + (١ × ٠٫١٢٥) + (٤ × ٠٫٠١٥٦٢٥)
                   = ٣٢٠ + ٤٨٠ + ٧ + ٠٫١٢٥ + ٠٫٠٦٢٥ = (٣٧٥٫١٨٧٥)١٠




           Octal-to-Binary Conversion ‫א‬‫א‬‫א‬‫א‬‫א‬٤J ١٠J ١
‫א‬‫א‬ (Digit)
                                                                               
‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬،(٣-bits)
                                               KE١J ١F‫א‬

        ‫א‬‫א‬        ٠          ١          ٢           ٣         ٤          ٥           ٦         ٧
      ‫א‬‫א‬       ٠٠٠         ٠٠١       ٠١٠          ٠١١      ١٠٠        ١٠١          ١١٠      ١١١
                           K‫א‬‫א‬‫א‬E١J ١F 
‫א‬‫א‬‫א‬
                                                                K‫א‬
                                   K‫א‬‫א‬(٣٥٧)٨‫א‬‫א‬WE١٦J ١F 
                                                                                                            W‫א‬
                 (٣٥٧)٨ =         ٣      ٥        ٧

                                 ٠١١    ١٠١ ١١١

                         = (٠١١١٠١١١١)٢
                                   K‫א‬(١٢٧٦٫٥٤٣)٨‫א‬‫א‬WE١٧J ١F 
                                                                                                            W‫א‬
                 (١٢٧٦٫٥٤٣)٨ =           ١        ٢       ٧         ٦ • ٥         ٤        ٣

                                       ٠٠١      ٠١٠ ١١١            ١١٠ • ١٠١ ١٠٠ ٠١١

                                  = (١٠١٠١١١١١٠٫١٠١١٠٠٠١١)٢
                                   K‫א‬‫א‬‫א‬
             Binary-to-Octal Conversion ‫א‬‫א‬‫א‬‫א‬‫ א‬٥J ١٠J ١
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
           
J –‫א‬‫א‬K‫א‬
                                       
‫א‬‫א‬‫א‬‫א‬
                     
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬
                                                                           K‫א‬‫א‬‫א‬‫א‬
         K‫א‬‫א‬(١٠١١٠٠١٠١١١٠٠٫٠٠١٠١)٢‫א‬‫א‬WE١٨J ١F 
                                                                                                            W‫א‬
                  ٠٠١      ٠١١     ٠٠١     ٠١١      ١٠٠     • ٠٠١        ٠١٠
                                                                                                                    
                    ١       ٣        ١       ٣        ٤     •     ١        ٢

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                                                W
                  (١٠١١٠٠١٠١١١٠٠٫٠٠١٠١)٢ = (١٣١٣٤٫١٢)٨
          Arithmetic Operations in Octal System                  ‫א‬‫א‬‫א‬‫א‬٦J ١٠J ١
                                      K‫א‬‫א‬‫א‬‫א‬
                                                              Octal Addition ‫א‬‫א‬١J ٦J ١٠J ١
‫א‬(٠،٩)‫א‬–‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                           
‫א‬(١٠)‫א‬(٩)‫א‬‫א‬‫א‬،(٩)
                                                            
‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬(١٠)‫א‬‫א‬ (٠،١)‫א‬‫א‬‫א‬‫א‬
                                
‫א‬K‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬(٧)‫א‬‫א‬‫א‬‫א‬–‫א‬‫א‬‫א‬(٧)
(١١, ١٢, ١٣, ١٤, ١٥, ١٦, ١٧)‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬(١٠)
   
K‫א‬ (٣٠, ٣١, ..... , ٣٧)‫א‬‫א‬‫א‬(٢٠،٢١, ٢٢, ...... , ٢٧) ‫א‬‫א‬‫א‬
                                                                               
‫א‬‫א‬‫א‬‫א‬‫א‬E٢J ١F ‫א‬
    
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                                                   W‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ •
                                                                                       K(٧)
(٢)‫א‬‫א‬(٧)‫א‬‫א‬‫א‬ •
‫א‬(٧)‫א‬(٨)‫א‬‫א‬(٧)‫א‬‫א‬،‫א‬
‫א‬‫א‬(٢)‫א‬(١٠)‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬F‫א‬‫א‬‫א‬
                                                      KE‫א‬‫א‬‫א‬
                            ٧     ٦     ٥     ٤ ٣ ٢ ١                 ٠    +
                             ٧     ٦     ٥     ٤  ٣ ٢  ١              ٠    ٠
                            ١٠     ٧     ٦     ٥  ٤ ٣  ٢              ١    ١
                            ١١    ١٠     ٧     ٦  ٥ ٤  ٣              ٢    ٢
                            ١٢    ١١    ١٠     ٧  ٦ ٥  ٤              ٣    ٣
                            ١٣    ١٢    ١١    ١٠ ٧  ٦  ٥              ٤    ٤
                            ١٤    ١٣    ١٢    ١١ ١٠ ٧  ٦              ٥    ٥
                            ١٥    ١٤    ١٣    ١٢ ١١ ١٠ ٧              ٦    ٦
                            ١٦    ١٥    ١٤    ١٣ ١٢ ١١ ١٠             ٧    ٧
                            K‫א‬‫א‬‫א‬E٢J ١F 
                                                  
                                               K(٤٢)٨، (٣٨)٨‫א‬‫א‬‫א‬WE١٩J ١F 
                                                  W‫א‬‫א‬W‫א‬
                      ٣٤
                   + ٤٢
                      ٧٦

        ∴(٣٤)٨ + (٤٢)٨ = (٧٦)٨
                                                                                                      
(٧)(٣،٤)(٤،٢)‫א‬‫א‬
                                                                                K‫א‬
                                                      K(٦٣)٨،(٥٦)٨‫א‬‫א‬‫א‬WE٢٠J ١F
                                                                                                                  W‫א‬
                                ٥ ٦
                            + ٦ ٣
                            ١ ٤ ١
                                                     
‫א‬(٢)(٧)‫א‬‫א‬‫א‬
                                                                               K‫א‬‫א‬(Carry)‫א‬
                                Subtraction in Octal System‫א‬‫א‬‫א‬٢J ٦J ١٠J ١
                                                    W‫א‬‫א‬‫א‬
           K‫א‬‫א‬‫א‬‫א‬‫א‬ •
             
‫א‬‫א‬‫א‬–‫א‬‫א‬(١)‫א‬‫א‬‫א‬ •
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬(٨)
                                                                                 K‫א‬‫א‬
                                                 (٦٥٧)٨ – (٣٤٦)٨          W‫א‬‫א‬WE٢١J ١F 
                                                                  W‫א‬W‫א‬
                              ٦ ٥ ٧               ‫א‬
                          – ٣ ٤ ٦                 ‫א‬
                              ٣ ١ ١

         ∴(٦٥٧)٨ – (٣٤٦)٨ = (٣١١)٨
            
‫א‬‫א‬‫א‬
                                                                                                 
                                                                                               K‫א‬‫א‬
                                           (٧٣٢)٨ – (٦٣٤)٨W‫א‬‫א‬WE٢٢J ١F
                                               W‫א‬
                             ٦ ٢ ١
                              ٧ ٣ ٢               ‫א‬
                          – ٦ ٣ ٤                 ‫א‬
                              ٠ ٧ ٦

         ∴(٧٣٢)٨ – (٦٣٤)٨ = (٧٦)٨
‫א‬‫א‬(٢)(٤)‫א‬‫א‬
‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬(١)‫א‬
                       K‫א‬‫א‬(٢)(٣)‫א‬‫א‬‫א‬
                                     Hexadecimal Numbering System            ‫א‬‫א‬‫א‬‫א‬١١J ١
(١٦)‫א‬‫א‬‫א‬‫א‬‫א‬
    (٠،١،٢،٣،٤،٥،٦،٧،٨،٩,A,B,C,D,E,F) ‫א‬(١٦)
                 K‫א‬(١٠, ١١, ١٢, ١٣, ١٤, ١٥)‫א‬‫א‬(A,B,C,D,E,F)‫א‬
           Hexadecimal–to–Decimal Conversion‫א‬‫א‬‫א‬‫א‬١J ١١J ١
    ١٦‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
     ... ٤٠٩٦ ٢٥٦ ١٦            )‫א‬‫א‬‫א‬‫א‬(……١٦٣ ١٦٢ ١٦١ ١٦٠)
                                     W(٥٢٢٫٣٩)١٦‫א‬‫א‬‫א‬(١
                                                                                                                 
                              ‫א‬‫א‬: ١٦٢ ١٦١ ١٦٠ • ١٦-١ ١٦-٢
             ‫א‬‫א‬: ٥                   ٢       ٢ • ٣            ٩

             ∴ (٥٢٢٫٣٩)١٦ = (٥ × ١٦٢) + (٢ × ١٦١) + (٢ × ١٦٠) + (٣ × ١٦-١) + (٩ × ١٦-٢)
                         = (٥ × ٢٥٦) + (٢ × ١٦) + (٢ × ١) + (٣ × ٠٫٠٦٢٥) + (٩ × ٠٫٠٠٣٩٠٦٢)
                          = ١٢٨٠ + ٣٢ + ٢ + ٠٫١٨٧٥ + ٠٫٠٣٥١٥٥٨ = (١٣١٤٫٢٢٢٦٥٥)١٠
    ‫א‬K‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬
            
          K‫א‬‫א‬(١٦)‫א‬‫א‬‫א‬
         Decimal-to-Hexadecimal Conversion ‫א‬‫א‬‫א‬‫א‬٢J ١١J ١
    (١٦)‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                            
    ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                          .(٢)(٨)(١٦)‫א‬‫א‬
                              ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬١J ٢J ١١J ١
    (١٦)٩٧‫א‬‫א‬‫א‬(٩٧)١٠‫א‬‫א‬
    ‫א‬(١٦)‫א‬‫א‬
    ‫א‬‫א‬‫א‬‫א‬‫א‬K(٠)
    ‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬K‫א‬‫א‬
                                          W‫א‬‫א‬(MSD)‫א‬‫א‬(LSD)
                    
                                             ‫א‬
                     ٩٧ ÷ ١٦ = ٦                 ١          (LSD)
                     ٦ ÷ ١٦ = ٠                  ٦          (MSD)
                                                                                           W‫א‬
        (٩٧)١٠ = (٦١)١٦
                 K‫א‬‫א‬‫א‬(٣١٤)١٠‫א‬‫א‬WE٢٣J ١F
                             
                                  ‫א‬                                                                      W‫א‬

               ٣١٤ ÷ ١٦ = ١٩           A        (LSD)
               ١٩ ÷ ١٦ = ١                      ٣
               ١ ÷ ١٦ = ٠                       ١     (MSD)
                                                                                 W‫א‬
        (٣١٤)١٠ = (١٣A)١٦
                                 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬٢J ٢J ١١J ١
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
(٠٫٧٨١٢٥)١٠‫א‬‫א‬K(١٦)‫א‬‫א‬‫א‬
‫א‬‫א‬(١٦)‫א‬‫א‬‫א‬‫א‬‫א‬
                                                              
(٠)‫א‬‫א‬‫א‬‫א‬‫א‬(١٦)‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬
(MSD)‫א‬‫א‬‫א‬(LSD)‫א‬‫א‬‫א‬K‫א‬‫א‬
                                                                                            W‫א‬
                                                  
                                                ‫اﻟﺤﺎﻣﻞ‬
               ٠٫٧٨١٢٥ × ١٦ = ١٢٫٥                 C
               ٠٫٥    × ١٦ = ٨٫٠٠                  ٨
                                                                                                  W
        ∴(٠٫٧٨١٢٥)١٠ = (٠.C٨)١٦
                     K‫א‬‫א‬(٣٢٩٫٥٢)١٠‫א‬‫א‬WE٢٤J ١F 
                      W١٦‫א‬‫א‬‫א‬‫א‬‫א‬W‫א‬
                           
                                ‫א‬
              ٣٢٩ ÷ ١٦ = ٢٠          ٩         (LSD)
              ٢٠ ÷ ١٦ = ١                      ٤
              ١ ÷ ١٦ = ٠                       ١     (MSD)
                                                                               W‫א‬
       ∴(٣٢٩)١٠ = (١٤٩)١٦
                                                    W‫א‬‫א‬(١٦)‫א‬‫א‬

                                         ‫א‬                                                                 

              ٠٫٥٢ × ١٦ = ٨٫٣٢               ٨ (MSD)
              ٠٫٣٢ × ١٦ = ٥٫١٢               ٥
              ٠٫١٢ × ١٦ = ١٫٩٢               ١
              ٠٫٩٢ × ١٦ = ١٤٫٧٢              E
              ٠٫٧٢ × ١٦ = ١١٫٥٢              B
              ٠٫٥٢ × ١٦ = ٨٫٣٢               ٨ (LSD)
                                                                                                               
     W‫א‬(٦)‫א‬‫א‬‫א‬‫א‬‫א‬
       (٠٫٥٢)١٠ = (٠٫٨٥١EB٨)١٦
                                                                     W‫א‬‫א‬‫א‬
       (٣٢٩٫٥٢)١٠ = (١٤٩٫٨٥١EB٨)١٦

    Hexadecimal-to-Decimal Conversion ‫א‬‫א‬‫א‬‫א‬ ٣J ١١J ١
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
              
‫א‬‫א‬‫א‬‫א‬‫א‬K(١٦)‫א‬
      W‫א‬‫א‬K‫א‬‫א‬
                  K‫א‬‫א‬(F٩B)١٦‫א‬‫א‬‫א‬WE٢٥J ١F 
                                                                                                             W‫א‬
                    ‫א‬‫א‬: ١٦٢ ١٦١ ١٦٠
       ‫א‬‫א‬: F             ٩     B
                               ٢
        ∴ (F٩B)١٦ = (F × ١٦ ) + (٩ × ١٦١) + (B × ١٦٠)
                = (١٥ × ٢٥٦) + (٩ × ١٦) + (١١ × ١)
                = ٣٨٤٠ + ١٤٤ + ١١ = (٣٩٩٥)١٠
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                           W‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                                                               
                            ٣            ٢        ١          ٠       -١          -٢     -٣
                  ……١٦              ١٦       ١٦            ١٦ • ١٦          ١٦        ١٦ …….
                                                                      ‫א‬‫א‬
                                                                                                                        
                     K‫א‬(A١٥.C٣)١٦‫א‬‫א‬‫א‬WE٢٦J ١F
                                                                                                                    W‫א‬
                          ‫א‬‫א‬: ١٦٢ ١٦١ ١٦٠ • ١٦-١ ١٦-٢
         ‫א‬‫א‬: A                       ١      ٥ • C          ٣

         ∴ (A١٥.C٣)١٦ = (A × ١٦٢) + (١ × ١٦١) + (٥ × ١٦٠) + (C × ١٦-١) + (٣ × ١٦-٢)
                     = (١٠ × ٢٥٦) + (١ × ١٦) + (٥ × ١) + (١٢ × ٠٫٠٦٢٥) + (٣ × ٠٫٠٠٣٩٠٦٢)
                      = ٢٥٦٠ + ١٦ + ٥ + ٠٫٧٥ + ٠٫٠١١٧١٨٦ = (٢٥٨١٫٧٦١٧)١٠

Hexadecimal-to-Binary Conversion‫א‬‫א‬‫א‬‫א‬‫א‬٤J ١١J ١
(٠،١،٢,……,٩,A,B,C,D,E,F)‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬(A,B,C,D,E,F)‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬K(١٠،١١،١٢،١٣،١٤،١٥)
(٤-bits)‫א‬‫א‬‫א‬،‫א‬‫א‬
                          WE٣J ١F‫א‬‫א‬
                                                            K‫א‬(٣A٥)١٦‫א‬WE٢٧J ١F 
                                                                                                                    W‫א‬
                   (٣A٥)١٦          =         ٣              A      ٥

                                             ٠٠١١           ١٠١٠ ٠١٠١

                                    = (٠٠١١١٠١٠٠١٠١)٢
                                                                                                                        
                 ‫א‬‫א‬‫א‬                       ‫א‬‫א‬              ‫א‬‫א‬
                                ٠                                ٠٠٠٠                        ٠
                                ١                                ٠٠٠١                        ١
                                ٢                                ٠٠١٠                        ٢
                                ٣                                ٠٠١١                        ٣
                                ٤                                ٠١٠٠                        ٤
                             ٥                      ٠١٠١                         ٥
                             ٦                      ٠١١٠                         ٦
                             ٧                      ٠١١١                         ٧
                             ٨                      ١٠٠٠                         ٨
                             ٩                      ١٠٠١                         ٩
                             A                      ١٠١٠                         ١٠
                             B                      ١٠١١                         ١١
                             C                      ١١٠٠                         ١٢
                             D                      ١١٠١                         ١٣
                             E                      ١١١٠                         ١٤
                             F                      ١١١١                         ١٥
               K‫א‬‫א‬‫א‬E٣J ١F 
                                                                                                            
                                      K‫א‬‫א‬(B٣٥.D١)١٦‫א‬WE٢٨J ١F 
                                                                                                       W‫א‬
        (B٣٥.D١)١٦ =             B            ٣      ٥       •   D         ١

                             ١٠١١ ٠٠١١ ٠١٠١ • ١١٠١ ٠٠٠١

                      = (١٠١١٠٠١١٠١٠١٫١١٠١٠٠٠١)٢

 Binary-to-Hexadecimal Conversion‫א‬‫א‬‫א‬‫א‬‫ א‬٥J ١١J ١
                                                                     
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K
                                                              
‫א‬‫א‬‫א‬
                           K‫א‬‫א‬‫א‬‫א‬
              K‫א‬‫א‬(١١٠١١١١٠١٫١٠١٠٠١)٢‫א‬‫א‬WE٢٩J ١F 
                                                                                                       W‫א‬
                ٠٠٠١ ١٠١١ ١١٠١ • ١٠١٠ ٠١٠٠
                                                                                                            
                  ١      B           D   •   A           ٤
                   K‫א‬‫א‬‫א‬
      ∴(١١٠١١١١٠١٫١٠١٠٠١)٢ = (١BD.A٤)١٦
 K‫א‬‫א‬‫א‬(١١٠١٠٠١٠٠١١٫٠١١٠٠١)٢‫א‬‫א‬WE٣٠J ١F 
                                                                                                           W‫א‬
                 ٠٠٠١ ١٠١٠ ١٠١١ • ٠١١٠ ١٠٠٠
                                                                                                               
                  ١       A       B        •    ٦         ٨

        ∴(١١٠١٠٠١٠٠١١٫٠١١٠٠١)٢ = (١AB.٦٨)١٦

  Hexadecimal-to-Octal Conversion‫א‬‫א‬‫א‬‫א‬‫א‬ ٦J ١١J ١
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                            W‫א‬‫א‬‫א‬
                                  K‫א‬‫א‬(AB٣E.٨٧D)١٦‫א‬WE٣١J ١F
                                       W‫א‬‫א‬‫א‬‫א‬W‫א‬
        (AB٣E.٨٧D)١٦ = (١٠١٠١٠١١٠٠١١١١١٠٫١٠٠٠٠١١١١١٠١)٢
‫א‬‫א‬‫א‬‫א‬‫א‬
                                                     W
                                                                                                               
                 ٠٠١ ٠١٠ ١٠١ ٠٠١ ١١١ ١١٠ • ١٠٠ ٠٠١ ١١١ ١٠١
                                                                                                               
                  ١       ٢      ٥     ٤       ٧     ٦     •     ٤      ١     ٧      ٥
      K‫א‬‫א‬

      ∴(AB٣E.٨٧D)١٦ = (١٢٥٤٧٦٫٤١٧٥)٨
 Octal-to-Hexadecimal Conversion‫א‬‫א‬‫א‬‫א‬‫א‬ ٧J ١١J ١
‫א‬‫א‬‫א‬‫א‬
                                               
‫א‬،
،‫א‬‫א‬‫א‬‫א‬
                                                          W‫א‬‫א‬‫א‬‫א‬
                   K‫א‬‫א‬‫א‬(٢٥٫٣٤٢)٨‫א‬‫א‬WE٣٢J ١F 
                                                          W‫א‬‫א‬W‫א‬
        ∴(٢٥٫٣٤٢)٨ = (٠١٠١٠١٫٠١١١٠٠٠١٠)٢
                                                                                                               
                                      W‫א‬‫א‬‫א‬‫א‬‫א‬
               ٠٠٠١ ٠١٠١ • ٠١١١ ٠٠٠١
                                                                                                  
                ١        ٢        •    ٧        ١
 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

        ∴(٢٥٫٣٤٢)٨ = (١٢٫٧١)١٦
                                             ‫א‬‫א‬‫א‬‫א‬‫א‬٨J ١١J ١
 Arithmetic Operations in Hexadecimal System
                                        K‫א‬‫א‬‫א‬‫א‬
                         Hexadecimal Addition‫א‬‫א‬‫א‬‫א‬١J ٨J ١١J ١
(F)‫א‬‫א‬‫א‬‫א‬(٠,F)‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬(١٠)‫א‬‫א‬،(١٠)
                                                            
‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
(B)١٦(٩)١٦‫א‬‫א‬(A)١٦‫א‬(٩)١٦‫א‬‫א‬
                                                                                K(F)١٦‫א‬
‫א‬‫א‬(١٠)١٦‫א‬(F)١٦‫א‬‫א‬
‫א‬‫א‬‫א‬(١١)١٦‫א‬(F)١٦‫א‬‫א‬‫א‬‫א‬‫א‬
                                                            K‫א‬‫א‬‫א‬‫א‬‫א‬
                                                 
،‫א‬‫א‬‫א‬‫א‬E٤J ١F‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                             K‫א‬‫א‬‫א‬‫א‬‫א‬

  F     E    D      C        B    A        ٩    ٨    ٧    ٦    ٥    ٤     ٣     ٢     ١     ٠     +
  F     E    D      C        B    A         ٩    ٨    ٧   ٦    ٥    ٤     ٣     ٢     ١     ٠     ٠
  ١٠    F    E      D        C    B        A     ٩    ٨   ٧    ٦    ٥     ٤     ٣     ٢     ١     ١
  ١١    ١٠   F      E        D    C        B    A     ٩   ٨    ٧    ٦     ٥     ٤     ٣     ٢     ٢
  ١٢    ١١   ١٠     F        E    D        C    B    A    ٩    ٨    ٧     ٦     ٥     ٤     ٣     ٣
  ١٣    ١٢   ١١     ١٠       F    E        D    C    B    A    ٩    ٨     ٧     ٦     ٥     ٤     ٤
  ١٤    ١٣   ١٢     ١١       ١٠   F        E    D    C    B    A    ٩     ٨     ٧     ٦     ٥     ٥
  ١٥    ١٤   ١٣     ١٢       ١١   ١٠       F    E    D    C    B    A     ٩     ٨     ٧     ٦     ٦
  ١٦    ١٥   ١٤     ١٣       ١٢   ١١       ١٠   F    E    D    C    B     A     ٩     ٨     ٧     ٧
  ١٧    ١٦   ١٥     ١٤       ١٣   ١٢       ١١   ١٠   F    E    D    C     B     A     ٩     ٨     ٨
  ١٨    ١٧   ١٦     ١٥       ١٤   ١٣       ١٢   ١١   ١٠   F    E    D     C     B     A     ٩     ٩
  ١٩    ١٨   ١٧     ١٦       ١٥   ١٤       ١٣   ١٢   ١١   ١٠   F    E     D     C     B     A     A
 ١A     ١٩ ١٨ ١٧ ١٦                 ١٥   ١٤    ١٣    ١٢     ١١     ١٠    F    E     D    C     B        B
 ١B     ١A ١٩ ١٨ ١٧                 ١٦   ١٥    ١٤    ١٣     ١٢     ١١    ١٠   F     E    D     C        C
 ١C     ١B ١A ١٩ ١٨                 ١٧   ١٦    ١٥    ١٤     ١٣     ١٢    ١١   ١٠    F    E     D        D
 ١D     ١C ١B ١A ١٩                 ١٨   ١٧    ١٦    ١٥     ١٤     ١٣    ١٢   ١١    ١٠   F     E        E
 ١E     ١D ١C ١B ١A                 ١٩   ١٨    ١٧    ١٦     ١٥     ١٤    ١٣   ١٢    ١١   ١٠    F        F
                      K‫א‬‫א‬‫א‬‫א‬E٤J ١F
                                                     W‫א‬‫א‬WE٣٣J ١F 
               (٣٥AB٢)١٦ + (١A٦٧٥)١٦
                                                                                                        
            K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬W‫א‬
                            ١            ١      ١
                            ٣            ٥     A        B    ٢
                          + ١            A     ٦        ٧    ٥
                             ٥           ٠     ١        ٢    ٧

        ∴(٣٥AB٢)١٦ + (١A٦٧٥)١٦ = (٥٠١٢٧)١٦


                      Hexadecimal Subtraction‫א‬‫א‬‫א‬‫א‬٢J ٨J ١١J ١
                                     W‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ •
       K‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬(١)‫א‬‫א‬‫א‬ •
                                                                       
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                        W‫א‬‫א‬
                                                                  W‫א‬‫א‬WE٣٤J ١F 
               (F٢ABD)١٦ – (EF٤CE)١٦
                                                                                                 W‫א‬
                    E                    ٩    ١A
                            ١                       ١
                    F           ٢        A     B        D
                  – E           F        ٤     C        E
                                ٣        ٥     E        D
                                                                                                        
                                      K‫א‬‫א‬‫א‬
                                                                                                        
                                                                                                        
    
    
    
    
    
    
    
    
    

                                             
                                                    
                                        W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E١
a) ٦٤                     b) ١١٢                  c) ٢٥٧               d) ٢٧{٢٦
e) ٧٧{٠٦٢٥             f) ٤٧{٨٧٥                 g) ٣٣{١٢٥

                                        W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E٢
a) ١١٠١١                  b) ١١١٠١٠١             c) ١١١١١١            d) ١١١٠{١١
e) ١٠١٠١{١١٠١          f) ١١٠٠٠٠١{١١٠١١

                                                    W‫א‬‫א‬‫א‬‫א‬E٣
a) ١٠٠ + ١١١                                    b) ١١١٠{١١ + ١١{١٠
c) ١١١١ + ١١٠١                                  d) ١٠٠١{١٠١ + ١١٠١{١١

                                         W‫א‬‫א‬‫א‬‫א‬‫א‬E٤
a) ١١٠١ – ٠١٠٠                                  b) ١٠٠١ – ٠١١١
c) ١١٠١٠ – ١٠١١١                                d) ١١٠٠ – ١٠٠١

                                                 W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E٥
a) ٠٠١١٠١٠١                    b) ١١١٠٠١٠٠                      c) ٠٠٠١٠١٠١

                                                   W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E٦
a) ١١١١٠١١٠                    b) ٠١٠١١١٠١                      c) ٠٠١١٠٠١١

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E٧
                                                         W(٨-bits) ‫א‬‫א‬
a) H٢٨          b) – ٨٣                c) H٩٩            d) – ١٢٠

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E٨
                                                         W(٨-bits) ‫א‬‫א‬
a) H١٤          b) – ٦٣                c) H١٠٧                  d) – ١٢٢


                                                                                                        
                      K‫א‬‫א‬‫א‬‫א‬E٨F‫א‬‫א‬E٩
                                                                                                
     W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E١٠
a) ١٠١١١٠٠٠١          b) ٠١١٠٠١٠٠                 c) ١٠١١٠٠١١

    W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E١١
a) ١٠٠١١١٠١                 b) ٠١١٠٠١١٠                     c) ١٠١٠١١٠١

     W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E١٢
a) ١٠١٠١٠١١                 b) ٠٠٠١١١١٠١          c) ١٠١١١٠١١
                                                                                                    
                                         W‫א‬‫א‬‫א‬‫א‬‫א‬E١٤
a) ٠٠٠١٠١١٠ – ٠٠١١٠٠١١                            b) ٠١١١٠٠٠٠ – ١٠١٠١١١١
c) ١٠٠٠١١٠٠ – ٠٠١١١٠٠١                            d) ١١٠١١٠٠١ – ١١١٠٠١١١

                          W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E١٥
a) ٥٠                  b) ١٠٠                  c) ٦٣٩١                    d) ٧٧{٣٧٥
e) ١٢٠{٥١٥٦٢٥ f) ١٤٤{٥٦٢٥         g) ٩١٥{١٤١

                                     W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E١٦
a) ٤٢                  b) ٢٥٤                  c) ١٠٥٧                    d) ٣٧{٥
e) ٩٦{١١               f) ١١٥{٣                g) ١٤٣٦٧{١٢

                                       W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E١٧
a) ٧٢                  b) ١١٣                  c) ١٦{٣                    d) ٣٧{٦
e) ١٢٢{٧٧٥             f) ٤١٧{٦٣٢              g) ٢٧٦{٦٢١

                                       W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E١٨
a) ١١٠١٠١{١١٠١                       b) ١١١١٠١٠٠{١١٠١٠١           c) ١١٠١١٠١١١{١٠١٠١
d) ١٠٠٠١٠٠١٠١١{١٠٠١                  e) ١٠١٠١١١{١١١٠١

                                                          W‫א‬‫א‬‫א‬‫א‬E١٩
a) (١٥)٨ + (١٧)٨                                  b) (٤٤)٨ + (٦٦)٨
c) (١٢٣)٨ + (٣٢١)٨                                d) (٢٧٢)٨ + (٤٥٦)٨
                                                              W‫א‬‫א‬‫א‬‫א‬E٢٠
a) (٣٢)٨ – (٢٥)٨                                         b) (١٤٧)٨ – (٧٤)٨
c) (٣١٥)٨ – (٢٢٢)٨                                       d) (٤٣٧)٨ – (٣٤٠)٨

                           W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E٢١
a) ١٤                   b) ٨٠                 c) ٥٦٠                     d) ٣٠٠٠
e) ٦٢٥٠٠                f) ٢٠٤{١٢٥            g) ٢٥٥{٨٧٥                 h) ٦٣١{٢٥

                            W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E٢٢
a) ٩F                   b) D٥٢                c) ٦٧F                     d) ABCD
e) F.٤                  f) B٣.E               g) ١١١١{١                  h) ٨٨٨{٨

                                    W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E٢٣
a) ٨           b) ١C                c) A٦٤                d) ١F.C               e) ٢٣٩{٤

                            W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E٢٤
a) ١٠٠١{١١١١              b) ١٠٠٠٠{١                   c) ١١٠١٠١{١١٠٠١
d) ١٠١٠٠١١١{١١١٠١١        e) ١٠٠٠٠٠٠{٠٠٠١١١                  f) ١١١١١٠٠{١٠٠٠٠١١

                                                  W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E٢٥
a) ١٣A               b) ٢٥E٦                 c) ٣٠١٦                d) B٤.C
e) ٧٨.D٣             f) ٢٦٥٩.F٤١

                                                  W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E٢٦
a) ٣٧                  b) ٧٢٥                   c) ٢٤٧٦{٢                      d) ١١١٧{١٦
e) ١٦٠٠{٥٢٤             f) ٣٠٠٠{٦١٢٥

                                                  W‫א‬‫א‬‫א‬‫א‬E٢٧
a) (٤١)١٦ + (٣٦)١٦                                       b) (C٨)١٦ + (٣A)١٦
c) (٩B)١٦ + (٦٥)١٦                                       d) (١١D)١٦ + (٢E١)١٦
f) (٧٧CB٥)١٦ + (A٥F٧٢)١٦                                 g) (١٣EFD)١٦ + (٢١BB٣)١٦

                                                                                                    
                                                   ‫א‬‫א‬‫א‬
                                                ã¹]<gè…‚jÖ]æ<ËÖ]<Üé×Ãj×Ö<íÚ^ÃÖ]<퉉ö¹]
                                                    ‫א‬‫א‬‫א‬‫א‬




                                 ‫א‬
                            ‫א‬‫א‬‫א‬‫א‬
 ‫א‬‫א‬‫א‬‫א‬




٢


                                        -١-
    ‫א‬‫א‬                         ‫٧٤١ א‬                                 ‫א‬
‫א‬‫א‬‫א‬‫א‬                   ‫א‬                       



                                   ‫א‬‫א‬‫א‬
                                             
                                                  W‫א‬‫א‬
                                   K‫א‬‫א‬‫א‬‫א‬‫א‬ •
                          K‫א‬‫א‬‫א‬‫א‬‫א‬ •
                                                          K‫א‬‫א‬‫א‬‫א‬ •
                                                 K‫א‬‫א‬‫א‬‫א‬‫א‬ •
                                                  K‫א‬‫א‬‫א‬‫א‬‫א‬ •
                                                 K‫א‬‫א‬‫א‬‫א‬ •
                                                  K‫א‬‫א‬‫א‬‫א‬‫• א‬
                                    K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ •




                                                 - ٣٥ -
             ‫א‬‫א‬                              ‫٧٤١ א‬                                    ‫א‬
         ‫א‬‫א‬‫א‬‫א‬                        ‫א‬                         



                                                                                      Introduction ١J ٢
                                                                               
J ‫א‬J ‫א‬J ‫א‬‫א‬ ‫א‬
                                                 
‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬J ‫א‬
‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬
                                                                                                 K‫א‬‫א‬‫א‬
،‫א‬‫א‬‫א‬‫א‬‫א‬
                                                   
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬?‫א‬‫א‬?
                                                  K‫א‬‫א‬
                                                                       
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬K(INVERTER)‫א‬NOT‫א‬،OR‫א‬،AND‫א‬‫א‬
،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                           K‫א‬‫א‬‫א‬‫א‬
                                        Logic Signal Levels‫א‬‫א‬٢J ٢
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                         
‫א‬‫א‬‫א‬‫א‬‫א‬K ‫א‬‫א‬،‫א‬‫א‬
،،
‫א‬‫א‬‫א‬،‫א‬
                                            
‫א‬J ‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬
(LOW)‫א‬،‫א‬(١)‫א‬(HIGH)‫א‬
                     
‫א‬‫א‬(١)‫א‬‫א‬،‫א‬(٠)‫א‬
‫א‬‫א‬‫א‬(٠)‫א‬‫א‬،(TRUE)
                                                                                                     K(FALSE)
‫א‬،(Positive Logic)‫א‬،‫א‬
‫א‬(١)‫א‬‫א‬‫א‬‫א‬‫א‬ K(Negative Logic)‫א‬
‫א‬(٠)‫א‬‫א‬،‫א‬‫א‬،‫א‬(٠)‫א‬‫א‬
                                                                                     
                               K‫א‬‫א‬‫א‬(١)‫א‬‫א‬

                                                         - ٣٦ -
            ‫א‬‫א‬                            ‫٧٤١ א‬                                ‫א‬
        ‫א‬‫א‬‫א‬‫א‬                      ‫א‬                      



                                                                        AND Gate AND‫א‬٣J ٢
‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬AND‫א‬‫א‬
                            
‫א‬‫א‬،‫א‬AND‫א‬‫א‬K(Logic Functions)
‫א‬‫א‬‫א‬‫א‬ ،(Logical Multiplication)‫א‬
‫א‬A, B‫א‬،E١J ٢F ‫א‬‫א‬‫א‬‫א‬
‫א‬(٠)(Two Binary Variables)‫א‬‫א‬‫א‬
                  K(Closed)‫א‬‫א‬(١)(Open)‫א‬
                                                                                                               
                                                      
                                                (A) 
                                                           (B)     (L)

                                                      
                       
                    Voltage Source                    
                                                      
                                                      
                        K‫א‬‫א‬AND‫א‬‫א‬E١J ٢F
                                                                                                     
(١)‫א‬‫א‬‫א‬"L"‫א‬
‫א‬‫א‬K(OFF)‫א‬(٠)(ON)‫א‬
‫א‬‫א‬E١J ٢F،‫א‬،
                                                       
(L)‫א‬‫א‬K‫א‬(L)‫א‬
                  K(Truth Table)‫א‬‫א‬‫א‬‫א‬،‫א‬
                                     A      B       L
                                       
                                                      
                                                      
                                                  
                                                      
                             KE١J ٢F ‫א‬‫א‬E١J ٢F 

                                                      - ٣٧ -
            ‫א‬‫א‬                             ‫٧٤١ א‬                              ‫א‬
        ‫א‬‫א‬‫א‬‫א‬                       ‫א‬                    



‫א‬،AND‫א‬(Standard)‫א‬‫א‬‫א‬E٢J ٢F‫א‬
‫א‬‫א‬E٢J ٢F‫א‬KAND‫א‬‫א‬،Y‫א‬A, B
                                                                                KAND
              ‫א‬                  ‫א‬
              A         B            Y
               ٠         ٠            ٠
               ٠         ١            ٠
                                                                           A
                                                                                                Y
          ١    ٠        ٠                                B
          ١      ١        ١
 KAND‫א‬‫א‬E٢J ٢FKAND‫א‬‫א‬E٢J ٢F 
                                                                                                     
‫א‬ (١)‫א‬،(bits)‫א‬
                                                                              
،‫א‬‫א‬AND‫א‬،‫א‬(١)A, B‫א‬
                                     K(١)‫א‬(١)‫א‬
‫א‬‫א‬‫א‬J ‫א‬‫א‬
                                                                                                     W‫א‬
         N = 2n
                                                                       ‫א‬‫א‬N W
                                                                          K‫א‬‫א‬n
                                                                                            W
                                   N = 2 2 = 4  ‫א‬‫א‬
                                   N = 2 3 = 8 ‫א‬‫א‬
                                   N = 2 4 = 16 ‫א‬‫א‬
                                                                                             WE١J ٢F 
                                               KAND‫א‬‫א‬‫• א‬
                                               ‫؟‬AND‫א‬‫א‬ •
‫א‬E٣J ٢F،‫א‬‫א‬AND‫א‬W‫א‬
                                                                                               K‫א‬‫א‬


                                                       - ٣٨ -
            ‫א‬‫א‬                       ‫٧٤١ א‬                              ‫א‬
        ‫א‬‫א‬‫א‬‫א‬                 ‫א‬                    



                                                                                                        
                                         ‫א‬                ‫א‬
                                   A    B         C       Y
                                     ٠     ٠        ٠       ٠
                                     ٠     ٠        ١       ٠
                                     ٠     ١        ٠       ٠
                                     ٠     ١        ١       ٠
                                    ١     ٠        ٠       ٠
                                     ١     ٠        ١       ٠
                                     ١     ١        ٠       ٠
                                     ١     ١        ١       ١
                        KAND‫א‬‫א‬E٣J ٢F
                                                 
                                   W‫א‬‫א‬‫א‬•
                  N = 2 n = 2 5 = 32
                                                                                              
‫א‬‫א‬‫א‬‫א‬(Boolean Algebra)‫א‬‫א‬
‫א‬‫א‬(Boolean Expression)‫א‬‫א‬،‫א‬
                                           W‫א‬AND‫א‬‫א‬‫א‬K
                 Y = A•B
                                                                                                        
‫א‬،EAND • FA AND BY‫א‬W‫א‬
                                                                              W‫א‬‫א‬
                 Y = AB
                                                                  KA AND BY‫א‬
‫א‬‫א‬‫א‬
                                                        
‫א‬K(LOW)‫א‬(HIGH)‫א‬‫א‬(Pulses)
‫א‬‫א‬،‫א‬‫א‬AND‫א‬
                                                           K‫א‬
‫א‬(١)A, B‫א‬E٣J ٢F،
A‫א‬،t٢‫א‬‫א‬،(١)‫א‬Y‫א‬‫א‬t١‫א‬

                                                 - ٣٩ -
                   ‫א‬‫א‬                                ‫٧٤١ א‬                                      ‫א‬
               ‫א‬‫א‬‫א‬‫א‬                          ‫א‬                           



     ‫א‬‫א‬‫א‬،(٠)Y‫א‬B‫א‬(٠)
                                                                                              
     ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬
                                                                                                      K(Timing Diagram)
                                                                
                        A                                                                A
                                                                                                                      Y
                                                                                         B
                    B                                           
                               t١ t٢ t٣       t٤    t٥     t٦ t٧
                                                                
                        Y                                       
                                                                
                                     KAND‫א‬‫א‬‫א‬E٣J ٢F 
                                                                                              OR Gate OR‫א‬ ٤J ٢
     ‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ OR‫א‬‫א‬
                 
‫א‬‫א‬‫א‬،‫א‬OR
     ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،(Logical Addition)
     A, B‫א‬AND‫א‬‫א‬KE٤J ٢F 
                                                               
     ‫א‬(١)(Open)‫א‬(٠)
                                                                                     
                                                                                                                 K(Closed)
                                                                 
                                                                      (A)
                                                                                                       
                                                                 
                                                         
                             Voltage Source                           (B)
                                                                 
                                                                
                                                                
                                K‫א‬‫א‬OR‫א‬‫א‬E٤J ٢F
     ‫א‬‫א‬،‫א‬‫א‬‫א‬E٤J ٢F
                                     K‫א‬(L)‫א‬‫א‬
                                                                                                                               
                                                                 - ٤٠ -
             ‫א‬‫א‬                          ‫٧٤١ א‬                             ‫א‬
         ‫א‬‫א‬‫א‬‫א‬                    ‫א‬                   


                                            A        B              L
                                                    
                                                
                                                 
                                                 
                           KE٤J ٢F‫א‬‫א‬E٤J ٢F
                                                     
 ‫א‬A, B‫א‬،OR‫א‬‫א‬‫א‬‫א‬E٥J ٢F‫א‬
                                            KOR‫א‬‫א‬E٥J ٢F‫א‬KY
                                                                                              
              ‫א‬              ‫א‬
              A         B         Y
               ٠          ٠         ٠
           ٠         ١       ١                              A
                                                                                 Y
           ١         ٠     ١                               B
          ١         ١       ١
 KOR‫א‬‫א‬E٥J ٢FKOR‫א‬‫א‬E٥J ٢F
                                                                                                  
 ‫א‬(١)‫א‬E٥J ٢F‫א‬
 ‫א‬(٠)‫א‬،(١)‫א‬
                                          W‫א‬OR‫א‬‫א‬‫א‬K‫א‬(٠)
                  Y=A+B
                                    K(OR+)A OR BY‫א‬W‫א‬
 ،‫א‬‫א‬OR‫א‬‫א‬
                                                                     
 ‫א‬‫א‬‫א‬AND‫א‬
                                                                               K‫א‬
 ‫א‬t١‫א‬‫א‬(١)A, B‫א‬E٦J ٢F
 A‫א‬،t٢‫א‬‫א‬،(١)‫א‬Y‫א‬
      K‫א‬‫א‬‫א‬‫א‬‫א‬،(١)Y‫א‬B‫א‬(٠)

                                                     - ٤١ -
             ‫א‬‫א‬                                    ‫٧٤١ א‬                            ‫א‬
         ‫א‬‫א‬‫א‬‫א‬                           ‫א‬                     



                                                                                                                    
                   A
                                                                                     A
                                                                                                             Y
                                                                                      B
                   B                                                                                                
                              t١   t٢   t٣    t٤    t٥   t٦       t٧
                                                                                                                    
                                                              
                   Y
                                                              
                                KOR‫א‬‫א‬‫א‬E٦J ٢F
                                                              
                                            NOT Gate (INVERTER) E‫א‬F NOT ‫א‬٥J ٢
‫א‬(Inversion)‫א‬NOT‫א‬‫א‬
(١)‫א‬،‫א‬‫א‬‫א‬K(Complementation)
                                                               K(١)(٠)‫א‬،(٠)‫א‬
                    
E٧J ٢FK‫א‬‫א‬‫א‬NOT‫א‬‫א‬
      K‫א‬‫א‬‫א‬E٦J ٢F‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                                                                    
                               ‫א‬         ‫א‬
                               A             Y
                                ٠              ١                                  A                      Y
                                   ١          ٠
  K‫א‬NOT‫א‬‫א‬E٦J ٢FKNOT‫א‬‫א‬E٧J ٢F
                                                                                                           
‫א‬،‫א‬‫א‬‫א‬
                                                                                                   W‫א‬‫א‬
                 Y= A
‫א‬barA‫א‬not AY‫א‬W‫א‬‫א‬
               
                                                                        KE A FA barY‫א‬،‫א‬
                                                                                                                    
                                                                             NAND Gate  NAND ‫א‬٦J ٢

                                                              - ٤٢ -
             ‫א‬‫א‬                        ‫٧٤١ א‬                              ‫א‬
         ‫א‬‫א‬‫א‬‫א‬                  ‫א‬                    



 ‫א‬‫א‬،AND(NOT AND)‫א‬(NAND)
       
  J ٢FAND‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                  
 ‫א‬AND‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،E٨
   KNAND‫א‬‫א‬E٧J ٢FK‫א‬‫א‬‫א‬‫א‬
                                                                                                          
                ‫א‬              ‫א‬
                A             B     Y
                 ٠              ٠     ١
                 ٠               ١     ١
                                                           A
            ١       ٠       ١                                                   Y
           ١       ١       ٠                              B
 KNAND‫א‬‫א‬E٧J ٢FKNAND‫א‬‫א‬E٨J ٢F
                                                                                                 
 (١)‫א‬‫א‬‫א‬(٠)‫א‬‫א‬
 ،‫א‬(٠)‫א‬‫א‬‫א‬ (١)‫א‬،‫א‬
 ،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬NAND‫א‬‫א‬KAND‫א‬‫א‬‫א‬
  NOT, ‫א‬‫א‬‫א‬‫א‬
         W‫א‬NAND‫א‬‫א‬،‫א‬‫א‬،OR, AND
                  Y = AB
 ،‫א‬‫א‬NAND‫א‬‫א‬ 
               K(١)‫א‬(٠)NAND‫א‬‫א‬
 ‫א‬t١‫א‬‫א‬(١)A, B‫א‬E٩J ٢F
 A‫א‬،t٢‫א‬‫א‬،(٠)‫א‬Y‫א‬
 ‫א‬‫א‬‫א‬،(١)Y‫א‬(١)B‫א‬(٠)
                                                                                       K‫א‬‫א‬




                                                   - ٤٣ -
           ‫א‬‫א‬                                       ‫٧٤١ א‬                         ‫א‬
       ‫א‬‫א‬‫א‬‫א‬                                 ‫א‬               



                                                                                                                  
                                                                                                                  
                A                                                                    A
                                                                                     B
                                                                                                              Y   
                B                                                                                                 
                            t١   t٢   t٣       t٤   t٥   t٦         t٧                                            
                 Y                                              
                                                                
                         KNAND‫א‬‫א‬‫א‬E٩J ٢F
                                                                    


                                                       NOR Gate  NOR ‫א‬٧J ٢
‫א‬‫א‬،OR(NOT OR)‫א‬(NOR)
OR‫א‬‫א‬(NOT gate)‫א‬‫א‬‫א‬
NOR‫א‬‫א‬KNOR‫א‬‫א‬‫א‬‫א‬،E١٠J ٢F
                                                                                KE٨J ٢F 
                                                                                                                  
             ‫א‬                  ‫א‬
             A          B                Y
              ٠           ٠               ١
          ٠       ١       ٠                             A
                                                                               Y
          ١       ٠       ٠                              B
         ١       ١       ٠
 KNOR‫א‬‫א‬E٨J ٢FKNOR‫א‬‫א‬E١٠J ٢F
                                                                                                          


‫א‬‫א‬(٠)(Y)‫א‬‫א‬
‫א‬‫א‬(١)‫א‬،‫א‬ (١)‫א‬
                                                                                                    K‫א‬(٠)
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬NAND‫א‬‫א‬‫א‬NOR‫א‬‫א‬
             
‫א‬K،NOT, OR, AND‫א‬،‫א‬
                                                                                       WNOR‫א‬‫א‬
                Y= A+B

                                                                - ٤٤ -
            ‫א‬‫א‬                             ‫٧٤١ א‬                             ‫א‬
        ‫א‬‫א‬‫א‬‫א‬                       ‫א‬                   



                                            
،‫א‬‫א‬A, B‫א‬NOR‫א‬E١١J ٢F
                              K‫א‬(Y)‫א‬‫א‬NOR‫א‬‫א‬
                                                                                                             
                                                                           A                                 
           A                                                                                            Y
                                                                            B                           
            B                                                                                           
                        t١          t٢     t٣   t٤    t٥                                                
             Y                                                                                          
                                                                                                        
                           KNOR‫א‬‫א‬‫א‬E١١J ٢F
                                  Exclusive-OR Gate E‫א‬F‫ א‬OR ‫א‬٨J ٢
،XOR-gate??‫א‬‫א‬OR‫א‬‫א‬
                             
‫א‬‫א‬‫א‬XOR‫א‬‫א‬K‫א‬‫א‬‫א‬E١٢J ٢F
                                                                  
                                                                             K‫א‬
                                                                                                             
                 ‫א‬                 ‫א‬
                 A           B          Y
                   ٠           ٠          ٠
                   ٠            ١          ١                          A
                                                                                                Y
                   ١            ٠          ١                          B
                  ١            ١          ٠
    KXOR‫א‬‫א‬E٩J ٢FKXOR‫א‬‫א‬E١٢J ٢F
(Y)‫א‬‫א‬،(٩ ٢)XOR‫א‬‫א‬
،‫א‬(٠)‫א‬(١)،A, B‫א‬‫א‬(١)
                                                 K‫א‬(٠)
‫א‬‫א‬‫א‬OR‫א‬‫א‬XOR‫א‬‫א‬
                       
(١)XOR‫א‬‫א‬،A = B = ١ 
،‫א‬‫א‬(١) (١)‫א‬
                                                  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

                                                       - ٤٥ -
                ‫א‬‫א‬                               ‫٧٤١ א‬                                 ‫א‬
            ‫א‬‫א‬‫א‬‫א‬                         ‫א‬                       



                                              W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                     Y = AB + AB
                                                                             W‫א‬‫א‬‫א‬‫א‬
                     Y=A⊕B
                                                                                                                       
    XOR‫א‬‫א‬‫א‬‫א‬KBA⊕‫א‬
    ‫א‬‫א‬E١٣J ٢F‫א‬‫א‬،AND, OR, NOT‫א‬‫א‬‫א‬‫א‬
                                                                                K‫א‬XOR‫א‬‫א‬‫א‬
                                                                                                                       
                                                                                                                       
                                      A
                                                                                                                       
                                      B
                                                                                            Y                          
                                                                                                                       
                                                                                                                       
                       KAND, OR, NOT‫א‬XOR‫א‬‫א‬E١٣J ٢F
                                                                                                              
    ‫א‬ XOR‫א‬‫א‬E١٤J ٢F
    ‫א‬‫א‬‫א‬،‫א‬
                                                                              K‫א‬

             A                                                                         A
                                                                                                                   Y
             B
                                                                                        B

                         t١ t٢        t٣   t٤   t٥   t٦ t ٧ t٨
        
              Y
    
                                       KXOR‫א‬‫א‬‫א‬E١٤J ٢F
                                                            

                                                             - ٤٦ -
            ‫א‬‫א‬                                ‫٧٤١ א‬                                 ‫א‬
        ‫א‬‫א‬‫א‬‫א‬                          ‫א‬                       



                               Exclusive-NOR Gate E‫א‬F‫ א‬NOR ‫א‬٩J ٢
‫א‬‫א‬،XNOR-gate‫א‬NOR‫א‬‫א‬
                                       K‫א‬‫א‬‫א‬E١٥J ٢F،XOR‫א‬‫א‬‫א‬
(Y)‫א‬‫א‬،E١٠J ٢F XNOR‫א‬‫א‬
(٠)A = B = ١A = B = ٠A, B‫א‬‫א‬(١)
                                                                          
،‫א‬(٠)‫א‬(١)‫א‬
                           
‫א‬‫א‬،‫א‬‫א‬(١)
                                                                                    K‫א‬‫א‬‫א‬‫א‬
                                                                                                          
                ‫א‬                    ‫א‬
                A            B            Y
                 ٠             ٠            ١
                   ٠              ١          ٠
                                                                             A
            ١        ٠      ٠                         B
                                                                             Y
          ١         ١      ١
   KXNOR‫א‬‫א‬E١٠J ٢FKXNOR‫א‬‫א‬E١٥J ٢F
                                       W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                 Y = AB + AB
                                                                          W‫א‬‫א‬‫א‬
                      Y=A B
                                                                             
‫א‬‫א‬XNOR‫א‬‫א‬‫א‬‫א‬K‫א‬ ‫א‬
‫א‬‫א‬‫א‬E١٦J ٢F‫א‬‫א‬،AND, OR, NOT‫א‬‫א‬
                                                                                   K‫א‬XNOR‫א‬‫א‬
                                                                                                                    
                                      A                                                                             
                                       B                                                                            
                                                                                        Y
                                                          
                                                         
                  KAND, OR, NOT‫א‬XNOR‫א‬‫א‬E١٦J ٢F

                                                          - ٤٧ -
            ‫א‬‫א‬                             ‫٧٤١ א‬                                ‫א‬
        ‫א‬‫א‬‫א‬‫א‬                       ‫א‬                      



،‫א‬A, B‫א‬XNOR‫א‬E١٧J ٢F
             K(Y)‫א‬‫א‬XNOR‫א‬‫א‬
                                                                                                      
                                                                                                                
             A                                                                A
                                                                             B
                                                                                                          Y

              B                                       
                         t١   t٢   t٣   t٤   t٥   t٦ t٧ t٨

               Y                                       
                                                       
                               KXNOR‫א‬‫א‬‫א‬E١٧J ٢F
                                      Rules of Boolean Algebra ‫א‬‫א‬‫א‬١٠J ٢
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E١١J ٢F
                                                                                                      K‫א‬
                                                                                                                
                              ١.   A   + ٠ =A               ٢. A + ١ = ١
                              ٣.   A   • ٠ =٠               ٤. A • ١ = A
                              ٥.   A   + A=A                ٦. A + A = ١
                              ٧.   A   • A=A                ٨. A • A = ٠
                              ٩.   A   =A                   ١٠. A + AB = A

                               K‫א‬‫א‬‫א‬‫א‬E١١J ٢F
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                                                K‫א‬
 
‫א‬‫א‬‫א‬A + ٠ = A :(١)‫א‬
A=١‫א‬K(٠)(١)‫א‬،A،‫א‬‫א‬(٠)‫א‬OR‫א‬
KA(٠)‫א‬A=٠‫א‬KA‫א‬(١)‫א‬
 K(A + ٠ = A)‫א‬‫א‬‫א‬(٠)OR‫א‬
‫א‬(١)‫א‬OR‫א‬‫א‬‫א‬‫א‬A + ١ = ١:(٢)‫א‬
‫א‬OR‫א‬‫א‬(١)K(٠)‫א‬(١)‫א‬،A،‫א‬

                                                       - ٤٨ -
                    ‫א‬‫א‬                                  ‫٧٤١ א‬                                        ‫א‬
               ‫א‬‫א‬‫א‬‫א‬                            ‫א‬                              



                                             
     K‫א‬‫א‬‫א‬‫א‬‫א‬(١)
                                                    K(A + ١ = ١) (١)‫א‬‫א‬(١)OR‫א‬
     (٠)‫א‬AND‫א‬‫א‬‫א‬‫א‬A • ٠ = ٠:(٣)‫א‬
                                                 
    K‫א‬‫א‬‫א‬‫א‬‫א‬(٠)‫א‬‫א‬،A،‫א‬‫א‬
(٠)‫א‬‫א‬(٠)AND‫א‬ 
                                                                                                                
                                                                                                                   K(A • ٠ = ٠)
     (١)‫א‬AND‫א‬‫א‬‫א‬‫א‬A • ١ = A:(٤)‫א‬
     AND‫א‬‫א‬A=٠‫א‬‫א‬،(A)‫א‬‫א‬،A،‫א‬‫א‬
     ‫א‬‫א‬(١)AND‫א‬‫א‬A=١‫א‬‫א‬،(٠)
                                                                                        
 ‫א‬‫א‬‫א‬(١)AND‫א‬K(١)
                                                                                        K(A • ١ = A)
    ،A‫א‬OR‫א‬‫א‬‫א‬‫א‬A + A = A:(٥)‫א‬
     A = ١‫א‬‫א‬،٠ + ٠ = ٠A = ٠‫א‬‫א‬K‫א‬‫א‬‫א‬
                                                                                                          K١ + ١ = ١‫א‬
                                               
     ‫א‬A‫א‬W‫א‬ A + A = 1 :(٦)‫א‬
                                                          
     A=٠‫א‬K(١)‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ A ‫א‬OR
                                                    K1 + 1 = 1 + 0 = 1A = ١‫א‬K 0 + 0 = 0 + 1 = 1
     ‫א‬‫א‬AND‫א‬‫א‬A‫א‬‫א‬A • A = A:(٧)‫א‬
     ،١ • ١ = ١‫א‬A = ١‫א‬‫א‬،٠ • ٠ = ٠A = ٠‫א‬‫א‬K‫א‬
                                               KA‫א‬AND‫א‬‫א‬‫א‬
     ‫א‬‫א‬ A ‫א‬AND‫א‬A‫א‬ A • A = 0 :(٨)‫א‬
      A A‫א‬‫א‬‫א‬،(٠)‫א‬‫א‬‫א‬‫א‬
                                                                                      
          K(٠)‫א‬‫א‬AND‫א‬(٠)،‫א‬(٠)
     ‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬ A = A :(٩)‫א‬
                        
     (٠)(١)‫א‬،(١)A = ٠
                                                                                                                  K‫א‬‫א‬
                                                                                                                                     

                                                                    - ٤٩ -
            ‫א‬‫א‬                                   ‫٧٤١ א‬                              ‫א‬
        ‫א‬‫א‬‫א‬‫א‬                             ‫א‬                    



                  W(٤)‫א‬(٢)‫א‬‫א‬‫א‬:(١٠)‫א‬
                     A + AB = A (١ + B)
                                          = A ( ١)
                                          =A
        The Boolean Expression for a Logic Circuit‫א‬‫א‬‫א‬١١J ٢
                                                   
‫א‬‫א‬،‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬،K‫א‬‫א‬‫א‬‫א‬‫א‬
                   W‫א‬‫א‬‫א‬‫א‬‫א‬KE١٨J ٢F‫א‬
                                              K AB A, B ‫א‬‫א‬AND‫א‬‫א‬‫א‬K١
                                               K AC  A ,C ‫א‬‫א‬AND‫א‬‫א‬‫א‬K٢
                      K AB + AC  AB, AC ‫א‬‫א‬OR‫א‬‫א‬‫א‬K٣
                                                                        W‫א‬‫א‬‫א‬
                 Y = AB + AC


                                      A                           AB
                                      B                B
                                                                                      Y                     
                                                       A
                                                                                                                    
                                      C                            AC
                                                                                                                    
               K‫א‬‫א‬‫א‬‫א‬E١٨J ٢F
                                                            
                     KE١٩J ٢F‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬WE٢J ٢F 
                                                                                                               W‫א‬
                                                                                                                    
                              A                                 B+C
                                                                            D( A + B )
                                  B                                                                                 
                                                                                              Y                     
                                  C                                B+C                                    
                                  D                                                                       
                                                                                                          

                                                             - ٥٠ -
             ‫א‬‫א‬                            ‫٧٤١ א‬                                  ‫א‬
         ‫א‬‫א‬‫א‬‫א‬                      ‫א‬                        



   K‫א‬‫א‬‫א‬E٢J ٢F‫א‬‫א‬‫א‬E١٩J ٢F
                                                           W‫א‬‫א‬‫א‬‫א‬‫א‬
                  Y = D ( A + B ) + ( B + C)
                                                          ‫א‬‫א‬‫א‬‫א‬١٢J ٢
 Implementation of a Logic Circuit Using a Boolean Expression
‫א‬‫א‬‫א‬‫א‬
                               W‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬
                                                                                                                  
                  Y = AB(CD + EF)
                                                                                                        
 (CD + EF) A, B‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                     
E,F،AND‫א‬ C, D  (CD + EF) ‫א‬،AND‫א‬
KOR‫א‬AND‫א‬‫א‬،AND‫א‬
                                                                              W‫א‬‫א‬
                                                                                                        
                                                  AND
                                                   NOT                                                  
                                                OR

                  Y = A B (CD + EF) 
                                                                                                                  
                                                 AND
                                                                                                                    
‫( ؛‬CD + EF) ‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫ ؛‬CD, EF ‫א‬‫א‬‫א‬‫א‬‫א‬
                       
K‫א‬‫א‬‫א‬، D
                                      W AB(CD + EF) ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                              K D ‫א‬NOT‫א‬K١
                                             K CD, EF ‫א‬AND‫א‬K٢
                                                       K (CD + EF) ‫א‬‫א‬OR‫א‬K٣
                                                  KY‫א‬‫א‬AND‫א‬K٤
                                                       - ٥١ -
            ‫א‬‫א‬                         ‫٧٤١ א‬                                 ‫א‬
        ‫א‬‫א‬‫א‬‫א‬                   ‫א‬                     



                          KE٢٠J ٢F ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                             A                                                                             
                             B                                                          Y
                                                                                                           
                             C
                                                                                                     
                             D
                                                                                                     
                             E                                                                       
                             F
                                                                                                     
                    K AB(CD + EF) ‫א‬‫א‬‫א‬‫א‬E٢٠J ٢F
                                                          ‫א‬‫א‬١٣J ٢
Implementation of a Logic Circuit via a Truth Table
‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬E١٢J ٢FK‫א‬
                         W‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬
‫א‬‫א‬‫א‬،Y = ١‫א‬‫א‬‫א‬‫א‬ K١
‫א‬،A = ٠, B = ١, C = ٠‫א‬Y = ١‫א‬
‫א‬،(١)‫א‬‫א‬ AB C ‫א‬
‫א‬‫א‬‫א‬‫א‬(١)‫א‬،(٠)
                                                                        K ABC ‫א‬‫א‬

                                         ‫א‬                  ‫א‬
                                     A      B          C         Y
                                       ٠      ٠          ٠         ٠
                                       ٠      ٠          ١         ٠
                                       ٠      ١          ٠         ١
                                       ٠      ١          ١         ٠
                                      ١      ٠          ٠         ٠
                                       ١      ٠          ١         ٠
                                       ١      ١          ٠         ١
                                       ١      ١          ١         ٠
                       K‫א‬‫א‬‫א‬E١٢J ٢F

                                                   - ٥٢ -
             ‫א‬‫א‬                            ‫٧٤١ א‬                                  ‫א‬
         ‫א‬‫א‬‫א‬‫א‬                      ‫א‬                        



                                                       
                                                           


                  WOR‫א‬Y = ١‫א‬‫א‬‫א‬‫א‬‫א‬ K٢
                                                                                                                  
                  Y = AB C + ABC

‫א‬‫א‬‫א‬ ABC ‫א‬‫א‬‫א‬‫א‬‫א‬
 ABC ‫א‬‫א‬‫א‬‫א‬،AND‫א‬ A, B, C
OR‫א‬‫א‬‫א‬‫א‬،AND‫א‬ A, B, C ‫א‬‫א‬‫א‬
                                                                       KY‫א‬‫א‬‫א‬
NOT‫א‬W ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                   
                                                 
OR‫א‬، ABC ، ABC ‫א‬‫א‬AND‫א‬‫ ؛‬A, C ‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬، ABC + ABC ‫א‬‫א‬‫א‬
                                                                                 KE٢١J ٢F 
                                   A                                                                              
                                   B                                                                              
                                   C
                                                                                   Y
                                                       
                                                       
                     K AB C + AB C ‫א‬‫א‬‫א‬‫א‬E٢١J ٢F
      KE١٣J ٢F ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫ א‬WE٣J ٢F 
                                                                                                                      


                                            ‫א‬                   ‫א‬
                                         A       B            C        Y
                                         ٠        ٠            ٠        ٠
                                         ٠        ٠            ١        ١
                                         ٠        ١            ٠        ٠
                                         ٠        ١            ١        ١
                                        ١        ٠            ٠        ٠
                                         ١        ٠            ١        ١
                                         ١        ١            ٠        ٠
                                         ١        ١            ١        ٠

                                                       - ٥٣ -
            ‫א‬‫א‬                          ‫٧٤١ א‬                                ‫א‬
        ‫א‬‫א‬‫א‬‫א‬                    ‫א‬                      



                       K‫א‬‫א‬‫א‬‫א‬‫א‬E١٣J ٢F
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬W‫א‬
                                      WOR‫א‬E‫א‬‫א‬FY = ١
                 Y = A BC + ABC + ABC 
                                                                                      
                                       KE٢٢J ٢F ‫א‬‫א‬‫א‬
                                                                                                             
                                  A
                                  B
                                                                                                             
                                  C                                                                          
                                                                                  Y
                                                                                                             
                                                                                                             
                                                                                                
                                                                                                
                                                                                                
              K A B C + ABC + AB C ‫א‬‫א‬‫א‬‫א‬E٢٢J ٢F
                                                              ‫א‬‫א‬‫א‬١٤J ٢
Converting a Boolean Expression to a Truth Table
  
‫א‬‫א‬‫א‬‫א‬‫א‬
،(٢٢ = ٤)،‫א‬‫א‬K(١or ٠)‫א‬
                 K‫א‬،(٢٣ = ٨)،‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬
،‫א‬‫א‬(Y)‫א‬(١)‫א‬‫א‬
                                                    K‫א‬‫א‬،‫א‬‫א‬(٠)
                                                   W‫א‬‫א‬‫א‬WE٤J ٢F 
                 Y = A B C + AB C + ABC + ABC
                                                                                                             




                                                    - ٥٤ -
            ‫א‬‫א‬                            ‫٧٤١ א‬                             ‫א‬
        ‫א‬‫א‬‫א‬‫א‬                      ‫א‬                   



                                                                                               
‫א‬،‫א‬‫א‬‫א‬(A, B, C)‫א‬W‫א‬
KE١٤J ٢F ‫א‬‫א‬‫א‬‫א‬‫א‬
           
                                           W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                 AB C = 000, ABC = 010, ABC = 110, ABC = 111
،(Y)‫א‬(١)‫א‬‫א‬
                                                K(Y)‫א‬(٠)‫א‬‫א‬‫א‬
                                                                                                            
                                             ‫א‬                 ‫א‬
                                A     B     C          Y
                               ٠      ٠      ٠          ١
                                ٠      ٠      ١          ٠
                                ٠      ١      ٠          ١
                                ٠      ١      ١          ٠
                               ١      ٠      ٠          ٠
                                ١      ٠      ١          ٠
                                ١      ١      ٠          ١
                                ١      ١      ١          ١
       K Y = A B C + AB C + AB C + ABC ‫א‬‫א‬E١٤J ٢F
                                                     
                                                  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬١٥J ٢
 Simplification of Boolean Expressions Using Boolean algebra
   
E‫א‬‫א‬‫א‬F‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                  
،‫א‬،‫א‬‫א‬‫א‬
‫א‬،‫א‬،‫א‬‫א‬‫א‬
                                                                K‫א‬‫א‬‫א‬
                                   W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬WE٥J ٢F 
                 Y = AB + A(A + C) + B(A + C)
                                                                                                            
                  W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬W‫א‬
               Y = AB + AA + AC + AB + BC
                                                                                                            

                                                      - ٥٥ -
                   ‫א‬‫א‬                              ‫٧٤١ א‬                           ‫א‬
               ‫א‬‫א‬‫א‬‫א‬                     ‫א‬                   



           W‫א‬‫א‬E‫א‬‫א‬‫א‬٧‫א‬‫א‬FAAA‫א‬
               Y = AB + A + AC + AB + BC
                                                                                                                  
                              W‫א‬‫א‬،AB + AB = AB،A + A = A٥‫א‬
               Y = AB + A + AC + BC
                                                                                                                  
                                          W‫א‬‫א‬‫א‬‫א‬A‫א‬
             Y = A(B + 1 + C) + BC
                                                                 W،A + ١ = ١٢‫א‬
               Y = A • ١ + BC
                                                     W،A • ١ = A٤‫א‬‫א‬
               Y = A + BC
                                                                        
     K‫א‬‫א‬‫א‬
                                      
     ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
     ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬
                                                                                                   K‫א‬‫א‬
                                  
     ‫א‬‫א‬‫א‬‫א‬E٢٣J ٢F
     ‫א‬‫א‬‫א‬،EEF‫א‬F‫א‬‫א‬
                                                                            KEEF‫א‬F‫א‬‫א‬
       A
       B
                                                                       Y
                                                                             A
                                                                                                                  Y
                                                                              B
           C                                                                   C
                                                        EF                                E F
 
                   KE٥J ٢F‫א‬‫א‬‫א‬E٢٣J ٢F
                                                                      
‫א‬،‫א‬‫א‬‫א‬‫א‬
                                                                  K‫א‬‫א‬‫א‬،A, B, C



                                                              - ٥٦ -
                 ‫א‬‫א‬                              ‫٧٤١ א‬                                 ‫א‬
             ‫א‬‫א‬‫א‬‫א‬                        ‫א‬                       



    ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬WE٦J ٢F
                                                                                                            K‫א‬
             Y = AB C + ABC + ABC + ABC
              W،‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬W‫א‬
                                                                                                                       
             Y = ( AB C + ABC) + ( ABC + ABC)
                      = AB( C + C) + BC( A + A )
                                                                                 W٦‫א‬
             Y = AB • 1 + BC • 1
                                                                                                                       
                                        W‫א‬‫א‬‫א‬٤‫א‬
                                                                                                                       
             Y = AB + BC 
                                                                                                                       
                              K‫א‬‫א‬‫א‬‫א‬E٢٤J ٢F
                                                       
    A
     B
     C
                                                                            A

                                                                            B
                                                                 Y
                                                                                                                       Y

                                                                            C


                                           EF                                          E F

                KE٦J ٢F‫א‬‫א‬‫א‬E٢٤J ٢F




                                                             - ٥٧ -
           ‫א‬‫א‬                      ‫٧٤١ א‬                            ‫א‬
       ‫א‬‫א‬‫א‬‫א‬                ‫א‬                  



                                         
                                              
‫א‬،A,B‫א‬‫א‬AND‫א‬X‫א‬‫א‬‫א‬E١
                                                       K١J ‫א‬‫א‬
                                              
                                              
                                 A
                                              
                                 B            
                                              
                                 X            
                                              
                                          ١J 
                                                                                                    
‫א‬،A,B‫א‬‫א‬OR‫א‬X‫א‬‫א‬‫א‬E٢
                                                       K١J ‫א‬‫א‬
                                                                                                    
‫א‬،A,B‫א‬‫א‬NAND‫א‬X‫א‬‫א‬‫א‬ E٣
                                                       K٢J ‫א‬‫א‬
                                                                                                    
                             A                
                                              
                             B                
                                              
                            X                 
                                              
                                          ٢J 


                                                  - ٥٨ -
           ‫א‬‫א‬                     ‫٧٤١ א‬                             ‫א‬
       ‫א‬‫א‬‫א‬‫א‬               ‫א‬                   



‫א‬‫א‬،A,B‫א‬‫א‬NOR‫א‬X‫א‬‫א‬‫א‬ E٤
                                                    K٣J ‫א‬‫א‬
                                              
                                 A



                                 B



                                 X
                            
                                          ٣J 
                                              
‫א‬‫א‬،A,B‫א‬‫א‬XOR‫א‬X‫א‬‫א‬‫א‬ E٥
                                                    K٣J ‫א‬‫א‬
                                                                                                    
‫א‬‫א‬،A,B‫א‬‫א‬XNOR‫א‬X‫א‬‫א‬‫א‬ E٦
                                                    K٣J ‫א‬‫א‬
                                                                                                    
                                          K٤J ‫א‬‫א‬‫א‬‫א‬‫א‬E٧
                                              
                                     A
                                     B
                                              
                                     C        
                                                                         Y
                                              
                                                                                                    
                                          ٤J 
                                                                                                    
                                                                                                    
                                                                                                    

                                              - ٥٩ -
    ‫א‬‫א‬                       ‫٧٤١ א‬                           ‫א‬
‫א‬‫א‬‫א‬‫א‬                 ‫א‬                 



                                W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E٨
a) AB + AB                       b) AB + AB + ABC
c) AB(C + D )                    d) A + B[C + D(B + C )]
                                                                                             
                                  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E٩
                                        
                            ‫א‬                     ‫א‬
                            A  B            C           Y
                           ٠   ٠            ٠           ٠
                            ٠   ٠            ١           ١
                            ٠   ١            ٠           ٠
                            ٠   ١            ١           ١
                           ١   ٠            ٠           ٠
                            ١   ٠            ١           ١
                            ١   ١           ٠           ٠
                           ١       ١         ١           ١
                                        
                                         W‫א‬‫א‬‫א‬‫א‬‫א‬E١٠
a) (A + B)C                      b) (A + B)( B + C)
c) A(AC + AB)                    d) A(A + AB)
                                     
                                W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E١١
a) (A + B)(A + C)               b) AB + ABC + ABCD + ABC DE
b) (A + A )(AB + ABC )          d) AB + (A + B)C + AB


                                                                                             




                                         - ٦٠ -
                                                       ‫א‬‫א‬‫א‬
                                                    ã¹]<gè…‚jÖ]æ<ËÖ]<Üé×Ãj×Ö<íÚ^ÃÖ]<퉉ö¹]
                                                        ‫א‬‫א‬‫א‬‫א‬




                                    ‫א‬
                              ‫א‬‫א‬‫א‬‫א‬‫א‬
 ‫א‬‫א‬‫א‬‫א‬‫א‬




٣
     ‫א‬‫א‬                       ‫٧٤١ א‬                                    ‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬                ‫א‬                          



                                  ‫א‬‫א‬‫א‬
                                            
                                                 W‫א‬‫א‬
                                                                                                        
                                                                       K •
                                       KNOR‫א‬‫א‬NAND‫א‬‫א‬‫א‬‫א‬ •
                            KNORNAND‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ •
                                      K‫א‬‫א‬‫א‬‫א‬‫א‬ •
                                                         K‫א‬‫א‬‫א‬‫א‬ •




                                                - ٦١ -
                          ‫א‬‫א‬                               ‫٧٤١ א‬                                       ‫א‬
                     ‫א‬‫א‬‫א‬‫א‬‫א‬                        ‫א‬                           


                                                                             Introduction١J ٣
                    
              ‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬       
                                                                                              
              ‫א‬‫א‬‫א‬‫א‬ K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                   
            ،،‫א‬‫א‬‫א‬
                                                                                   
              ،‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬ ‫א‬‫א‬‫א‬
                                                    K‫א‬‫א‬‫א‬(١٠)‫א‬
              ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                 
            K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬NOR‫א‬‫א‬NAND
          ‫א‬‫א‬‫א‬‫א‬ 
                                                  K(K–map)K –‫א‬‫א‬ (Karnaugh-Map)
              ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                                                          K‫א‬‫א‬‫א‬
                                                                            Demorgan's Theorems٣J ٢
                                                                          
              ‫א‬‫א‬‫א‬،‫א‬‫א‬
                                                    
              ‫א‬‫א‬KOR‫א‬AND‫א‬
                          W‫א‬‫א‬،‫א‬‫א‬‫א‬(bars)
                                                                                                                             
                                                          A+B=A•B                          W‫א‬
                                                          A • B = A + B                   W‫א‬ 
                                                                                                                             
   AND‫א‬OR‫א‬‫א‬
              AND‫א‬‫א‬‫א‬‫א‬NOR‫א‬‫א‬E١J ٣F
                                                  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
              KE١J ٣F‫א‬‫א‬‫א‬
                                            K(negative AND)‫א‬AND‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬




                                                                        -٦٢-
                          ‫א‬‫א‬                               ‫٧٤١ א‬                               ‫א‬
                     ‫א‬‫א‬‫א‬‫א‬‫א‬                        ‫א‬                    


                                                                                                                      
                                                                                                                      
                                           A                   A+B           A                AB
                                           B                                 B                            

                                    KANDOR‫א‬E١J ٣F

                                                          ‫א‬                 ‫א‬
                                                          A          B       
                                                                             A+B      
                                                                                      A•B
                                                           ٠         ٠           ١        ١
                                                           ٠         ١           ٠        ٠
                                                           ١         ٠           ٠        ٠
                                                           ١         ١           ٠        ٠
                                                   K‫א‬‫א‬E١J ٣F

     OR‫א‬AND‫א‬‫א‬
              ‫א‬OR‫א‬‫א‬‫א‬‫א‬NAND‫א‬‫א‬E٢J ٣F
              ‫א‬،E‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬F‫א‬
              OR‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬KE٢J ٣F‫א‬‫א‬‫א‬
                                                                                                    K(negative OR)‫א‬
                                                                                                                               
                                                                     ≡
                                  A                                         A
                                                               AB                                  A+B
                                   B                                        B                                     

                                    KORAND‫א‬E٢J ٣F

                                                          ‫א‬                 ‫א‬
                                                          A          B       
                                                                             A•B      
                                                                                      A+B
                                                           ٠         ٠           ١        ١
                                                           ٠         ١           ٠        ٠
                                                           ١         ٠           ٠        ٠
                                                           ١         ١           ٠        ٠
                                                  K‫א‬‫א‬E٢J ٣F

                                                                         -٦٣-
                          ‫א‬‫א‬                          ‫٧٤١ א‬                                  ‫א‬
                     ‫א‬‫א‬‫א‬‫א‬‫א‬                   ‫א‬                       


                                 
            K‫א‬‫א‬‫א‬‫א‬
                              K‫א‬‫א‬‫א‬‫א‬
                                                    W‫א‬‫א‬‫א‬WE١J ٣F
                                                                                                                             
                      Y = (A + B + C) • (A + B + C )

                                                                                                                      W‫א‬
                      Y = (A + B + C) • (A + B + C)
                          = (A + B + C ) + (A + B + C )
                          = A BC + A BC= ABC+ A BC
                                                                                                                             
                                                    W‫א‬‫א‬‫ א‬ WE٢J ٣F
                     Y = (A + B) + CD
                                                                                                                      W‫א‬
                      Y = (A + B) + CD
                         = (A + B).CD
                         = (A.B)(C + D)
                         = A B(C + D)


                                                                           NOR , NAND‫א‬‫א‬‫א‬‫א‬٣J ٣
               The Universal Property of NAND and NOR Gates
              ‫א‬،AND‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
              ‫א‬NOR‫א‬NAND‫א‬‫א‬‫א‬K‫א‬‫א‬،OR
                                                                             
              ‫א‬‫א‬‫א‬K (Universal Gates)
            KNOR،AND‫א‬‫א‬‫א‬NAND‫א‬
              NOR‫א‬‫א‬‫א‬NOR‫א‬
                                                     KNANDOR،AND‫א‬‫א‬



                                                                   -٦٤-
                           ‫א‬‫א‬                            ‫٧٤١ א‬                                 ‫א‬
                      ‫א‬‫א‬‫א‬‫א‬‫א‬                     ‫א‬                       

                                                                                                                         


                     NAND gate as a Universal Logic Element NAND‫א‬‫א‬١J ٣J ٣
              ،AND،‫א‬‫א‬‫א‬‫א‬NAND‫א‬‫א‬
              NAND‫א‬‫א‬‫א‬KNOR،OR
            K‫א‬NAND‫א‬EF٣J ٣‫א‬‫א‬‫א‬
            KEF٣J ٣NAND‫א‬‫א‬AND  
                                                                                    
                   
              NOR ‫א‬‫א‬‫א‬KEF٣J ٣NAND‫א‬ ‫א‬OR‫א‬‫א‬
                                                                           KEF٣J ٣
                                                                                                                     
                                   A                          A    ≡       A                        A


                                                                   EF



                          A
                           B
                                                      AB          AB = AB
                                                                                    ≡   A
                                                                                        B
                                                                                                               AB

                                                                   E F


                                                  A
                     A
                                                                                    ≡
                                                                                        A
                                                               A .B = A + B                                        A+B
                                                  B                                         B
                     B

                                                                    EF


                                                  A         A .B = A + B
                     A
                                                                                        ≡
                                                                                                A
                                                                                A+B
                                                                                                                       A+B
                                                  B                                             B
                     B


                                                                    EF
             
                                                   KNAND‫א‬‫א‬‫א‬E٣J ٣F

                                                                         -٦٥-
                                ‫א‬‫א‬                          ‫٧٤١ א‬                                    ‫א‬
                        ‫א‬‫א‬‫א‬‫א‬‫א‬                      ‫א‬                          


                            NOR Gate as a Universal Logic Element NOR‫א‬‫א‬٢J ٣J ٣
              ،OR،AND،‫א‬‫א‬‫א‬NOR ‫א‬‫א‬،NAND ‫א‬
                                                                                   
                    ‫א‬NOR‫א‬‫א‬E٤J ٣FKNAND‫א‬
                                                                                  KNAND‫א‬‫א‬OR‫א‬NOT
                                                                                                                           

                                         A                       A              ≡             A                     A


                                                                                EF
                                                 A+B
                        A

                        B
                                                                 A+B = A+B
                                                                                        ≡     A
                                                                                                  B
                                                                                                                        A+B



                                                                                E F


                            A                          A

                                                                               A + B = A .B       ≡   A
                                                                                                      B
                                                                                                                           AB
                            B
                                                       B
                                                                               EF




                    A                            A          A + B = A .B

                                                                                        A         ≡       A
                                                                                                          B
                                                                                                                                 AB
                    B
                                                 B

                                                                                EF
      
                                                      KNOR‫א‬‫א‬‫א‬E٤J ٣F

                                                                           
                                                                               -٦٦-
                                ‫א‬‫א‬                                 ‫٧٤١ א‬                               ‫א‬
                           ‫א‬‫א‬‫א‬‫א‬‫א‬                       ‫א‬                        


                                                           NOR،NAND‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬٤J ٣
               Design of Combinational Logic Circuits using NAND and NOR Gates
              ‫א‬‫א‬NOR‫א‬،NAND‫א‬‫א‬‫א‬
                                                                                       
              ،(Negative-OR)‫א‬OR‫א‬‫א‬NAND‫א‬‫א‬‫א‬‫א‬‫א‬
              ‫א‬K(Negative - AND)‫א‬AND‫א‬‫א‬NOR‫א‬‫א‬
                            K‫א‬ (Logic diagram) ‫א‬‫א‬‫א‬‫א‬AND،OR‫א‬
                                                                NAND Logic NAND‫א‬‫א‬‫א‬١J ٤J ٣
              ‫א‬،‫א‬OR ‫א‬NAND ‫א‬NAND‫א‬،
                                                                                                                  W‫א‬
                     A • B = A + B
                                  NAND                                                    Negative-OR                                   
                                                                                                                                        
                                                             KE٥J ٣F‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                                                                                        
                                                       A                                                                                 
                                                                         AB
                                                       B                                                                                
                                                                                                  Y = AB + CD
                                                       C                                                                                
                                                       D                 CD                                               
                                       KNAND‫א‬‫א‬‫א‬E٥J ٣F
                                                                               
                                              W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬(Y)‫א‬‫א‬
                            Y = (AB)(CD)
                                                                                            W‫א‬
                            Y = AB + CD
                                                                               W(bars)‫א‬‫א‬‫א‬
                            Y = AB + CD
       AND‫א‬،AB+CD ،(Y)‫א‬
 ‫א‬NAND‫א‬‫א‬(Y)‫א‬‫א‬‫א‬.OR‫א‬
                                                                                   -٦٧-
                             ‫א‬‫א‬                          ‫٧٤١ א‬                                ‫א‬
                        ‫א‬‫א‬‫א‬‫א‬‫א‬                ‫א‬                         


              KOR‫א‬‫א‬NAND‫א‬AND‫א‬E٥J ٣F
              NAND‫א‬‫א‬‫א‬‫א‬EF٦J ٣‫א‬(Y)‫א‬‫א‬
                                 
              ‫א‬‫א‬K‫א‬OR ‫א‬‫א‬
                                                                           
              ،EF٦J ٣‫א‬‫א‬E٥-٣F‫א‬‫א‬،EF٦J ٣‫א‬
                                                                                                                   W
                                         (NAND-NAND-NAND)(AND-AND-OR)

                    A                                                            A
                                              AB
                    B

                    C
                                                        Y = AB + CD
                                                                            ≡    B                              Y = AB + CD
                                                                                 C
                    D                                    EF                                                     E F
                                              CD                                 D

                        KE٥J ٣F‫א‬‫א‬AND-AND-OR  E٦J ٣F 
              ‫א‬‫א‬‫א‬NAND‫א‬‫א‬E٧J ٣F

                                                                                      K‫א‬J OR‫א‬‫א‬‫א‬

                                                    A          AB                                                              
                                                    B                           ABC
                                                                     
                                                    C                                             Y
                                                    D          DE                                                              
                                                    E
                                                                               DEF
                                                    F
                                                                                                                               
                             K‫א‬J OR‫א‬‫א‬‫א‬‫א‬‫א‬‫ א‬E٧J ٣F
                                                                                                                               
                                                            WE٧J ٣F‫א‬(Y)‫א‬
                         F = [(AB)C] • [(DE )F]
                            = [(A + B)C] • [( D + E )F]
                            = ( A + B )C + ( D + E ) F
                            = ( A + B )C + ( D + E ) F


                                                                         -٦٨-
                                ‫א‬‫א‬                           ‫٧٤١ א‬                                 ‫א‬
                           ‫א‬‫א‬‫א‬‫א‬‫א‬                    ‫א‬                     


              ‫א‬‫א‬‫א‬ NAND‫א‬‫א‬‫א‬J OR‫א‬‫א‬
                         K‫א‬‫א‬‫א‬(Y)‫א‬،E٨J ٣F
                                                                           


                                      A                A+B
                                                                                                                                  
                                                                       ( A + B )C
                                      B                                                                                           
                                      C                                                       Y = ( A + B )C + ( D + E )F         
                                      D
                                                       D+E                                                                        
                                      E
                                                                       ( D + E )F
                                                                                                                                  
                                      F                                                                                           
                                  K‫א‬J OR‫א‬‫א‬ E٧J ٣F ‫א‬‫א‬‫ א‬E٨J ٣F                             
                                     WNAND‫א‬‫א‬‫א‬‫א‬WE٣J ٣F
                           (a ) Y = ABC + DE
                           (b) Y = ABC + D + E
                                                                                          KE٩J ٣F‫א‬‫א‬W‫א‬
                                                                                                                                  
                    A                                                          A
                                           ABC                                            ABC
                    B                                                          B
                    C                                  Y = ABC + DE            C                              Y = ABC + D + E

                    D                                                           D
                                                        E F                                                   E F
                    E                                                          E
                                           DE
                                          KE٣J ٣F‫א‬‫א‬‫א‬‫ א‬E٩J ٣F 
                                                                NOR Logic NOR‫א‬‫א‬‫א‬٢J ٤J ٣
              ‫א‬‫א‬J AND‫א‬NOR‫א‬NOR‫א‬‫א‬
                                                                                                     W‫א‬
                                                                                                                            



                                  A + B = A • B
                                                                                                
                                          NOR                                  Negative-AND
                                                                                                                                  
                                            KE١٠J ٣F‫א‬‫א‬‫א‬‫א‬

                                                                          -٦٩-
                              ‫א‬‫א‬                                 ‫٧٤١ א‬                                ‫א‬
                         ‫א‬‫א‬‫א‬‫א‬‫א‬                          ‫א‬                      


                                                                                                                                       
                                                                             
                                                     A                       A+B
                                                     B                                                                                 
                                                                                             (A + B) (C + D)
                                                     C                                                                                 
                                                     D                      C+D                                                        
                                                                                                                                       
                                         KNOR‫א‬‫א‬‫א‬E١٠J ٣F
                                                                                                                                       
                                                                            W‫א‬‫א‬‫א‬‫א‬‫א‬
                                   Y = (A + B) + (C + D)
                                                                                         W‫א‬

                                   Y = (A + B) • (C + D)                                         W‫א‬‫א‬‫א‬

                                    Y = (A + B) • (C + D)                                                                   
              ‫א‬،AND‫א‬OR‫א‬(A + B)(C + D)‫א‬
              AND‫א‬‫א‬‫א‬‫א‬OR‫א‬‫א‬‫א‬‫א‬
            K‫א‬J AND‫א‬‫א‬EF١١J ٣‫א‬‫א‬‫א‬KEF١١J ٣
                                                                                                                            

                    A                                                              A
                                       A+B                                                           A+B
                    B                                                              B
                                                                            ≡
                                                         (A + B) (C + D)                                           (A + B) (C + D)
                    C                                                              C
                    D                 C+ D                                         D
                                                          E F                                                    E F

                         K‫א‬J AND‫א‬‫א‬E١٠J ٣F‫א‬‫א‬‫א‬E١١J ٣F
                                                                                                                            
              ‫א‬‫א‬‫א‬،NOR‫א‬‫א‬E١٢J ٣F
                                                W‫א‬(Y)‫א‬K‫א‬J AND‫א‬‫א‬


                                                                                 -٧٠-
                           ‫א‬‫א‬                           ‫٧٤١ א‬                                  ‫א‬
                      ‫א‬‫א‬‫א‬‫א‬‫א‬                    ‫א‬                      


                                                                                                                   
                                Y = [(A + B) + C] + [(D + E ) + F]
                                                                                                                   
                                    = [ AB + C] + [ D E + F]
                                                                                                                               
                                    = ( AB + C)( D E + F)
                                                                                                                               
                                                                                                                               
                                             A              A+B
                                                                                                                               
                                             B                                 ( A + B) + C                                    
                                                                                                                       
                                             C
                                                                                                          Y            
                                             D              D+E                                                                
                                             E
                                                                                                                               
                                                                               ( D + E) + F
                                             F                                                                                 
                                                                                                                               
                                       KNOR‫א‬‫א‬E١٢J ٣F
                                                                                                                               
                     KE١٣J ٣F‫א‬‫א‬NOR‫א‬‫א‬‫א‬J AND‫א‬‫א‬
                                                                                                                               
                                                                                                                           
                                     A              AB
                                     B
                                                                     AB + C                                                
                                      C                                                                                    
                                                                                              Y = ( A B + C) (D E + F)     
                                         D          DE                                                                     
                                       E
                                                                     DE + F
                                                                                                                           
                                       F
                                                                                                                           
                                      KE١٢J ٣F‫א‬‫א‬‫א‬‫א‬E١٣J ٣F




                                                                     -٧١-
                           ‫א‬‫א‬                               ‫٧٤١ א‬                                      ‫א‬
                      ‫א‬‫א‬‫א‬‫א‬‫א‬                        ‫א‬                           


                                                   WNOR‫א‬‫א‬‫א‬‫א‬‫א‬WE٤J ٣F

                                Y = AB C + (D + E )                                           KE١٤J ٣F‫א‬‫א‬W‫א‬
                                                                        
                                     A
                                                                A + B + C = AB C
                                      B
                                    C                                                          Y = A B C + ( D + E)

                                      D

                                    E
                           
                                 KNOR‫א‬‫א‬‫א‬‫א‬‫א‬E١٤J ٣F
                                                                         Karnaugh Map٥J ٣
              ‫א‬‫א‬،‫א‬‫א‬‫א‬K-
                                                
              ‫א‬‫א‬K‫א‬‫א‬
              ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                        
              ‫א‬‫א‬‫ א‬،‫א‬‫א‬‫א‬
                         KK‫א‬‫א‬‫א‬
              ‫א‬‫א‬‫א‬
              ،‫א‬K‫א‬
              ‫א‬‫א‬،(cells)‫א‬ (array)
                                                                                                     
              ‫א‬‫א‬‫א‬‫א‬K‫א‬
                                                                                                                      K‫א‬
              ،،،‫א‬‫א‬‫א‬‫א‬
                        
              K‫א‬‫א‬،‫א‬
                                                                     
              ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                      
              ‫א‬‫א‬‫א‬‫א‬‫א‬
              ‫א‬‫א‬‫א‬‫א‬‫א‬ (Quine - McClusky)
                                                                                          
              ‫א‬‫א‬‫א‬K‫א‬

                                                                            -٧٢-
                          ‫א‬‫א‬                            ‫٧٤١ א‬                           ‫א‬
                     ‫א‬‫א‬‫א‬‫א‬‫א‬                     ‫א‬                 


                                                             
              ‫א‬‫א‬K ‫א‬‫א‬،
                                                  K 2 4 = 16 ‫א‬‫א‬ 2 3 = 8 
                                                                                                              
                                                                                                              
                               Simplification using Karnaugh-map ‫א‬‫א‬‫א‬٦J ٣
              KE‫א‬F‫א‬‫א‬‫א‬
              ( A, B )‫א‬(A، B)‫א‬،E١٥J ٣F
                                                                                     
                      K(٠٠{٠١{١٠{١١)E‫א‬F
                                                                                                              

                                      A           B        Y
                                                                                   B     B
                                      ٠           ٠      AB
                                      ٠           ١                            A   AB   AB
                                                         AB
                                      ١           ٠      AB                    A   AB   AB
                                      ١           ١      AB

                                                                                                              

                              K‫א‬E١٥J ٣F

                       
              K‫א‬‫א‬‫א‬‫א‬
              E١٦J ٣F‫א‬(Input Labels)‫א‬
                                           
              ،‫א‬‫א‬ A ‫א‬‫א‬‫א‬،K‫א‬‫א‬
                                                                                        
                                                                         
              ‫א‬‫א‬ B ‫א‬‫א‬K‫א‬‫א‬A‫א‬
                                                              
              ‫א‬‫א‬‫א‬‫א‬،K‫א‬‫א‬‫א‬B‫א‬،‫א‬
                                                                                                K AB ‫א‬
                                                                                                              
                                                                                                              
                                                                                                              
                                                                                                              
                                                                     -٧٣-
                          ‫א‬‫א‬                                   ‫٧٤١ א‬                                          ‫א‬
                     ‫א‬‫א‬‫א‬‫א‬‫א‬                          ‫א‬                                


                                                                      B          B

                                                               A
                                                                                                                                     
                                                              A
                                                                                                                                     

                                        KE٢٢ = ٤FE١٦J ٣F

                                                                          

                         
              ،EF‫א‬EF١٧J ٣،EF١٧J ٣
                                                                                                            KEF‫א‬
                                                                                                                                              
                                                                                                                                      
                                                                                             CD        CD           CD       CD
                                                                                                                                     
                                                                                      AB
                                 BC         BC         BC     BC     
                                                                                      AB
                         A
                                                                                                                                              
                            A                                                         AB
                                                         

                                                 EF                                 AB

                                                                                                             E F
                                                                           

                                        K‫א‬‫א‬E١٧J ٣F

              ،‫א‬
                                                                                           
              ‫א‬‫א‬،K‫א‬‫א‬‫א‬
                                                                                                        KEF١٨J ٣‫א‬




                                                                               -٧٤-
                          ‫א‬‫א‬                        ‫٧٤١ א‬                               ‫א‬
                     ‫א‬‫א‬‫א‬‫א‬‫א‬                 ‫א‬                     


              ،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
              OR ‫א‬‫א‬‫א‬‫א‬(١)‫א‬‫א‬
                                                                                                 KEF١٨J ٣
              ‫א‬‫א‬KEF١٨J ٣‫א‬‫א‬‫א‬‫א‬‫א‬
                                      KEF١٨J ٣‫א‬‫א‬‫א‬
                                                                                                              
                                                                                                              




                                                                 -٧٥-
                               ‫א‬‫א‬                                         ‫٧٤١ א‬                                                ‫א‬
                          ‫א‬‫א‬‫א‬‫א‬‫א‬                                 ‫א‬                                    


                                                                                                                                                        
                                                                                                                     
                                                                                                                  A A B B
                     ‫א‬                 ‫א‬
                                                                                                                                                                Y
                     A            B             Y
                     ٠            ٠              ٠                              Y=AB+AB
                     ٠            ١              ٠                                                                                              EF

                     ١            ٠              ١                AB
                     ١            ١              ١                AB

                                                                                                 E F                        A A B B
                                                                                                                                                                 
                                  E F

                           B             B                                            
                                                                                      B           B                                                 Y

                           0             0                                            0            0
                    A                                                          A      

                    A      1             ١                                    A       1
                                                                                                 ١
                                                                                                                     A
                     EFEFEF

                                 K‫א‬‫א‬‫א‬E١٨J ٣F

                                                                         
               ‫א‬‫א‬
                                                        
              ‫א‬(١)‫א‬K‫א‬‫א‬‫א‬‫א‬
              (٠)‫א‬(٠)‫א‬،‫א‬‫א‬ (١)
              ‫א‬‫א‬(١)K‫א‬‫א‬
                                                                                               
 ‫א‬‫א‬KEABF‫א‬‫א‬‫א‬،E A B F‫א‬
                      K‫א‬‫א‬(٠)،‫א‬(٠)( AB, A B )
              ‫א‬‫א‬‫א‬‫א‬
              ‫א‬‫א‬‫א‬K A + A = 1 ‫א‬،EComplements)
            K‫א‬‫א‬‫א‬‫א‬‫א‬،EF١٨J ٣

                                                                                          -٧٦-
                                ‫א‬‫א‬                          ‫٧٤١ א‬                                  ‫א‬
                           ‫א‬‫א‬‫א‬‫א‬‫א‬                   ‫א‬                       


                    
                    ‫א‬‫א‬EF١٨J ٣‫א‬
              ‫א‬‫א‬K‫א‬(adjacent cells)
                                                                                       
              ‫א‬‫א‬‫א‬K‫א‬،‫א‬
              ‫א‬‫א‬‫א‬ EF١٨J ٣‫א‬(١)
                                                   
              ،‫א‬ B ، B  AB , A B ‫א‬‫א‬‫א‬K‫א‬
                                                                                               
                                                                                                WA،‫א‬
                          Y = A B + AB E‫א‬‫א‬‫א‬F

                                 Y = A (B + B)
                                   = A •1= A
              ‫א‬EF١٨J ٣‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
              ‫א‬‫א‬‫א‬K(A)‫א‬(Y)‫א‬
                                                                                                          KEF١٨J ٣
               
              EF١٩J ٣‫א‬‫א‬‫א‬WE٥J ٣F
                                                                                                 K‫א‬
                                                                 
              ،‫א‬‫א‬‫א‬،‫א‬W‫א‬
                                                                                                 KEF١٩J ٣
              EF١٩J ٣‫א‬(١)‫א‬‫א‬‫א‬‫א‬
 ‫א‬‫א‬‫א‬
              ‫א‬‫א‬،‫א‬‫א‬‫א‬(٠)KEF١٩J ٣
              E‫א‬‫א‬F‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،EF١٩J ٣
               A , A ‫א‬‫א‬‫א‬K‫א‬
                                                                
                                                  K A B ‫א‬ C , C ‫א‬‫א‬‫א‬، BC ‫א‬
              ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
              ‫א‬‫א‬‫א‬‫א‬KEF١٩J ٣،‫א‬
                                            
              ‫א‬ OR ‫א‬‫א‬AND‫א‬
              ‫א‬‫א‬‫א‬،١٦‫א‬‫א‬‫א‬


                                                                         -٧٧-
                          ‫א‬‫א‬                                  ‫٧٤١ א‬                                                ‫א‬
                     ‫א‬‫א‬‫א‬‫א‬‫א‬                           ‫א‬                                   


              ‫א‬‫א‬‫א‬، OR‫א‬AND‫א‬
                                              KEF١٩J ٣‫א‬٦‫א‬‫א‬
                                                                                                                                          
                                                                  ‫א‬                   ‫א‬
                                                             A         B            C         Y
                                                             ٠         ٠            ٠         ٠
                                                              ٠         ٠           ١         ٠
                                                              ٠         ١           ٠         ١
                                                              ٠         ١           ١         ٠
                                                              ١         ٠           ٠         ١
                                                              ١         ٠           ١         ١
                                                              ١         ١           ٠         ١
                                                              ١         ١           ١         ٠
                                                                             EF

                                                                                                        BC                     BC
                                                                                                                                                     
                       A A B B              CC                                                                      BC                     BC
                                                                                                                                                     
                                                                                                  A                                           ١
                                                                        Y
                                                                          
                                                                    
                                                                                               A ١              ١                    ١

                                                                   
                                                   Y = AB + B C
                                                   
                                                                                                         AB
                                                                                                                           E F      BC
                                                       EF
                             K‫א‬‫א‬E١٩J ٣F

              E‫א‬F‫א‬(١'s)‫א‬
              ،‫א‬E٢٠J ٣FK٢‫א‬‫א‬،،
                                                              
                                                                
              ‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬
              ‫א‬‫א‬‫א‬E١'sF‫א‬‫א‬
                                                                                   
              ‫א‬‫א‬‫א‬‫א‬K‫א‬
                                                                                           
              ‫א‬‫א‬F‫א‬‫א‬،‫א‬

                                                                             -٧٨-
                         ‫א‬‫א‬                                                    ‫٧٤١ א‬                                              ‫א‬
                    ‫א‬‫א‬‫א‬‫א‬‫א‬                                             ‫א‬                                 


                                                                                        
              ‫א‬،‫א‬‫א‬،
                                                                                          KE‫א‬‫א‬‫א‬
                                                                                                                                                          

                                                                        AB                                             AC
                                       CD          CD         CD           CD                                                CD       CD        CD

                                                    ١           ١            ١                           AB        ١        ٠              ١    ١
                            AB            ١

                             AB           ١         ٠           ٠          ١                             AB        ١        ٠          ١        ١

                     AD                                                                                                                 ٠
                                          ١         ١           ١          ٠                             AB        ١                            ١

                    AB C       AB         ٠         ١           ١          ٠                              AB        ١        ٠          ١        ١
                                                                                     
                                    AD                                                                         D        BC
                          Y = A B C D + A B C D + A B CD + A B C D                                       Y = A B C D + A B CD + A B C D + AB C D
                              + A B C D + A BC D + AB C D + AB C D                                           + ABCD + ABC D + AB C D + ABC D
                                                                         E‫א‬F                       + A B C D + A B CD + A B C D        E‫א‬F
                              + ABCD + A B C D + A B CD
                                                                                                                                                          
                          Y = AB C + AD + AB D + A B                    E‫א‬F                     Y = AC + B C + D   E‫א‬F
                                                        EF                                                                      E F
                                                                                                                                                                   
                                                                                                                                                                   
                                                                                               B
                                              CD     C D CD                  CD                                         CD       CD         CD       CD            
                                                                                                                                                              BD
                                AB            ١         ١           ١            ١                              AB ٠             ١          ٠        ٠             

                                  AB                    ١           ١                                          AB       ١         ١         ٠        ١             
                                                                                             D
                                                                                                             AB
                                                                                                                                                                  
                                                                                                                                                                 CD
                                 AB           ٠         ١           ١          ٠                                        ١        ١          ٠        ١
                                                                                                                                                                   
                                              ١         ١                        ١                                      ١        ١          ١        ١
                                 AB                                 ١                                          AB                                                 
                                                                                                                                                                 AB
                                                                                                             Y = AB C D + ABC D + ABC D + ABCD
                           Y=     A B C D + A B C D + A B CD + A B C D
                                + AB C D + ABCD + A B CD + ABCD                                                  + ABC D + ABC D + ABCD + AB C D
                                + A B C D + A B C D + AB C D + A B C D                      E‫א‬F        + AB C D + ABCD + ABCD E‫א‬F
                           Y = B+D                E‫א‬F                                              Y = C D + AB + BD              E‫א‬F
                                                                                                                                                                   
                                                         EF                                                                           EF                        
                                                                                                                                                                   
                                          K‫א‬‫א‬E٢٠J ٣F
                                                                                            -٧٩-
                          ‫א‬‫א‬                       ‫٧٤١ א‬                              ‫א‬
                     ‫א‬‫א‬‫א‬‫א‬‫א‬                ‫א‬                    


              EF٢١J ٣‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬W٦J ٣
                                                                                          K‫א‬
                                                                                                                       
                                                        ‫א‬                   ‫א‬
                                                  A      B          C         D    Y
                                                  ٠      ٠          ٠         ٠    ٠
                                                  ٠      ٠          ٠         ١    ١
                                                  ٠      ٠          ١         ٠    ٠
                                                  ٠      ٠          ١         ١    ١
                                                  ٠      ١          ٠         ٠    ٠
                                                  ٠      ١          ٠         ١    ١
                                                  ٠      ١          ١         ٠    ٠
                                                  ٠      ١          ١         ١    ١
                                                  ١      ٠          ٠         ٠    ٠
                                                  ١      ٠          ٠         ١    ٠
                                                  ١      ٠          ١         ٠    ٠
                                                  ١      ٠          ١         ١    ١
                                                  ١      ١          ٠         ٠    ٠
                                                  ١      ١          ٠         ١    ٠
                                                  ١      ١          ١         ٠    ٠
                                                  ١      ١          ١         ١    ١
                                        K‫א‬‫א‬‫א‬‫א‬EF٢١J ٣

              (Y)‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                           KEF٢١J ٣،(١)‫א‬‫א‬
                                                   W‫א‬‫א‬‫א‬‫א‬
                                                                                                                       
                      Y = A BCD + A BCD + ABCD + ABCD + A BCD + ABCD
                                                                                                            
              ،EF٢١J ٣‫א‬‫א‬‫א‬
                     K‫א‬‫א‬‫א‬(Y)‫א‬‫א‬‫א‬
                                                               

                                                               

                                                                   -٨٠-
                           ‫א‬‫א‬                          ‫٧٤١ א‬                                   ‫א‬
                      ‫א‬‫א‬‫א‬‫א‬‫א‬                   ‫א‬                       



                                                                             AD
                                                                                                                                

                                                           CD      CD        CD       CD                                        
                                                     AB     ٠        ١        ١       ٠
                                                                                                                                
                                                            ٠        ١            ١   ٠
                                                                                                                                

                                                    AB      ٠        ٠            ١   ٠                                         

                                                    AB      ٠        ٠            ١   ٠                                         

                                                                 CD                                                             

                                         K٦J ٣‫א‬EF٢١J ٣
                                                                                                     
              ‫א‬EF٢١J ٣
              ‫א‬‫א‬‫א‬‫א‬K(١'s)‫א‬
                                                         
            K AD  ‫א‬ C ‫א‬، C ‫א‬ B ‫א‬ B ‫א‬
                                                                                                        
                                   
              ‫א‬‫א‬‫א‬
                           W‫א‬‫א‬‫א‬K CD ‫א‬ A ، A ، B ، B ‫א‬‫א‬
                       Y = AD + CD
                                            Binary Adders and Subtractors ‫א‬‫א‬‫א‬‫א‬٧J ٣
              ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                       
              K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬
              ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                            The Half-Adder Circuit ‫א‬‫א‬‫א‬١J ٧J ٣
              ‫א‬‫א‬‫א‬E٣J ٣F‫א‬،‫א‬‫א‬‫א‬‫א‬
                     .[Carry (C)]‫א‬‫א‬‫א‬[Sum(S)]‫א‬‫א‬ A , B ‫א‬
                                                                                                                      
                                                                    -٨١-
                           ‫א‬‫א‬                                    ‫٧٤١ א‬                                            ‫א‬
                      ‫א‬‫א‬‫א‬‫א‬‫א‬                             ‫א‬                               


                          ‫א‬                   ‫א‬                                        
                             A           B          S            C
                             ٠           ٠          ٠            ٠     ٠+٠=٠             
                             ٠           ١          ١            ٠     ٠+١=١             
                             ١           ٠          ١            ٠     ١+٠=١             
                             ١           ١          ٠            ١     ١ + ١ = ١٠٢ or ٢١٠                ١  ٠ ‫א‬
                                                   K‫א‬‫א‬‫א‬‫א‬E٣J ٣F

              ‫א‬‫א‬K(XOR)‫א‬‫א‬‫א‬ (S )‫א‬‫א‬
                                                                  
              EF٢٢J ٣KAND‫א‬‫א‬(c)‫א‬
                                                       
            K‫א‬‫א‬‫א‬‫א‬ C, S ‫א‬‫א‬ A, B ‫א‬‫א‬‫א‬
                                                                               
                                                                                                  K‫א‬‫א‬‫א‬‫א‬
                                                                                                                                                 
                                                                                                                      A      B
                                 A
                                                                 S(sum) ‫א‬
                                 B

                                                                                                    ≡                    HA

                                                                 C(carry) ‫א‬
                                                                             

                                                     EFEF
                                                                                                                      S        C


                                                 K‫א‬‫א‬‫א‬‫א‬E٢٢J ٣F

              ‫א‬EF٢٢J ٣‫א‬‫א‬‫א‬‫א‬‫א‬
              S,C‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬EHalf AdderF HA
                                                   W‫א‬،‫א‬‫א‬
                      S = AB + A B
                                                                                                     
                      C = AB
                                                              The Full-Adder Circuit ‫א‬‫א‬‫א‬٢J ٧J ٣
              (٢-bits)‫א‬‫א‬‫א‬‫א‬
              ،‫א‬‫א‬‫א‬(carry)‫א‬‫א‬‫א‬‫א‬

                                                                                 -٨٢-
                          ‫א‬‫א‬                                   ‫٧٤١ א‬                           ‫א‬
                    ‫א‬‫א‬‫א‬‫א‬‫א‬                             ‫א‬                 


                   
            (bits)‫א‬‫א‬‫א‬
                                                          
              ‫א‬،‫א‬‫א‬‫א‬‫א‬
                                                          K‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬
              ،‫א‬(bits)‫א‬‫א‬‫א‬‫א‬‫א‬
              ‫א‬‫א‬‫א‬‫א‬‫א‬A,B‫א‬‫א‬،
              ‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬EInput carryFCin
                       KE٤J ٣F‫א‬‫א‬‫א‬‫א‬.(Sum)‫א‬ ، (Carry)
                                                                               ٍ
                                                                                                                                 
                              ‫א‬                          ‫א‬
                     A            B         Cin          S           C
                     ٠            ٠          ٠           ٠           ٠     ٠+٠+٠=٠         
                      ٠           ٠             ١         ١          ٠     ٠+٠+١=١         
                      ٠           ١             ٠         ١          ٠     ٠+١+٠=١         
                      ٠           ١             ١         ٠          ١     ٠ + ١ + ١ = ١٠٢ or ٢١٠ ١  ٠‫א‬
                      ١           ٠             ٠         ١          ٠     ١+٠+٠=١         
                      ١           ٠             ١         ٠          ١     ١ + ٠ + ١ = ١٠٢ or ٢١٠ ١  ٠ ‫א‬
                      ١           ١             ٠         ٠          ١     ١ + ١ + ٠ = ١٠٢ or ٢١٠ ١  ٠ ‫א‬
                      ١           ١             ١         ١          ١     ١ + ١ + ١ = ١١٢ or ٣١٠ ١  ١ ‫א‬
                                            K‫א‬‫א‬‫א‬‫א‬E٤J ٣F

              ‫א‬ A, B, C ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                  
                                                                       
              ‫א‬ C, S ‫א‬‫א‬K‫א‬E 2 3 = 8 F‫א‬
                             
              K‫א‬‫א‬‫א‬‫א‬‫א‬
                                                     W‫א‬ S , C ‫א‬‫א‬‫א‬‫א‬
                                                                                                                      
                     S = A BC in + ABC in + A BC in + ABC in
                     C = ABC in + A BC in + ABC in + ABC in
                                                                                                                     


                                                                            -٨٣-
                           ‫א‬‫א‬                         ‫٧٤١ א‬                                ‫א‬
                      ‫א‬‫א‬‫א‬‫א‬‫א‬                  ‫א‬                      


              ‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                         WS‫א‬‫א‬‫א‬‫א‬
                                                                                                                 
                       S = A BC in + ABC in + A BC in + ABC in
                          = (AB + A B)C in + (A B + AB)C in
                                                                                                                 
                    XNOR   A B + AB ‫א‬‫א‬،XOR AB + A B ‫א‬‫א‬
                                                 
                                                             W‫א‬‫א‬‫א‬‫א‬
                                                                                                                 
                       S = (A ⊕ B)C in + (A ⊕ B)C in
                                                                                                                            
                                               
               Cin ‫א‬ (A ⊕ B) XOR‫א‬
                                                                                   WS‫א‬‫א‬
                                                                                                                 
                       S = (A ⊕ B) ⊕ C in = A ⊕ B ⊕ C in 
                                                                                                                            
              ‫א‬ A, B ‫א‬، XOR ‫א‬‫א‬ S 
                                                                        
                                                                                                          K Cin ‫א‬
                                                   W‫א‬‫א‬ C ‫א‬
                                                                                                                 
                       C = ABC in + A BC in + ABC in + ABC in
                          = (AB + A B)C in + AB(C in + C in )
                          = (A ⊕ B)C in + AB ⇐ ( C in + C in = 1)
                                                                                                                 
              ‫א‬‫א‬‫א‬KEF٢٣J ٣‫א‬CS
 ‫א‬FA‫א‬EF٢٣J ٣‫א‬‫א‬
                                                                                    K‫א‬‫א‬ (Full Adder)
                                                                                                                 

                                                                   -٨٤-
                          ‫א‬‫א‬                               ‫٧٤١ א‬                               ‫א‬
                     ‫א‬‫א‬‫א‬‫א‬‫א‬                        ‫א‬                     



                                                                                                              A        B       Cin
                     A
                    B                                                                  S(sum)


                                                                                                    ≡                  FA


                    Cin                                                               C(carry)
                                                                                                                   S           C
                                                      EF                                                              E F
                                              K‫א‬‫א‬‫א‬‫א‬E٢٣J ٣F

                      
              ‫א‬‫א‬‫א‬EF٢٣J ٣‫א‬‫א‬
              OR‫א‬٢‫א‬‫א‬‫א‬‫א‬ OR‫א‬‫א‬
                                                                                                  KE٢٤J ٣F‫א‬
                                                                                                                           
                             Cin                             A          S                                              
                                                                                                        S
                                                                 HA
                                                       S
                                                                                                               
                             A                               B           C

                                                 HA                                                            
                                                                                                        C
                             B                          C
                                                                                                               
                                        K‫א‬‫א‬‫א‬E٢٤J ٣F
                                                                                                                                     
                                                             Half Subtractor Circuit ‫א‬‫א‬‫א‬٣J ٧J ٣
              ‫א‬‫א‬‫א‬
               
            K‫א‬‫א‬‫א‬‫א‬K
               
            K ‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
              ‫א‬‫א‬‫א‬‫א‬(bit)،‫א‬
              ،‫א‬‫א‬‫א‬K(difference)‫א‬‫א‬(bit)


                                                                        -٨٥-
                          ‫א‬‫א‬                             ‫٧٤١ א‬                              ‫א‬
                     ‫א‬‫א‬‫א‬‫א‬‫א‬                      ‫א‬                    


                                                   
              K‫א‬‫א‬(Borrowed)(١)‫א‬
                                                                  K،
              ‫א‬(٢-bits)‫א‬‫א‬‫א‬‫א‬
                                                                           
              ‫א‬A K‫א‬‫א‬(١)
                                                          
              ، A ≥ B KB, A ‫א‬(A – B)KB
              ‫א‬.(Difference bit)‫א‬‫א‬٠ – ٠ = ٠, ١ – ٠ = ١, ١ – ١ = ٠W‫א‬
                                   
              ‫א‬‫א‬‫א‬K‫א‬‫א‬(١)‫א‬‫א‬‫א‬،٠ – ١A<B
              (١٠)‫א‬،‫א‬‫א‬،‫א‬٢
                                     K٢ – ١ = ١‫א‬،(٢)‫א‬K‫א‬
              ‫א‬‫א‬ (D)‫א‬،‫א‬‫א‬
                                                                                K(B٠)‫א‬‫א‬
     ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
              ‫א‬‫א‬( B 0 )‫א‬،(D)‫א‬‫א‬KE٥J ٣F
                                                                                                                  W‫א‬
                      D = AB + A B
                      B 0 = AB

                                                          ‫א‬              ‫א‬
                                                           A       B          D      B٠
                                                           ٠       ٠          ٠      ٠
                                                           ٠       ١          ١      ١
                                                           ١       ٠          ١      ٠
                                                           ١       ١          ٠      ٠
                                                  K‫א‬‫א‬‫א‬‫א‬E٥J ٣F

              ‫א‬(S)‫א‬(D)‫א‬
                
            A ‫א‬‫א‬‫א‬(C)‫א‬( B 0 )‫א‬، XOR  ‫א‬
                                                                                                     
                                 K B ، A ‫א‬ AND ‫א‬( B 0 )‫א‬
              ‫א‬EF٢٥J ٣،‫א‬‫א‬EF٢٥J ٣
                                       K(Half Subtractor)‫א‬ HS ‫א‬،‫א‬
                                                                       -٨٦-
                          ‫א‬‫א‬                              ‫٧٤١ א‬                           ‫א‬
                     ‫א‬‫א‬‫א‬‫א‬‫א‬                     ‫א‬                   

                                                                                                   A     B
                               A                                                                                  
                                                           D(difference) ‫א‬
                              B
                                                                                                                      
                                                                                              ≡        HS

                                                           B٠(borrow) ‫א‬                                        

                                                                                                                      
                                                                                                   D         B٠
                                                 K‫א‬‫א‬‫א‬‫ א‬E٢٥J ٣F 
                                                                                                                           

                                                      The Full-Subtractor Circuit ‫א‬‫א‬‫א‬٤J ٧J ٣
              ‫א‬‫א‬ (٢-bits)‫א‬‫א‬‫א‬‫א‬‫א‬
                          
                                                                             
              ‫א‬‫א‬K‫א‬‫א‬K‫א‬‫א‬(١)
                                              
              ‫א‬K‫א‬( B i n ) ‫א‬‫א‬(B)‫א‬(A)‫א‬ A, B, B in
                        KE٦J ٣F‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬ D, B 0
                                                                                                                  

                                                            ‫א‬                     ‫א‬
                                                       A      B        Bin         D          B٠
                                                       ٠      ٠         ٠          ٠          ٠
                                                       ٠      ٠         ١          ١          ١
                                                       ٠      ١         ٠          ١          ١
                                                       ٠      ١         ١          ٠          ١
                                                       ١      ٠         ٠          ١          ٠
                                                       ١      ٠         ١          ٠          ٠
                                                       ١      ١         ٠          ٠          ٠
                                                       ١      ١         ١          ١          ١
                                            K‫א‬‫א‬‫א‬‫א‬E٦J ٣F

              ‫א‬ 0's,1's ‫א‬‫א‬‫א‬‫א‬‫א‬
                                                            
            K A − B − B in ‫א‬‫א‬‫א‬ 0's,1's K‫א‬‫א‬
                                                                                            
              K‫א‬‫א‬‫א‬‫א‬ B in = 0 ‫א‬‫א‬
                                                                                          
              (٢) B 0 = 1‫א‬‫א‬‫א‬(١) A = 0, B = 0, B in = 1
                                                                   K D = 1 ،٢ – ٠ – ١ = ١،A
                                                                       -٨٧-
                           ‫א‬‫א‬                             ‫٧٤١ א‬                                 ‫א‬
                      ‫א‬‫א‬‫א‬‫א‬‫א‬                      ‫א‬                       


              ‫א‬‫א‬‫א‬(١) A = 0, B = 1, B in = 1 
                                                           K D = 0 ،٢ – ١ – ١ = ٠،A = ٢، B 0 = 1
          K D = 0 ، B 0 = 0 ‫א‬A – B – Bin = ٠، A = 1, B = 0, B in = 1 
              ‫א‬‫א‬‫א‬(١) A = 1, B = 1, B in = 1 ‫א‬
                                                                 K D = 1 ،٣ – ١ – ١ = ١،A=٣، B 0 = 1
                                                   W‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                                                                                 
                       D = ABB in + ABBin + AB Bin + ABBin
                                                                                                                                 
              ‫א‬‫א‬،‫א‬‫א‬(S)
                                                                                                                      W‫א‬
                      D = (A ⊕ B) ⊕ Bin = A ⊕ B ⊕ Bin



                                                              W‫א‬‫א‬،(B٠)‫א‬
                                                                                                                                 
                      B 0 = ABB in + ABBin + ABB in + ABBin
                                                                                                                                 
                            = B in ( AB + AB) + AB( Bin + B in )
                                                                                                                                 
                      B 0 = B in (A ⊕ B) + AB ⇐ ( Bin + B in = 1)
                      
              ‫א‬‫א‬‫א‬‫א‬،EF٢٦J ٣(B٠), (D)‫א‬
              (Full Subtractor)‫א‬FS‫א‬،EF٢٦J ٣‫א‬
                                                                                                         K‫א‬‫א‬
              ‫א‬‫א‬‫א‬EF٢٦J ٣‫א‬‫א‬‫א‬

              ‫א‬٢‫א‬‫א‬‫א‬‫א‬،OR‫א‬‫א‬

                                                                                          KE٢٧J ٣F‫א‬OR




                                                                       -٨٨-
                               ‫א‬‫א‬                                ‫٧٤١ א‬                      ‫א‬
                          ‫א‬‫א‬‫א‬‫א‬‫א‬                      ‫א‬               


                                                                                                              A           B      Bin
                    A
                    B                                                                    D


                                                                                                  ≡                       FS


                    Bin                                                                      B٠
                                                                                                               D                 B٠
                                                            EF                                                           E F
                                                       K‫א‬‫א‬‫א‬‫א‬E٢٦J ٣F
        
                                                                                                                                  
                                   Bin                             A            D
                                                                                                     D
                                                                       HS
                                                                                                                                  
                                                           D       B                B٠
                                  A
                                                                                                                                  
                                                      HS
                                                                  B٠                                 B٠
                                   B                                                                                  

                                             K‫א‬‫א‬‫א‬E٢٧J ٣F                            
                                                                                                                  
                                                                            
                                                                            
                                                                            
                                                                            
                                                                            
                                                                            
                                                                            
                                                                            


                                                                                -٨٩-
                         ‫א‬‫א‬                          ‫٧٤١ א‬                             ‫א‬
                    ‫א‬‫א‬‫א‬‫א‬‫א‬                ‫א‬                      



                                                         
                                                                 
                                                          W‫א‬‫א‬‫א‬E١
                    a) AB(C + D )                                   b) AB(CD + EF)

                    c) (A + B + C + D ) + ABCD                               d) (A + B + C + D) (AB C D)
                                                                                                                        
                                     WNAND‫א‬‫א‬‫א‬‫א‬‫א‬E٢
                    a) ABCD + DE                           b) ABC + AB + D
                    c) AB C + D + E                        d) ABC + ABC + ABC + ABC

                                         WNOR‫א‬‫א‬‫א‬‫א‬‫א‬E٣
                                                
                    a) (A + B + C) (A + B)                    b) ABC + (D + E )

                    c) (AB + C) (DE + F)                                     d) (A + B) + ( C + D)
                                                                                                                        
                         W‫א‬‫א‬‫א‬‫א‬‫א‬E٤
                                                                                                                        
                                                        ‫א‬               ‫א‬
                                                    A      B            C      Y
                                                    ٠       ٠           ٠       ١
                                                    ٠       ٠           ١       ١
                                                    ٠       ١           ٠       ٠
                                                    ٠       ١           ١       ٠
                                                    ١       ٠           ٠       ١
                                                    ١       ٠           ١       ٠
                                                    ١       ١           ٠       ١
                                                    ١       ١           ١       ١
                                                                 

                                                                     -٩٠-
                             ‫א‬‫א‬                         ‫٧٤١ א‬                            ‫א‬
                        ‫א‬‫א‬‫א‬‫א‬‫א‬                  ‫א‬                  


                                                     W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E٥
                                                                                                                          
                         a) F1 = AB C D + ABCD + ABCD + ABC D + ABC D + ABCD
                                                                                                                          
                         b) F2 = ABCD + ABC D + AB C D + ABC D + ABCD + ABCD + ABCD
                                                                                                                          
                         c) F3 = ABC D + ABC D + ABC D + ABC D + AB C D
                                                                                                                          
                         d) F4 = AB C D + + AB C D + ABC D + ABC D + ABCD + ABCD + AB C D + ABCD
                                                                                              
              (١ or ٠)‫א‬‫א‬،E٢٣J ٣F‫א‬‫א‬‫א‬‫א‬E٦
                                                                                             W‫א‬‫א‬
                         a) A = ١, B = ١, Cin = ١                      b) A = ٠, B = ١, Cin = ١
                         c) A = ٠, B = ١, Cin = ٠                      d) A = ١, B = ١, Cin = ٠

                     W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ E٧
                         a) S = ٠, Cout = ٠                            b) S = ١, Cout = ٠
                         c) S = ١, Cout = ١                            d) S = ٠, Cout = ١

              (١ or ٠)‫א‬‫א‬،E٢٦J ٣F‫א‬‫א‬‫א‬‫א‬E٨
                                                                                             W‫א‬‫א‬
                      a) A = ١, B = ١, Bin = ١                         b) A = ١, B = ٠, Bin = ١
                      c) A = ١, B = ١, Bin = ٠                         d) A = ٠, B = ١, Bin = ١

                                                                                                                          

                                                                                                                          
                                                                                                                          




                                                                     -٩١-
                                                     ‫א‬‫א‬‫א‬
                                                  ã¹]<gè…‚jÖ]æ<ËÖ]<Üé×Ãj×Ö<íÚ^ÃÖ]<퉉ö¹]
                                                        ‫א‬‫א‬‫א‬‫א‬




                                  ‫א‬
                             ‫א‬‫א‬‫א‬‫א‬
 ‫א‬‫א‬‫א‬‫א‬




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      ‫א‬‫א‬‫א‬                        ‫٧٤١ א‬                            ‫א‬
    ‫א‬‫א‬‫א‬‫א‬                ‫א‬                  



                                   ‫א‬‫א‬‫א‬
                                            
                                                 W‫א‬‫א‬
                K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ •
                  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ •
                  K‫א‬‫א‬‫א‬J ‫א‬‫א‬‫א‬‫א‬ •
                                           K‫א‬‫א‬‫א‬‫א‬ •
                                           K‫א‬٥٥٥‫א‬‫א‬ •
                                                       K‫א‬‫א‬‫א‬‫א‬‫א‬ •
         K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ •
                                     K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ •
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           ‫א‬‫א‬‫א‬                           ‫٧٤١ א‬                                  ‫א‬
        ‫א‬‫א‬‫א‬‫א‬                    ‫א‬                       



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                                               ‫א‬‫א‬
                                                                                    Introduction١J ٤
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬
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‫א‬‫א‬‫א‬‫א‬(Combinational Logic Circuits)
‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬
‫א‬‫א‬‫א‬‫א‬ (Sequential Logic Circuits) ‫א‬‫א‬‫א‬‫א‬
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‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬(Memory)‫א‬
                                                                                                     K‫א‬
‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬ ،(Flip-Flop Circuit)‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬(٠)‫א‬‫א‬‫א‬
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‫א‬،(١)‫א‬(١)‫א‬‫א‬‫א‬‫א‬K(١)
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‫א‬‫א‬‫א‬‫א‬K(٠)‫א‬(٠)‫א‬‫א‬
‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬.(Bistable Multivibrator)‫א‬‫א‬‫א‬‫א‬‫א‬
K(Digital Integrated Circuits)‫א‬‫א‬NOR‫א‬NAND
‫א‬‫א‬‫א‬،(Timers)‫א‬‫א‬‫א‬‫א‬‫א‬
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‫א‬‫א‬‫א‬ (Shift Registers)‫א‬‫א‬،(Counters)
                                                                                     K‫א‬
                                                                  Latches‫א‬٢J ٤
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‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
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‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬
                                                                   
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬
                                                                                            K‫א‬‫א‬

                                                      -٩٣-
           ‫א‬‫א‬‫א‬                            ‫٧٤١ א‬                             ‫א‬
         ‫א‬‫א‬‫א‬‫א‬                    ‫א‬                  



K(Bistable Multivibrator)‫א‬‫א‬‫א‬‫א‬‫א‬(Latch)‫א‬
 S-R‫א‬‫א‬‫א‬‫א‬‫א‬E١J ٤F
 (Set Input)"١"‫א‬‫א‬‫א‬S 
 (Reset Input)"٠"‫א‬‫א‬‫א‬R
 K‫א‬ Q ‫א‬Q
                                                                                                 
                                     SET
                                    INPUT       S      Q             Q output


                                    RESET       R      Q             Q output
                                    INPUT
                           
                     KS-R‫א‬‫א‬‫א‬‫א‬‫א‬E١J ٤F
                                                                                                     


   Q =١,  Q =٠(Set Condition)‫א‬‫א‬
 ‫א‬ .Q =٠, Q = ١(Reset Condition)
 ‫א‬‫א‬(١)‫א‬S‫א‬‫א‬
 ‫א‬‫א‬‫א‬،‫א‬ Q‫א‬E‫א‬‫א‬FQ = ١
                          
 ‫א‬E‫א‬‫א‬F Q = ٠‫א‬R‫א‬‫א‬K Q = ٠
 (١)‫א‬‫א‬S,R‫א‬، Q = ١‫א‬
 ،(unpredictable)‫א‬‫א‬
                                                                                 K‫א‬‫א‬‫א‬
 ‫א‬‫א‬‫א‬‫א‬ NOR‫א‬S-R‫א‬‫א‬
                       KE٢J ٤F‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                                                     


                                            S
                                                                        Q




                                                                        Q
                                            R
                                       
                         K‫א‬‫א‬‫א‬S-R‫א‬‫א‬E٢J ٤F
                                                       -٩٤-
                   ‫א‬‫א‬‫א‬                                    ‫٧٤١ א‬                                           ‫א‬
                ‫א‬‫א‬‫א‬‫א‬                             ‫א‬                               



     ‫א‬‫א‬F(١)NOR‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                                     
     ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،E‫א‬
                                                    
 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،E١J ٤F
                                                                                                           K(Active High Inputs)
                                                                                                                                 
                                            ‫א‬          ‫א‬                   ‫א‬
                                           S     R           Q             (Mode of Operation)
                                                                            E‫א‬F‫א‬
                                           ٠        ٠        Q٠
                                                                                  No Change
                                                                                ‫א‬‫א‬
                                           ٠        ١         ٠
                                                                               Latch RESETS
                                                                                   ‫א‬‫א‬
                                           ١        ٠         ١
                                                                                 Latch SETS
                                                                        ‫א‬
                                           ١        ١         ?
                                                                              Invalid condition
                         K‫א‬‫א‬‫א‬S-R‫א‬‫א‬‫א‬E١J ٤F
                                                                                                                                          
                                                               W‫א‬‫א‬‫א‬
     ‫א‬‫א‬ S,R‫א‬(٠)‫א‬‫א‬ -١
     ‫א‬‫א‬‫א‬E‫א‬‫א‬‫א‬F(Q)‫א‬
                                                                                                                  K‫א‬
     Q‫א‬‫א‬(١)(٠)R‫א‬‫א‬‫א‬ -٢
    ‫א‬‫א‬،‫א‬‫א‬‫א‬ E‫א‬‫א‬FQ = ٠ (٠)
                                                                                KQ = ٠
     ‫א‬‫א‬‫א‬(١)(٠)S ‫א‬‫א‬‫א‬ -٣
     ‫א‬،‫א‬‫א‬‫א‬E‫א‬‫א‬FQ = ١(١)(٠)Q
                                                                          KQ = ١‫א‬
     ‫א‬‫א‬‫א‬S,R‫א‬(١)‫א‬‫א‬ -٤
     ‫א‬‫א‬‫א‬‫א‬،NOR‫א‬‫א‬
                                                                                                                          K‫א‬


                                                                        -٩٥-
           ‫א‬‫א‬‫א‬                             ‫٧٤١ א‬                                 ‫א‬
        ‫א‬‫א‬‫א‬‫א‬                      ‫א‬                    



‫א‬‫א‬‫א‬‫א‬‫א‬ -٥
،‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬
                                                         K‫א‬
‫א‬‫א‬‫א‬E٣J ٤FNAND‫א‬‫א‬‫א‬
                                                                    
E٢J ٤F‫א‬‫א‬‫א‬‫א‬‫א‬(٠)NAND‫א‬
  K(Active Low Inputs)‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                                                               
                                             S
                                                                        Q
                                                                                                               

                                                                                            
                                                                        Q
                                             R                                             
                     K‫א‬‫א‬‫א‬S-R‫א‬‫א‬E٣J ٤F
                                                                                                     

                                   ‫א‬    ‫א‬              ‫א‬
                                   S    R     Q            (Mode of Operation)
                                                        ‫א‬
                                   ٠    ٠        ?
                                                              Invalid condition
                                                                   ‫א‬‫א‬
                                   ٠    ١        ١
                                                                 Latch SETS
                                                                ‫א‬‫א‬
                                   ١    ٠        ٠
                                                               Latch RESETS
                                                            E‫א‬F‫א‬
                                   ١    ١     Q٠
                                                                  No Change
              K‫א‬‫א‬‫א‬S-R‫א‬‫א‬‫א‬E٢J ٤F

                                             W‫א‬‫א‬‫א‬
Q‫א‬‫א‬‫א‬‫א‬‫א‬(١)‫א‬‫א‬ -١
                                                                             KE‫א‬‫א‬F
‫א‬‫א‬ R = ١‫א‬، S = ٠‫א‬‫א‬‫א‬ -٢
Q = ١‫א‬‫א‬،‫א‬‫א‬‫א‬ (١)
                                                                                        K
                                                        -٩٦-
         ‫א‬‫א‬‫א‬                                         ‫٧٤١ א‬                                         ‫א‬
       ‫א‬‫א‬‫א‬‫א‬                                 ‫א‬                               



‫א‬‫א‬ R = ٠‫א‬، S = ١ ‫א‬‫א‬‫א‬ -٣
Q = ٠‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬،(٠)
                                                                                                                        K
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬(٠)‫א‬ -٤
                                                      K‫א‬NAND
                     
‫א‬‫א‬‫א‬‫א‬‫א‬(Logic Symbol)‫א‬‫א‬E٤J ٤F‫א‬
                                                                  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                                                                         
                                                                                                                         
                             S        Q             Q                       S              S         Q       Q



                             R         Q             Q                      R             R          Q        Q
             
                               EFEF
       K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E٤J ٤F
                                             
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
، S = 0, R = 0 K(Q)‫א‬ S, R 
                                                                  
                                                                         K‫א‬‫א‬
‫א‬KE٥J ٤F S, R ‫א‬‫א‬W١J ٤
      KQ = ٠‫א‬Q‫א‬‫א‬‫א‬(Q)‫א‬
                                                                                                                              W‫א‬
                         S


                         R



                         Q
                  
                              K‫א‬‫א‬‫א‬‫א‬E٥J ٤F

                                                                  -٩٧-
           ‫א‬‫א‬‫א‬                                  ‫٧٤١ א‬                                        ‫א‬
         ‫א‬‫א‬‫א‬‫א‬                          ‫א‬                            



                                                    Clocked S-R Flip–Flop ‫א‬‫א‬S-R‫א‬٣J ٤
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ S − R S-R‫א‬
‫א‬‫א‬‫א‬‫א‬(Q)‫א‬‫א‬
 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬
E‫א‬F‫א‬‫א‬‫א‬‫א‬‫א‬
 
 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬S-R‫א‬‫א‬،‫א‬‫א‬
                                                                          
                                                                                                                       
                                                                                                                   K‫א‬
‫א‬‫א‬‫א‬
،(CK)‫א‬‫א‬(Clock Pulse)‫א‬‫א‬‫א‬
                                                      K‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬S-R‫א‬‫א‬E٦J ٤F
                                                                                       K(CK)‫א‬‫א‬‫א‬
                                                                                                                    
                                    S               Q                         S                   Q
                                    CK                                       CK
                                    R                Q                        R                    Q
                   
                                          EFEF
                          K‫א‬‫א‬S-R‫א‬‫א‬E٦J ٤F
‫א‬‫א‬‫א‬EF٦J ٤‫א‬
                                                                   
‫א‬(Positive Edge Trigger)‫א‬‫א‬S-R‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬EF٦J ٤‫א‬،(١)(٠)‫א‬
‫א‬ (Negative Edge Trigger)‫א‬‫א‬‫א‬
                                                                                             K(٠)(١)‫א‬
‫א‬،NAND‫א‬‫א‬‫א‬‫א‬S-R‫א‬‫א‬E٧J ٤F
                                            
‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬ NAND

                                                             -٩٨-
           ‫א‬‫א‬‫א‬                                      ‫٧٤١ א‬                                               ‫א‬
        ‫א‬‫א‬‫א‬‫א‬                               ‫א‬                                 



                             
‫א‬‫א‬‫א‬‫א‬(Q)‫א‬S,R‫א‬
                                                                                         K‫א‬‫א‬‫א‬
                                       S                  
                                                                                           Q

                                     CK                   

                                                                                           Q
                                      R
                               K‫א‬‫א‬S-R‫א‬‫א‬E٧J ٤F

             W‫א‬‫א‬‫א‬‫א‬S-R‫א‬E٣J ٤F‫א‬
(٠)‫א‬‫א‬S,R‫א‬‫א‬،‫א‬CK‫א‬‫א‬ J ١
           K‫א‬‫א‬‫א‬‫א‬‫א‬
(٠)‫א‬‫א‬(S = ٠,R = ١)‫א‬R‫א‬‫א‬ J ٢
                                                                  
             .(Reset)‫א‬‫א‬‫א‬(٠) ‫א‬(١)
(٠)‫א‬‫א‬(S = ١,R = ٠)‫א‬‫א‬S‫א‬‫א‬ J ٣
                                           .(Set)‫א‬‫א‬‫א‬Q = ١‫א‬(١)
 
‫א‬S = ١, R = ١‫א‬‫א‬
                                                                                                 K‫א‬
                                      ‫א‬             ‫א‬                ‫א‬
                                    S   R    CK           Q          (Mode of Operation)
                                                                      E‫א‬F‫א‬
                                    ٠      ٠      X      Q٠
                                                                            No Change
                                                                          ‫א‬‫א‬
                                    ٠      ١              ٠
                                                                         Latch RESETS
                                                                             ‫א‬‫א‬
                                    ١      ٠              ١
                                                                           Latch SETS
                                                                  ‫א‬
                                    ١      ١               ?
                                                                        Invalid condition
                                    ↑Z(١)‫א‬(٠)‫א‬                                          
                                XZ               
                              Q٠Z‫א‬‫א‬‫א‬
                    K‫א‬‫א‬S-R‫א‬‫א‬‫א‬E٣J ٤F
                                                                 -٩٩-
         ‫א‬‫א‬‫א‬                          ‫٧٤١ א‬                           ‫א‬
       ‫א‬‫א‬‫א‬‫א‬                  ‫א‬                 



‫א‬]‫א‬‫א‬‫א‬ S-R‫א‬‫א‬
‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬[(٠)(١)
                                                                        K(٠)(١)‫א‬‫א‬
‫א‬،E٦J ٤F‫א‬S-R‫א‬‫א‬ (Q)‫א‬‫א‬W٢J ٤
‫א‬‫א‬‫א‬KE٧J ٤FS,R,CK‫א‬
                                                        K‫א‬‫א‬Q = ٠
                                                                                                       
                                      ١    ٢       ٣         ٤     ٥      ٦              
                              CK

                                                                                        
                                  S                                                     

                                  R                                                     

                                  Q                                                     

                      K‫א‬‫א‬S-R‫א‬‫א‬‫א‬‫א‬E٧J ٤F

                                                                                               W‫א‬
            KQ = ٠(Q)‫א‬،S = ٠, R = ٠‫א‬‫א‬‫א‬ -١
                        K(Reset)Q = ٠‫א‬،S = ٠, R = ١‫א‬‫א‬‫א‬ -٢
   K(Set)Q = ١(١)Q ‫א‬،S = ١, R = ٠‫א‬‫א‬‫א‬ -٣
                    .(Reset)Q = ٠‫א‬،S = ٠, R = ١‫א‬‫א‬‫א‬‫א‬ -٤
                      K(Set)Q =١‫א‬،S = ١, R = ٠‫א‬‫א‬‫א‬ -٥
       KQ = ١ (١)‫א‬،S = ١, R = ٠ ‫א‬‫א‬‫א‬ -٦
                                                                                                 
                                                                                                 
                                                                                                 


                                                  -١٠٠-
           ‫א‬‫א‬‫א‬                                         ‫٧٤١ א‬                                                  ‫א‬
         ‫א‬‫א‬‫א‬‫א‬                                 ‫א‬                                     



                                             D-Type Flip-FlopD ‫א‬‫א‬‫א‬٤J ٤
(Single Bit)‫א‬‫א‬‫א‬D‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬S-R‫א‬‫א‬‫א‬K(١٠)‫א‬
                                                                                         KE٨J ٤FD
                                                                                                                                      
                                                 D              S                        Q

                                                                CK

                                                                R                         Q
                                         
                                       KD‫א‬‫א‬‫א‬E٨J ٤F
                                                                                                                                      
‫א‬‫א‬D‫א‬‫א‬D‫א‬‫א‬‫א‬
‫א‬،CK‫א‬‫א‬‫א‬(١)‫א‬‫א‬D‫א‬KCK
R = ٠‫א‬،S = ١‫א‬‫א‬،[Set](١)‫א‬‫א‬‫א‬
‫א‬KQ = ١‫א‬E٣J ٤F‫א‬‫א‬S-R‫א‬‫א‬‫א‬
‫א‬‫א‬،CK‫א‬‫א‬‫א‬(٠)‫א‬‫א‬D
R = ١ ‫א‬،S = ٠‫א‬‫א‬،[Reset](٠)‫א‬‫א‬
‫א‬(١)(Set)‫א‬‫א‬KQ = ٠‫א‬E٣J ٤F
                                     K‫א‬‫א‬(٠)(٠)‫א‬‫א‬،‫א‬
‫א‬‫א‬‫א‬‫א‬D‫א‬‫א‬‫א‬‫א‬‫א‬
                                       KE٤J ٤F‫א‬(Positive Edge Trigger) ‫א‬‫א‬
                                                                                                                                      
                                       ‫א‬             ‫א‬               ‫א‬
                                      D    CK              Q             (Mode of Operation)
                                                                           ‫א‬‫א‬(SET)
                                      ١                     ١
                                                                                 (stores a ١)
                                                                      ‫א‬‫א‬(RESET)
                                      ٠                     ٠
                                                                                 (stores a ٠)
                                       ↑Z(١)‫א‬(٠)‫א‬


                                                                    -١٠١-
             ‫א‬‫א‬‫א‬                         ‫٧٤١ א‬                               ‫א‬
           ‫א‬‫א‬‫א‬‫א‬                 ‫א‬                     



                              K‫א‬‫א‬D ‫א‬‫א‬‫א‬E٣J ٤F
                
‫א‬K‫א‬‫א‬(D)‫א‬(Q)‫א‬‫א‬
   (D)‫א‬‫א‬‫א‬D‫א‬‫א‬E٩J ٤F
                                            
   E١٠J ٤F‫א‬K‫א‬‫א‬‫א‬(CK) ‫א‬‫א‬
                                                                     KNAND‫א‬D‫א‬‫א‬
                                                    
                                                              S                                         
                                              D
                                                                                                  Q     
                    D                 Q                    CK
                                                                                                        
                                                                                                        
                   CK
                                                                                                  Q     
                                      Q                       R


   KD‫א‬‫א‬E٩J ٤FKNAND‫א‬D‫א‬‫א‬E١٠J ٤F
                                                                                                              
   ‫א‬E٩J ٤F‫א‬D‫א‬‫א‬‫א‬EQF‫א‬‫א‬W٣J ٤
          
   Q = ٠ ‫א‬‫א‬‫א‬KE١١J ٤FEDF‫א‬
                                                                               K‫א‬
                                                                                                       W‫א‬

                                      CK
                                                    
                                          D
                                                    
                                          Q
                                                    

                          KD‫א‬‫א‬‫א‬‫א‬‫א‬E١١J ٤F

   ‫א‬(١)(٠)‫א‬‫א‬‫א‬‫א‬(D)‫א‬(Q)‫א‬
                                                                                                    K‫א‬


                                                     -١٠٢-
          ‫א‬‫א‬‫א‬                         ‫٧٤١ א‬                                  ‫א‬
        ‫א‬‫א‬‫א‬‫א‬                 ‫א‬                        



                                                      J-K Flip Flop‫א‬‫א‬J-K‫א‬٥J ٤
‫א‬‫א‬J,K‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬J-K‫א‬‫א‬
                                  
‫א‬S-R‫א‬‫א‬‫א‬،‫א‬
‫א‬‫א‬‫א‬S-R‫א‬J-K‫א‬K‫א‬
J-K‫א‬‫א‬.(Reset)‫א‬‫א‬(Set)‫א‬‫א‬‫א‬‫א‬
                                                     KS-R‫א‬‫א‬
K‫א‬‫א‬‫א‬‫א‬J-K‫א‬‫א‬E١٢J ٤F‫א‬
                                                                                              
‫א‬‫א‬‫א‬S-R‫א‬‫א‬‫א‬
                       K‫א‬‫א‬(١)‫א‬‫א‬J,K‫א‬‫א‬‫א‬
                                                                                                   
                                                                                                         

         J                                                                                               
                                                          Q
                                                                             J                    Q
                  CK                                                                                      
                                                                                 CK

                                                          Q                  K                    Q       
         K
                                                                                                          

                       K‫א‬‫א‬‫א‬‫א‬J-K‫א‬‫א‬E١٢J ٤F

‫א‬SR‫א‬‫א‬‫א‬‫א‬‫א‬E١٢J ٤F
                                                                  K‫א‬ Q ،Q
‫א‬‫א‬‫א‬J-K‫א‬E٥J ٤F‫א‬
‫א‬‫א‬‫א‬‫א‬، (٠)J,K‫א‬
‫א‬،‫א‬‫א‬J = ٠, K = ١‫א‬‫א‬(٠)‫א‬(Reset)‫א‬
J = ١, K = ٠ ‫א‬‫א‬J-K(Set)‫א‬‫א‬‫א‬‫א‬
،(Toggle)‫א‬J-K‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬
                                                                                      
‫א‬‫א‬Q‫א‬(١)‫א‬‫א‬J,K‫א‬
                                                                           
                                                           KCK‫א‬‫א‬‫א‬
                                                  -١٠٣-
         ‫א‬‫א‬‫א‬                                ‫٧٤١ א‬                                ‫א‬
      ‫א‬‫א‬‫א‬‫א‬                         ‫א‬                      



                                                                                                       
                                   ‫א‬           ‫א‬                 ‫א‬
                                 J   K CK            Q         (Mode of Operation)
                                                                E‫א‬F‫א‬
                              ٠      ٠               Q٠
                                                                         No Change
                                                                      ‫א‬‫א‬
                              ٠      ١               ٠
                                                                          (RESET)
                                                                         ‫א‬‫א‬
                              ١      ٠               ١
                                                                            (SET)
                                                                         ‫א‬
                              ١      ١               Q0
                                                                           Toggle
                            ↓Z(٠)‫א‬(١)‫א‬
                            Q٠Z‫א‬‫א‬‫א‬
                            K‫א‬‫א‬J-K‫א‬E٥J ٤F

                                           
‫א‬E١٢J ٤F‫א‬J-K‫א‬‫א‬(Q)‫א‬‫א‬W٤J ٤
‫א‬‫א‬KE١٣J ٤FCKJ-K‫א‬
                                                                         K‫א‬Q = ٠
                                                                                                            W‫א‬
                                                                                                                  
                                  CK         ١                                   ٥
                                                      ٢           ٣       ٤

                                     J

                                     K


                                     Q
                             
                    K‫א‬‫א‬J-K‫א‬‫א‬‫א‬‫א‬E١٣J ٤F

Q ‫א‬‫א‬‫א‬(١)J,K،‫א‬‫א‬‫א‬ -١
                                                                                     K(١)‫א‬
  KJ = K = ٠‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ -٢
     KQ = ٠(Reset)J = ٠, K = ١،‫א‬‫א‬ -٣
                                                          -١٠٤-
           ‫א‬‫א‬‫א‬                                       ‫٧٤١ א‬                                             ‫א‬
         ‫א‬‫א‬‫א‬‫א‬                               ‫א‬                               



             KQ = ١(Set)J = ١, K = ٠،‫א‬‫א‬‫א‬ -٤
Q‫א‬J,K‫א‬‫א‬‫א‬ (Set)‫٥- א‬
                                                                                                                 K(١)‫א‬
                                                    T-Type Flip-Flop T ‫א‬‫א‬‫א‬٦J ٤
‫א‬‫א‬J-K‫א‬‫א‬T‫א‬‫א‬‫א‬
‫א‬‫א‬،E١٤J ٤F‫א‬J,K‫א‬
(Toggle)‫א‬T‫א‬K‫א‬‫א‬T‫א‬‫א‬T
                                                                                           K‫א‬‫א‬
،‫א‬‫א‬CK‫א‬(١)‫א‬(T)‫א‬
‫א‬‫א‬‫א‬‫א‬CK‫א‬‫א‬‫א‬‫א‬‫א‬
 KE١٤J ٤FCK‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                                                                                 
                                                                                                                                 
                                               T                J                  Q

                                                           CK
                                                                K                  Q
                                         
                      KT‫א‬‫א‬‫א‬‫א‬‫א‬E١٤J ٤F

                                              KE٦J ٤FT‫א‬‫א‬‫א‬‫א‬

                                        ‫א‬          ‫א‬            ‫א‬
                                       T    CK           Q      (Mode of Operation)
                                                                 E‫א‬F‫א‬
                                    ٠                Q٠
                                                                       No Change
                                                                        ‫א‬
                                    ١               Q0
                                                                          Toggle
                                 ↓Z(٠)‫א‬(١)‫א‬                                            
                                    Q٠Z‫א‬‫א‬‫א‬    
                                KT‫א‬‫א‬E٥J ٤F


                                                                 -١٠٥-
          ‫א‬‫א‬‫א‬                        ‫٧٤١ א‬                               ‫א‬
        ‫א‬‫א‬‫א‬‫א‬                ‫א‬                     



‫א‬E١٤J ٤F‫א‬(T)‫א‬‫א‬‫א‬Q‫א‬‫א‬W٥J ٤
‫א‬‫א‬E١٥J ٤FCK‫א‬T‫א‬
                                                                 K‫א‬Q = ٠ 
                                                                                                    W‫א‬
                                                

                               CK                                                          

                                   T                                                       
                                   Q                                                       
                                                                                           
                        KT‫א‬‫א‬‫א‬‫א‬‫א‬E١٥J ٤F
،‫א‬‫א‬‫א‬T = ١‫א‬Q‫א‬‫א‬
T = ١‫א‬‫א‬،Q = ٠QT = ٠‫א‬‫א‬‫א‬
                                                                      K‫א‬(١)(٠)Q‫א‬
                                                Master-Slave Flip-Flop‫א‬–‫א‬٧J ٤
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                        K(Edge Triggered)‫א‬‫א‬‫א‬‫א‬‫א‬
                       
‫א‬‫א‬‫א‬‫א‬‫א‬
                       
‫א‬‫א‬،(Master-Slave)‫א‬–‫א‬‫א‬(Pulse Triggered)
‫א‬(Complete Clock Pulse)‫א‬‫א‬‫א‬
                                                                                     K‫א‬‫א‬
                                     
‫א‬،‫א‬J ‫א‬‫א‬S-R‫א‬EF١٦J ٤
(Master)‫א‬‫א‬،(Slave)‫א‬(Master)‫א‬‫א‬‫א‬S-R
(Slave)‫א‬‫א‬، (CK)‫א‬‫א‬‫א‬‫א‬
                                                                            K( CK )‫א‬‫א‬
                                                                                               


                                                 -١٠٦-
          ‫א‬‫א‬‫א‬                              ‫٧٤١ א‬                             ‫א‬
        ‫א‬‫א‬‫א‬‫א‬                      ‫א‬                   



                                          Master                           Slave                       
                 S
                                                          Y
                                                                                                       
                                                                                             Q
               CK
                                                                                                       
                                                                      CK
                                                                                              Q        
                                                           Y
                                                                                                       
                 R
                                                                                                       
                                                                                                       
                             K‫א‬J ‫א‬S-R‫א‬‫א‬EF١٦J ٤
                                                                                                   
،EF١٦J ٤CK، CK  ‫א‬‫א‬
                                        
‫א‬‫א‬،(CK)‫א‬‫א‬‫א‬‫א‬ (Master)‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬(Slave)
                                                                K( CK )‫א‬‫א‬‫א‬
                WS,R‫א‬Q، Q 
(Master)‫א‬‫א‬(CK)(High)‫א‬‫א‬W‫א‬‫א‬
                                                                               
(Reset)‫א‬‫א‬ (Set)‫א‬‫א‬‫א‬ (Enabled)‫א‬
                                                        KS,R‫א‬‫א‬
 (slave) ‫א‬‫א‬(CK)(Low)‫א‬‫א‬W‫א‬‫א‬
                                                                                
                                    KY‫א‬‫א‬‫א‬‫א‬Q‫א‬(Enabled)‫א‬
S-R‫א‬‫א‬‫א‬EF١٦J ٤‫א‬‫א‬
         
K‫א‬‫א‬S-R‫א‬‫א‬‫א‬‫א‬K‫א‬J ‫א‬
                                                                       
                                               
‫א‬‫א‬‫א‬‫א‬‫א‬(CK)‫א‬
                                             K‫א‬‫א‬(Low)‫א‬(High)
                            
،‫א‬J ‫א‬S-R‫א‬‫א‬‫א‬EF١٦J ٤
‫א‬‫א‬‫א‬t٥t٠‫א‬(CK)‫א‬‫א‬
                                                                                                        KS,R


                                                       -١٠٧-
          ‫א‬‫א‬‫א‬                              ‫٧٤١ א‬                              ‫א‬
        ‫א‬‫א‬‫א‬‫א‬                    ‫א‬                      



‫א‬‫א‬(Enabled)‫א‬ (Master)‫א‬‫א‬،t٠‫א‬ •
‫א‬(Set)‫א‬‫א‬ S = ١, R = ٠‫א‬(CK)‫א‬‫א‬(High)
                                                                    K( Y = 0 )Y = ١‫א‬،‫א‬
(Low)‫א‬‫א‬(Disabled)‫א‬‫א‬،t١‫א‬                •
‫א‬(Enabled)‫א‬(Slave)‫א‬‫א‬،CK
                      
Q‫א‬،‫א‬‫א‬‫א‬ Y, Y K CK (High)‫א‬
‫א‬‫א‬‫א‬‫א‬KQ = ١(Set )‫א‬‫א‬
                                                                        
F‫א‬‫א‬‫א‬
KE CK = 1‫א‬‫א‬ Q = 1, Q = 0 ‫א‬ Y = 1, Y = 0
                                             K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                                                               
                                                                                                      
                                     ‫א‬      ‫א‬               ‫א‬
                                   S   R    CK    Q         (Mode of Operation)
                                   ٠   ٠          Q٠         E‫א‬F‫א‬
                                   ٠   ١          ٠        ‫א‬‫( א‬RESET)
                                   ١   ٠          ١            ‫א‬‫(א‬SET)
                                   ١   ١          ‫؟‬                 ‫א‬
                                                      
                 K‫א‬J ‫א‬S-R‫א‬‫א‬‫א‬EF١٦J ٤
                                                      
                                                      




                                                      -١٠٨-
           ‫א‬‫א‬‫א‬                                   ‫٧٤١ א‬                                   ‫א‬
         ‫א‬‫א‬‫א‬‫א‬                        ‫א‬                            



                                   Master           Master            Master            Master
                                    Enable           Enable            Enable            Enable
                         CK          t٠      t١       t٢       t٣       t٤       t٥


                    S (SET)
                                                                                                         ‫ﻜﺎل‬       ‫أﺷ‬
              R (RESET)
                                                                                                         ‫ﻧﺒﻀﺎت اﻟﺘﺎﺑﻊ‬
                                                                                                          (Master)

                            Y
                              Y



                                             Slave             Slave             Slave
                                            Enabl            Enable            Enable
                           CK

              Y (Slave Set)                                                                           ‫أﺷﻜﺎت ﻧﺒﻀﺎت‬
                                                                                                        ‫اﻟﻤﺘﺒﻮع‬
          Y (Slave Re set )                                                                             (Slave)

                             Q


                    K‫א‬‫א‬S-R‫א‬‫א‬‫א‬‫א‬EF١٦J ٤

                                                                                                                
(High)‫א‬‫א‬،‫א‬‫א‬‫א‬،t٢‫א‬                                     •
‫א‬‫א‬ Y = 0, Y = 1 ‫א‬S = ٠, R = ١‫א‬CK
                                                                                 .(Reset)
،CK (Low)‫א‬‫א‬‫א‬‫א‬،t٣‫א‬
                                                                                          •
(Reset)‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬
                                                                               
                                                                                  KQ = ٠‫א‬
Y‫א‬(Low)‫א‬S,R‫א‬،t٤‫א‬                          •
S‫א‬،t٤‫א‬‫א‬K(Y = ٠)‫א‬‫א‬‫א‬،
                                           KY = ١‫א‬‫א‬(High)‫א‬

                                                            -١٠٩-
           ‫א‬‫א‬‫א‬                            ‫٧٤١ א‬                               ‫א‬
        ‫א‬‫א‬‫א‬‫א‬                     ‫א‬                     



،‫א‬‫א‬‫א‬‫א‬‫א‬،t٥‫א‬
                                                                                                                  •
                                                            KQ = ١Q‫א‬Y = ١‫א‬
                                                                                                               
                                                                                                               
                                   ‫א‬     ‫א‬               ‫א‬
                                   D CK        Q            (Mode of Operation)
                                                             (SET)‫א‬‫א‬
                                   ١            ١
                                                                  (stores a ١)
                                                            (RESET)‫א‬‫א‬
                                   ٠            ٠
                                                                  (stores a ٠)

                                                     E F


                             D           S                            S                Q
                Clock in                   CK                          CK
                                                                       CK
                                          R                          R                Q

                                                       
                                                           EF
                                                      
         K‫א‬‫א‬‫א‬J ‫א‬D‫א‬‫א‬‫א‬E١٧J ٤F
                                                                                                    
EF١٧J ٤،‫–א‬‫א‬D‫א‬‫א‬EF١٧J ٤
                                             
‫–א‬‫א‬D‫א‬‫א‬،‫–א‬‫א‬S-R‫א‬‫א‬K‫א‬‫א‬
                                                                           
                                    KQ‫א‬CK‫א‬‫א‬
                                        
EF١٨J ٤‫א‬،‫–א‬‫א‬J-K‫א‬‫א‬EF١٨J ٤
                                                    
‫א‬‫א‬‫א‬EF١٨J ٤‫א‬K‫א‬‫א‬‫א‬‫א‬
                                                                      
(Q)‫א‬‫א‬‫–א‬‫א‬J-K
      K‫–א‬‫א‬S-R‫א‬‫א‬‫א‬‫א‬‫א‬



                                                       -١١٠-
  ‫א‬‫א‬‫א‬                            ‫٧٤١ א‬                               ‫א‬
‫א‬‫א‬‫א‬‫א‬                  ‫א‬                       



                                                                                              
                               Master                             Slave


        J                                       Y
                                                                                      Q
     CK                                                 CK
                                                                                      Q
                                                Y
       K


                                                                                              

                      K‫א‬J ‫א‬J-K‫א‬‫א‬EF١٨J ٤

                                            

                             ‫א‬ ‫א‬                    ‫א‬
                           J   K CK   Q             (Mode of Operation)
                           ٠   ٠     Q٠              E‫א‬F‫א‬
                           ٠   ١      ٠             ‫א‬‫( א‬RESET)
                           ١   ٠        ١             ‫א‬‫א‬(SET)
                           ١   ١        Q0           ‫א‬(Toggle)

                                            
          K‫א‬J ‫א‬J-K‫א‬‫א‬‫א‬EF١٨J ٤




                                             -١١١-
           ‫א‬‫א‬‫א‬                           ‫٧٤١ א‬                            ‫א‬
         ‫א‬‫א‬‫א‬‫א‬                   ‫א‬                  




              ME      ME      ME    ME   ME   ME   ME     ME    ME   ME
   CK

                                                                              ME = Master Enabled
     J

    K                                                                       (Master) ‫أﺷﻜﺎل ﻧﺒﻀﺎت اﻟﺘﺎﺑﻊ‬


     Y

     Y


                      SE      SE    SE   SE   SE   SE     SE    SE   SE
   CK
                                                                                  SE = Slave Enabled

     Y
                                                                            (Slave) ‫أﺷﻜﺎل ﻧﺒﻀﺎت اﻟﻤﺘﺒﻮع‬
     Y


     Q




                       K‫א‬J ‫א‬J-K‫א‬‫א‬‫א‬EF١٨J ٤

‫א‬‫א‬‫א‬‫א‬
‫א‬ (PRE ) (PRESET)‫א‬‫א‬‫א‬K‫א‬‫א‬
‫א‬‫א‬E١٩J ٤F‫א‬ (CLR ) (CLEAR)‫א‬‫א‬
                                                                 
‫א‬‫א‬K CLR ، PRE  S-R ‫א‬
،Q = ١(SET)‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬
‫א‬،Q = ٠ (RESET)‫א‬‫א‬
                                   
(RESET)‫א‬‫א‬‫א‬K‫א‬Q‫א‬
                     
 (PRE )  ‫א‬K‫א‬‫א‬‫א‬ ‫א‬(CLEAR)‫א‬
، PRE = 0 (١)‫א‬Q‫א‬،‫א‬
                                                        -١١٢-
          ‫א‬‫א‬‫א‬                            ‫٧٤١ א‬                                      ‫א‬
        ‫א‬‫א‬‫א‬‫א‬                    ‫א‬                            



(٠)‫א‬Q‫א‬ (CLR ) ‫א‬
                                               
S-R‫א‬‫א‬‫א‬ ‫א‬E٧J ٤FK CLR = 0
                             
Q‫א‬EF PRE = 0 ‫א‬ CLR = 1‫א‬
 PRE = 1 ‫א‬‫א‬‫א‬KCK, S, R‫א‬‫א‬،(١)
‫א‬(٠)Q‫א‬‫א‬EF CLR = 0 
                                                                                          KCK, S, R‫א‬
                                                PRE 

                                                      
                                            S                    Q

                                           CK         
                                            R                    Q
                                                      

                                                CLR 

        K CLR ، PRE S-R‫א‬‫א‬‫א‬‫א‬E١٩J ٤F

                                                      

                                   ‫א‬                 ‫א‬             ‫א‬
                            PRE CLR CK S          R        Q         (Mode of Operation)
                             ٠   ١   X    X       X         ١          ‫א‬‫א‬(SET)
                             ١   ٠   X    X       X        ٠         ‫א‬‫( א‬RESET)
                             ٠     ٠   X    X     X        ?                ‫א‬
                                                      

               KS-R‫א‬‫א‬ CLR ، PRE ‫א‬E٧J ٤F




                                                      -١١٣-
             ‫א‬‫א‬‫א‬                                   ‫٧٤١ א‬                            ‫א‬
          ‫א‬‫א‬‫א‬‫א‬                         ‫א‬                     




                                                        ‫א‬‫א‬


                                                                      Timer Circuits ‫א‬‫א‬٨J ٤
                  
  ،‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬
  ‫א‬K ‫א‬‫א‬‫א‬‫א‬(Clock Signal)‫א‬
                          
  (Positive Edge)‫א‬‫א‬(Sharp)‫א‬‫א‬K
                                                                      
  K‫א‬‫א‬‫א‬‫א‬(Negative Edge)‫א‬‫א‬‫א‬
                                
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬J-K, S-R,D-Type‫א‬
  .(Set and Reset States)(bi)،(Bistable Multivibrator)
  ‫א‬(Astable Multivibrator)‫א‬‫א‬‫א‬،‫א‬
                                    
  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،
  (Mono)‫א‬‫א‬‫א‬‫א‬(Monostable Multivibrator)
       K(Fixed Duration)(Rectangular Pulse)(Triggered)
                           Astable Multivibrator Circuit‫א‬‫א‬‫א‬‫א‬‫א‬١J ٨J ٤
  (Free running)‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
  ‫א‬E٢٠J ٤F‫א‬‫א‬
                                      K (Schmitt-trigger)(Inverter)‫א‬
                                                                                                          
                                                                                                          

                                                                +٥V              E‫א‬F Charge
                                              R                                                      
                        E‫א‬FDischarge            ٠ (١)                ١(٠
                                                               ∫ ∫                                   
                                                  +




                                             C                                                       

                          K‫א‬‫א‬‫א‬‫א‬‫א‬E٢٠J ٤F


                                                              -١١٤-
              ‫א‬‫א‬‫א‬                         ‫٧٤١ א‬                                   ‫א‬
           ‫א‬‫א‬‫א‬‫א‬                  ‫א‬                       



                                           
   ‫א‬‫א‬،‫א‬‫א‬‫א‬
    .(High)(Not)‫א‬‫א‬ (Low)‫א‬‫א‬،(٠)
                                                                
   ‫א‬‫א‬‫א‬،(R)‫א‬‫א‬(C)‫א‬
   (High)‫א‬‫א‬‫א‬‫א‬،R,C‫א‬‫א‬
                       
   ‫א‬،(Low)‫א‬‫א‬‫א‬K‫א‬
                                                                                     
   ‫א‬‫א‬،(Low)‫א‬‫א‬‫א‬K
                                                                 
                                                                      K‫א‬(High)
              Monostable Multivibrator Circuit‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬٢J ٨J ٤
                                
   ‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬EF٢١J ٤
   NOR‫א‬‫א‬‫א‬،(Low)Q‫א‬‫א‬،(Low)‫א‬(Trigger)
                                                                            
   ‫א‬‫א‬‫א‬(Low)‫א‬‫א‬‫א‬(High)
                                                                                                    K‫א‬
                              
   ‫א‬K(Low)‫א‬ NOR ‫א‬‫א‬،(High)‫א‬
   ،‫א‬‫א‬‫א‬،NOR‫א‬‫א‬ (Low)(High)‫א‬
‫א‬‫א‬Q‫א‬(High)‫א‬
   ‫א‬‫א‬NOR‫א‬‫א‬‫א‬Q‫א‬‫א‬KEF٢١J ٤
                                                                    K‫א‬‫א‬ (Low)‫א‬
                                                                                                          
                                                                   +٥V
                                                                                                          
                                                                     R
                         Input
                      Trigger (T)                                                                         
                                                         C
                                                               +
                                                                                      Output
                                                                                     Pulse (Q)
                                                                                                          
                                                        E F
                                                                                                          
                                         Input
                                      Trigger (T)                                                         
                                       Output
                                      Pulse (Q)                                                           
                                                        EF

                            K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E٢١J ٤F
                                                      -١١٥-
                 ‫א‬‫א‬‫א‬                                            ‫٧٤١ א‬                               ‫א‬
               ‫א‬‫א‬‫א‬‫א‬                                   ‫א‬                      



‫א‬‫א‬NOR‫א‬‫א‬
                                                          
     K‫א‬‫א‬،(resistor–capacitor network)
     ‫א‬‫א‬،R‫א‬C‫א‬‫א‬
       KQ‫א‬(Low)‫א‬(High)‫א‬‫א‬
                                                             The ٥٥٥ Timer Circuit ٥٥٥‫א‬‫א‬٣J ٨J ٤
     ،‫א‬‫א‬‫א‬‫א‬٥٥٥‫א‬‫א‬
     ٥٥٥‫א‬،E٢٢J ٤F‫א‬‫א‬(IC)
             K 5KΩ ‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                           

                                                            Discharge Threshold
                                                             E‫א‬F E‫א‬F
                                               +VCC                                        Control Voltage
                                            E‫א‬F                                  E‫א‬F
                                                            ٨        ٧         ٦      ٥

                                                                           

                                                                           
                                                            ١        ٢         ٣      ٤

                                            Ground                                          Reset
                                            E‫א‬F                                       E‫א‬‫א‬F
                                                                Trigger
                                                                E‫א‬F    Output
                                                                             E‫א‬F


                                           K٥٥٥‫א‬‫א‬E٢٢J ٤F

      ‫א‬‫א‬،
     ‫א‬‫א‬(Monostable mode)‫א‬‫א‬‫א‬‫א‬‫א‬(Astable mode)
     ‫א‬‫א‬‫א‬(Modulator)(Frequency Divider)
                                                                                                              K‫א‬
                                                                                                                          
                                                                   ‫א‬‫א‬‫א‬‫א‬٥٥٥‫א‬١J ٣J ٨J ٤
      ٥٥٥ Timer as an Astable Multivibrator

                                                                           -١١٦-
            ‫א‬‫א‬‫א‬                                      ‫٧٤١ א‬                                         ‫א‬
          ‫א‬‫א‬‫א‬‫א‬                              ‫א‬                             



     
   ‫א‬‫א‬٥٥٥‫א‬EF٢٣J ٤
‫א‬‫א‬K(Free running)‫א‬(Astable)
  ،‫א‬C‫א‬‫א‬EF٢٣J ٤
                                                     K(٠)E‫א‬F+Vcc‫א‬‫א‬
                                                                                                                       
                                                                            +٥V

                                        ٨                                     ٤
  
                                                                                        ٥٥٥ Timer
                                  ٥KΩ
         RA
                                            -
                       ٥
                            ١/٣ VCC                                                                               RL
                                                Comparator
                                           +      (A)
                                                                   R
                                                                                               Inverting
                                                                                              Buffer/Driver
                              ٦
                                                                         S-R    Q                                          Output
          RB                      ٥KΩ
                                                                     Flip-Flop                               ٣            E‫א‬F
                              ٢             -                       S            Inverter
                           ٢/٣ VCC                                                   EF
                                           +
                                              Comparator
                                                 (B)
               +




           C
  
                                  ٥KΩ
                                                             Discharge Transistor
                      ٧                                      E‫א‬‫א‬F


  

                                                                                                   ١



  

                K‫א‬‫א‬٥٥٥‫א‬EF٢٣J ٤




                                                                  -١١٧-
            ‫א‬‫א‬‫א‬                                 ‫٧٤١ א‬                         ‫א‬
          ‫א‬‫א‬‫א‬‫א‬                         ‫א‬               



                                                                                                
                                                T١        T٢         T٣    T٤    T٥
                                 ٢/٣ VCC
                                    Voltage
                                                                                                
                                  Across "C"

                                                                                                
                                      ١/٣ VCC
                                                                                                
                                      (+VCC)
                                     Output          tp         tn
                                         (٠)                                                    

         K‫א‬C‫א‬EF٢٣J ٤

  T١‫]א‬(High)‫א‬S-R‫א‬‫א‬‫א‬‫א‬‫א‬
  ‫א‬(Low)‫א‬‫א‬‫א‬‫א‬‫א‬K[‫א‬
                                                                                          
                                                       KOFF‫א‬(Discharge Transistor)‫א‬‫א‬‫א‬
  ‫א‬‫א‬(C)‫א‬‫א‬،OFF‫א‬‫א‬‫א‬‫א‬
  ‫א‬‫א‬‫א‬،T٢‫א‬KRB, RA‫א‬+Vcc
   1                                                                                                    2
        
  VCC ‫א‬‫א‬(High) A‫א‬‫א‬، VCC
   3                                                                                                    3
  ٥٥٥(٣)‫א‬‫א‬KQ = ٠(RESET)‫א‬‫א‬‫א‬
        KON‫א‬،(High)‫א‬‫א‬،(Low)‫א‬
                 
  ‫א‬KC‫א‬،ON‫א‬‫א‬‫א‬‫א‬
                                            1
  B‫א‬، VCC ‫א‬‫א‬،T٣
                                            3
  ‫א‬‫א‬،Q = ١(SET)‫א‬S-R‫א‬‫א‬(High)‫א‬
 K‫א‬C،OFF‫א‬‫א‬‫א‬K
  ‫א‬RB, RA‫א‬C‫א‬،EF٢٣J ٤‫א‬
                                                                1                                       2
   (Positive time) tp‫א‬K VCC ‫א‬RB‫א‬، VCC
                                                                3                                       3
                                                                                             W‫א‬
                                                                                                    
          t p = 0.7(R A + R B )C

                                                               -١١٨-
          ‫א‬‫א‬‫א‬                             ‫٧٤١ א‬                          ‫א‬
       ‫א‬‫א‬‫א‬‫א‬                      ‫א‬                



                                              W‫א‬(Negative time) tn‫א‬
                                                                                                          
        t n = 0 .7 R B C
                                   Wtn‫א‬،tp‫א‬E‫א‬‫א‬FT‫א‬
                                                                                                          
       T = t p + tn
    = 0.7(R A + 2R B )C
                                               W‫א‬‫א‬٥٥٥‫א‬
                                                                                                          
              1            1
        f =     =
              T 0 .7 ( R A + 2 R B ) C
                                                                 W‫א‬‫א‬‫א‬
                                                                                                          
                    1.43
        f=
              ( R A + 2 R B )C

                                              ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬٢J ٣J ٨J ٤
٥٥٥ Timer as a Monostable Multivibrator
‫א‬‫א‬‫א‬‫א‬‫א‬٥٥٥‫א‬EF٢٤J ٤
‫א‬EF٢٤J ٤‫א‬‫א‬.(one-shot)
‫א‬K٥٥٥‫א‬‫א‬،‫א‬،(Input - trigger)‫א‬
                                                           KRA,C‫א‬‫א‬(Pw)
(RESET)S-R‫א‬‫א‬،EF٢٤J ٤T١‫א‬
‫א‬S-R‫א‬‫א‬(Low)‫א‬‫א‬KQ = ٠(Low)
‫א‬،‫א‬‫א‬(inverted and buffered)،‫א‬
                                                      K(Low)٠V(٣)‫א‬٥٥٥
‫א‬(High)S-R‫א‬‫א‬(Low)‫א‬
      K‫א‬‫א‬‫א‬‫א‬، ON‫א‬،‫א‬


                                                      -١١٩-
           ‫א‬‫א‬‫א‬                                        ‫٧٤١ א‬                                        ‫א‬
         ‫א‬‫א‬‫א‬‫א‬                                ‫א‬                            



٥٥٥‫א‬‫א‬(٢)‫א‬(Trigger)‫א‬،T٢‫א‬
                      1
                    
، VCC  B‫א‬‫א‬‫א‬‫א‬ K‫א‬‫א‬
                      3
                                                                                       
‫א‬KQ = ١‫א‬(SET)‫א‬S-R‫א‬‫א‬،(High)B‫א‬
‫א‬٥٥٥(٣)‫א‬‫א‬‫א‬S-R‫א‬‫א‬ (High)‫א‬
                                                        KOFF‫א‬‫א‬‫א‬(High)
                                                                                                                          
                                                                             +٥V                                                
                                       ٨                                      ٤


                                                                                          ٥٥٥ Timer
                                 ٥KΩ
               RA
                                           -
                      ٥
                          ١/٣ VCC              Comparator
                                                                                                                  RL
                                           +      (A)                                          Inverting
                                                                     R
                             ٦                                                                Buffer/Driver
                                                                            S-R    Q
                                 ٥KΩ                                     Flip-Flop                            ٣        Output
              Trigger        ٢             -                         S                 Inverter
               Input      ٢/٣ VCC              Comparator
                                           +      (B)



                                 ٥KΩ

                      ٧
                                                            Discharge Transistor
              +




                  C

                                                                                                    ١




        K‫א‬‫א‬‫א‬٥٥٥‫א‬EF٢٤J ٤

                                                                 

                                                                 

                                                                 


                                                                  -١٢٠-
          ‫א‬‫א‬‫א‬                             ‫٧٤١ א‬                          ‫א‬
        ‫א‬‫א‬‫א‬‫א‬                     ‫א‬                



                                            T١ T٢    
                    Trigger ١/٣ VCC
                     Input
                                ٠V                   
                                                     
                            ٢/٣ VCC
                                                     
                                                     
                             Voltage                 
                            Across "C"
                                                     
                                   Output
                                                     
                                                     
 K‫א‬‫א‬C‫א‬‫א‬EF٢٤J ٤
                                                                                               
+VCCRA‫א‬‫א‬C‫א‬‫א‬
‫א‬(High)‫א‬٥٥٥‫א‬KEF٢٤J ٤‫א‬
                                                                2
،(High)A‫א‬،(T٣)‫א‬K VCC ‫א‬
                                                                3
(٣)‫א‬‫א‬،(RESET)‫א‬S-R‫א‬‫א‬
C‫א‬ON‫א‬‫א‬‫א‬،(Low)‫א‬
                                                                                               K
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                                           K
              
‫א‬،‫א‬‫א‬(Leading edge)‫א‬‫א‬
‫א‬RA‫א‬C‫א‬‫א‬(Trailing edge)‫א‬
           W‫א‬‫א‬‫א‬K‫א‬
                                                                                               
                  Pw = 1.1R A C
                                                                                                          
                                                                                                          
                                                                                                          
                                                      -١٢١-
                ‫א‬‫א‬‫א‬                                       ‫٧٤١ א‬                                              ‫א‬
            ‫א‬‫א‬‫א‬‫א‬                                ‫א‬                                    



                                                           Shift Registers‫א‬‫א‬٩J ٤
   ،‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
   ‫א‬‫א‬(bit)‫א‬‫א‬‫א‬‫א‬
   ‫א‬،‫א‬‫א‬‫א‬،
   ‫א‬‫א‬‫א‬
    Shift )‫א‬ (Shift Left)‫א‬‫א‬‫א‬(Buffer Register)‫א‬‫א‬
   ‫א‬(Parallel Data)‫א‬(Serial Data)‫א‬‫א‬‫א‬(Right
                                                                                               K(Shift Registers)‫א‬‫א‬
                                                                           Buffer Registers‫א‬١J ٩J ٤
   (Digital word)‫א‬
‫א‬EF٢٥J ٤K(bits)‫א‬‫א‬
   ‫א‬‫א‬‫א‬‫א‬‫א‬ D ‫א‬‫א‬‫א‬‫א‬(٤-stages)
                                                                                                         K(Positive edge-triggered)
                                                                      
                                         (٤-bit word to be stored)‫א‬‫א‬‫א‬‫א‬


                          D١                           D٢                                D٣                      D٤


                               D         Q                  D         Q                       D         Q              D         Q



                                         Q                            Q                                 Q                        Q
                                   CLR                          CLR                               CLR                      CLR
                CK
         CLR

                                               Q١                            Q٢                             Q٣                       Q٤


                                                                  (parallel data outputs)‫א‬‫א‬‫א‬

                                                                                  E F
         KD‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬EF٢٥J ٤
                                                                      

                                                                      -١٢٢-
          ‫א‬‫א‬‫א‬                             ‫٧٤١ א‬                           ‫א‬
        ‫א‬‫א‬‫א‬‫א‬                     ‫א‬                 



                                                     
                                                                                                
                                      Clock                                                     
                                                               ١                                
                                            D١
                                                                                                
                                                               ٠
                                         D٢
                       ‫א‬                                                             
                       Input data                              ١
                                       D٣                                                       
                                            D٤                 ٠                                
                                                                                                
                                            Q١
                                                                                                
                                            Q٢
                      ‫א‬                                                               
                     Output data
                                            Q٣                                                  
                                            Q٤                                                  
                                                                     EF
                                                                                                
            KEF٢٥J ٤‫א‬‫א‬‫א‬EF٢٥J ٤
                                                                                                
D٤‫א‬‫א‬(٤-bits)‫א‬‫א‬‫א‬
‫א‬Q١,Q٣, Q٢,Q٤‫א‬D١,D٢,D٣,
                                                                                 K(CK)‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬EF٢٥J ٤‫א‬‫א‬‫א‬
‫א‬‫א‬Q١,Q٣, Q٢,Q٤‫א‬
                             K‫א‬‫א‬K‫א‬‫א‬‫א‬
‫א‬،‫א‬‫א‬‫א‬
‫א‬‫א‬J ‫א‬‫א‬‫א‬،‫א‬‫א‬
‫א‬‫א‬‫א‬(Clear-input)‫א‬K(Parallel-in, Parallel-out Registers)
                                       KE‫א‬F‫א‬‫א‬(active-low)
                                                                                                           

                                                      -١٢٣-
          ‫א‬‫א‬‫א‬                                       ‫٧٤١ א‬                                              ‫א‬
       ‫א‬‫א‬‫א‬‫א‬                                ‫א‬                                   



                                                                        Shift Registers‫א‬‫א‬٢J ٩J ٤
 
‫א‬(Shift)‫א‬(move)‫א‬‫א‬‫א‬‫א‬
                                                                                   
                  WKE٢٦J ٤F‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K
(Serial-in, Serial-out Shift Registers)‫א‬‫א‬–‫א‬‫א‬‫א‬ -١
                                                                                              K(SISO)‫א‬‫א‬
(Serial-in, Parallel-out Shift Registers)‫א‬‫א‬–‫א‬‫א‬‫א‬ -٢
                                                                                              .(SIPO)‫א‬‫א‬
                                           
(Parallel-in, Serial-out Shift Registers) ‫א‬‫א‬–‫א‬‫א‬‫א‬J ٣
                                                                                              K(PISO)‫א‬‫א‬
                                                                                                                                       
                                                                                                                                       
                                        Serial-in, serial-out (SISO) Shift Registers

                                                                
                                        Shift Right                                          Shift Left
                        Serial-In                             
                                                           Serial-Out                                           Serial-In
                                                                

                                       Rotate Right                                        Rotate Left


                                                                       EF

                                                                
                      Serial-in, parallel-out (SIPO) Shift Registers          Parallel-in, Serial-out Shift (PISO) Registers
                                                                
                                                                                            Parallel Data In
                      Serial-In
                                                                
                                                                                                                 Serial-Out
                                                                
                                    Parallel Data Out            EF

                                   K‫א‬‫א‬EF٢٦J ٤



                                                                -١٢٤-
            ‫א‬‫א‬‫א‬                            ‫٧٤١ א‬                                   ‫א‬
         ‫א‬‫א‬‫א‬‫א‬                     ‫א‬                        



‫א‬‫א‬‫א‬‫א‬
                                                                                               W‫א‬
                                          ‫א‬‫א‬–‫א‬‫א‬‫א‬‫א‬١J ٢J ٩J ٤
 Serial-in, Serial-out (SISO) Shift registers
                           
‫א‬‫א‬K ‫א‬‫א‬‫א‬،E٨J ٤F
                                                   
١٠٠١‫א‬‫א‬‫א‬‫א‬E‫א‬‫א‬F٠١١٠‫א‬‫א‬
                                                                       K‫א‬‫א‬‫א‬‫א‬
                                                                                                         
                  ‫א‬‫א‬        ‫א‬‫א‬‫א‬                ‫א‬

                       Clock                 Input                    Q٠     Q١       Q٢        Q٣
                       —                     —                      ٠       ١        ١         ٠
                           ١st                   ١                    ١       ٠        ١         ١
                          ٢nd                    ٠                    ٠       ١        ٠         ١
                          ٣rd                    ٠                    ٠       ٠        ١         ٠
                          ٤th                    ١                    ١       ٠        ٠         ١
                                  K‫א‬‫א‬E٨J ٤F
                                                                                                         
‫א‬‫א‬‫١( א‬st Clock pulse)‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
،(٢nd Clock pulse)‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬
                                                         
‫א‬‫א‬‫א‬ (٠١١٠)‫א‬‫א‬
K‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬K(١٠٠١)‫א‬‫א‬‫א‬
‫א‬(٠١١٠)‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬
                                                                                   
‫א‬‫א‬‫א‬‫א‬ (١٠٠١)‫א‬‫א‬‫א‬،‫א‬
                                                                                                       K


                                                       -١٢٥-
                 ‫א‬‫א‬‫א‬                                          ‫٧٤١ א‬                                      ‫א‬
               ‫א‬‫א‬‫א‬‫א‬                                  ‫א‬                           



    ‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                                      K‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                         

                                FF٠                       FF١                              FF٢                    FF٣
           Serial
                                                                                                                                 Serial
           Data             D         Q               D         Q                    D           Q           D
                                          0                      1                                   2                           Data Out
           Input
                                                       CK



      Clock
      Input
                                                                SISO Shift Right

                                                                             E F

                                                                                                                                   Serial
      Serial                                                                                                                       Data
      Data Out                                                                                                                     Input
                                      Q               D         Q                     D          Q           D          Q
                                          3                         2                             1                         0
                                                       CK                                 CK                     CK



       Clock                    FF٣                       FF٢                              FF١                    FF٠
       Input
                                                                    SISO Shift Left

                                                                             EF




                                              SISO Rotate Right                           SISO Rotate Left

                                                                             EF

        K‫א‬‫א‬‫א‬‫א‬‫א‬E٢٧J ٤F

    ‫א‬‫א‬(٤-bits)‫א‬‫א‬EF٢٧J ٤
    ‫א‬،(FF٠)‫א‬‫א‬‫א‬D‫א‬‫א‬‫א‬‫א‬KD‫א‬‫א‬
    (Q١)‫א‬‫א‬‫א‬،(FF١)‫א‬‫א‬‫א‬D‫א‬(Q٠)‫א‬‫א‬
                                                                          -١٢٦-
                  ‫א‬‫א‬‫א‬                                  ‫٧٤١ א‬                                       ‫א‬
               ‫א‬‫א‬‫א‬‫א‬                           ‫א‬                            



     ‫א‬‫א‬(Q٢)‫א‬‫א‬‫א‬،(FF٢)‫א‬‫א‬‫א‬‫א‬
     ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،(FF٣)‫א‬‫א‬‫א‬
                                                                                                                   K‫א‬
     ،‫א‬‫א‬(Clock input)‫א‬‫א‬
    ،‫א‬‫א‬(١-bit)‫א‬‫א‬‫א‬ (Positive edge)
     ‫א‬‫א‬‫א‬‫א‬‫א‬–‫א‬‫א‬‫א‬‫א‬
                                                                
     ‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬
                                                                                                                    K‫א‬
                                                                   
     EF٢٧J ٤‫א‬‫א‬‫א‬،
     ‫א‬‫א‬–‫א‬‫א‬‫א‬‫א‬‫א‬D‫א‬‫א‬
     EF٢٧J ٤‫א‬‫א‬‫א‬ .(SISO Shift-Right Shift Register)
       
     ‫א‬–‫א‬‫א‬D‫א‬‫א‬‫א‬‫א‬
                                                                                       
                                                                            K(SISO Shift- Left Shift Register)‫א‬
     EF٢٧J ٤،EF٢٧J ٤‫א‬‫א‬‫א‬،‫א‬
                                                        
     ‫א‬‫א‬،‫א‬‫א‬‫א‬
                                                                                                             
‫א‬‫א‬‫א‬–‫א‬‫א‬‫א‬ 
      (SISO Rotate-Left) ‫א‬‫א‬‫א‬–‫א‬‫א‬(SISO Rotate-Right)
                                                                                               KEF٢٧J ٤
                                                     ‫א‬‫א‬–‫א‬‫א‬‫א‬٢J ٢J ٩J ٤
      Serial-in, parallel out (SIPO) Shift registers
     ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E٢٨J ٤F‫א‬
                                                                                                      K‫א‬‫א‬–‫א‬
     (٤-bits)‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬
     ‫א‬F‫א‬‫א‬‫א‬‫א‬‫א‬(Serial data input)‫א‬‫א‬‫א‬
                                                                                        KE‫א‬‫א‬




                                                                   -١٢٧-
           ‫א‬‫א‬‫א‬                                           ‫٧٤١ א‬                                         ‫א‬
         ‫א‬‫א‬‫א‬‫א‬                                ‫א‬                                  



                                                                                                                                    
                                                              FF١                         FF٢                         FF٣
            Serial
                                 FF٠
                                                                    
            Data             D         Q                  D         Q                D          Q                 D         Q
            Input                          0                        1                              2                           3
                              CK                           CK                            CK                         CK
                                                                    
        Clock
                                                                    
        Input
                                                                    
                                                                    
                                               Q                         Q                              Q                               Q
                                                   0                      1                                 2                               3
                                                                    
                                                                             Parallel data outputs

                        K‫א‬‫א‬J ‫א‬‫א‬‫א‬‫א‬E٢٨J ٤F
                                                                                                                                    
                                    
‫א‬‫א‬‫א‬‫א‬‫א‬(٤-bits)
                                                                     
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬
                                                            K‫א‬‫א‬(٤-bits)(Q٣,Q٢,Q١,Q٠)
                                                        ‫א‬‫א‬–‫א‬‫א‬‫א‬٣J ٢J ٩J ٤
Parallel-in, Serial-out (PISO) Shift registers
‫א‬‫א‬‫א‬‫א‬E٢٩J ٤F
‫א‬‫א‬‫א‬KD‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬–
،(Low)‫א‬ SHIFT / LOAD ‫א‬K SHIFT / LOAD ‫א‬
‫א‬(Enabled)‫א‬‫א‬AND ‫א‬‫א‬
                                                                 
‫א‬‫א‬‫א‬‫א‬K‫א‬Inverter‫א‬
‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬(D٣,D٢,D١,D٠)‫א‬
‫א‬‫א‬‫א‬‫א‬،(Clock pulse)
                                                                                                         .(Q٣,Q٢,Q١,Q٠)
                                                           

                                                                    



                                                                    -١٢٨-
            ‫א‬‫א‬‫א‬                                   ‫٧٤١ א‬                                        ‫א‬
         ‫א‬‫א‬‫א‬‫א‬                            ‫א‬                          



     (SHIFT / LOAD) control

     (1 for shift , 0 for load )                   Parallel data inputs


                       D                          D                          D                        D
                           0                       1                             2                        3




                                    FF٠                FF١                            FF٢                      FF٣           Serial
                                                                                                                             Out
                               D          Q        D           Q                 D          Q             D          Q
                                              0                 1                               2                        3
                                   CK                  CK                            CK                       CK



         Clock
         Input

                         K‫א‬‫א‬J ‫א‬‫א‬‫א‬E٢٩J ٤F

AND‫א‬‫א‬،(High)‫א‬ SHIFT / LOAD ‫א‬
Q٠‫א‬‫א‬‫א‬‫א‬K(Enabled)‫א‬‫א‬
،(FF٢)‫א‬‫א‬‫א‬‫א‬Q١‫א‬،(FF١)‫א‬‫א‬‫א‬D‫א‬
                       
‫א‬‫א‬،‫א‬‫א‬K(FF٣)‫א‬‫א‬‫א‬‫א‬Q٢‫א‬
                                                                                  
(١-bit)‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                               .(clock inputF‫א‬‫א‬‫א‬‫א‬
    Shift Register Sequencer (Ring Counter)E‫א‬F‫א‬‫א‬‫א‬٤J ٢J ٩J ٤
‫א‬‫א‬‫א‬EF٣٠J ٤
                 KED٠Q٣‫א‬FFF٠‫א‬‫א‬‫א‬(FF٣)‫א‬‫א‬‫א‬
                                            
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬Q٠‫א‬Low‫א‬ SRART ‫א‬K
                                                         
E CLR = 0 FLow‫א‬ Q١,Q٢,Q٣‫א‬،( PRE = 0 )High
                                                                                       KEF٣٠J ٤‫א‬
                                                              -١٢٩-
     ‫א‬‫א‬‫א‬                                                                       ‫٧٤١ א‬                                                     ‫א‬
   ‫א‬‫א‬‫א‬‫א‬                                                            ‫א‬                                          



                                                                                                                                                                    
                                                                                                                                                                    
                                                        Q                                     Q                                       Q                                 Q
                                                            0                                  1                                          2                                 3


                               PRE                                              PRE                                 PRE                               PRE
                       D                Q                               D             Q                     D             Q                   D             Q
                           0                0                            1             1                        2             2                   3             3
                       CK                                               CK                                  CK                                    CK


                               CLR                                           CLR                                    CLR                            CLR
                                    FF٠                                              FF١                                FF٢                             FF٣
Clock
START

                                                                                                  EF

          K‫א‬‫א‬‫א‬EF٣٠J ٤


                                ٠               ١           ٢           ٣             ٠       ١         ٢           ٣             ٠       ١   ٢

           Clock

         START



                                            ١           ٠           ٠            ٠
               Q
                   0

                                    ٠               ١           ٠       ٠
               Q
                1

                                    ٠               ٠           ١       ٠
               Q
                   2

                                    ٠               ٠           ٠           ١
               Q
                   3
                                                                                              EF
                                      K‫א‬‫א‬‫א‬EF٣٠J ٤




                                                                                           -١٣٠-
            ‫א‬‫א‬‫א‬                                 ‫٧٤١ א‬                                   ‫א‬
         ‫א‬‫א‬‫א‬‫א‬                          ‫א‬                         




                         Clock                 ‫א‬‫א‬
                         Pulses
                                       Q٠      Q١     Q٢      Q٣
                              ٠         ١       ٠     ٠        ٠
                              ١         ٠       ١     ٠        ٠           Four flip-flops will have
                              ٢         ٠       ٠     ١        ٠           Four output states.
                              ٣         ٠       ٠     ٠        ١

                                            Repeat Sequence
                                     K‫א‬‫א‬‫א‬E٩J ٤F

‫א‬،‫א‬‫א‬‫א‬(١٠٠٠)‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬(١)
                                                                                                   KE٩J ٤F
                                                        Johnson Counter‫א‬٥J ٢J ٩J ٤
                                                       
‫א‬،‫א‬‫א‬‫א‬EF٣١J ٤
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                               K(D٠)‫א‬‫א‬‫א‬‫א‬E Q 3 F
                                                                    
‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬
Q٣،١٠٠٠،E١٠J ٤F‫א‬‫א‬EF٣١J ٤‫א‬
‫א‬‫א‬(High)‫א‬ Q 3 ،‫א‬‫א‬(Low)‫א‬
‫א‬ (High inputs)‫א‬‫א‬‫א‬‫א‬،D٠‫א‬
K(High)‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                         
،(Low)‫א‬ Q 3 ،E‫א‬‫א‬‫א‬F(High)‫א‬Q٣
‫א‬‫א‬‫א‬‫א‬‫א‬K(Low) D٠
K(Low)‫א‬‫א‬‫א‬‫א‬(Low inputs)‫א‬
‫א‬ Q 3 ،E‫א‬‫א‬‫א‬F(Low)‫א‬Q٣
 K‫א‬‫א‬‫א‬‫א‬(High)D٠(High)
                                                                                                              




                                                            -١٣١-
        ‫א‬‫א‬‫א‬                                              ‫٧٤١ א‬                                                     ‫א‬
     ‫א‬‫א‬‫א‬‫א‬                                    ‫א‬                                       



                                               Q                             Q                               Q                                 Q
                                                   0                          1                                  2                                 3


                                 PRE                        PRE                                PRE                               PRE
                         D             Q               D            Q                  D             Q                   D             Q
                             0             0            1            1                     2             2                   3             3
                          CK                               CK                          CK                                CK

                                                                                                                                       Q
                                 CLR                        CLR                                CLR                           CLR
                                                                                                                                           3
                                     FF٠                        FF١                              FF٢                                  FF٣
    Clock


                                                                             EF

                                 ٠         ١       ٢   ٣        ٤        ٥         ٦       ٧         ٠       ١       ٢            ٣
             Clock

            START




                 Q
                     0


                 Q
                  1


                 Q
                     2


                 Q
                     3


                 Q
                     3

                                                                             EF

 K‫א‬‫א‬‫א‬‫א‬‫א‬E٣١J ٤F

                                                            

                                                            



                                                                    -١٣٢-
               ‫א‬‫א‬‫א‬                                 ‫٧٤١ א‬                                    ‫א‬
             ‫א‬‫א‬‫א‬‫א‬                         ‫א‬                          


                          Clock                ‫א‬‫א‬
                         Pulses
                                         Q٠    Q١    Q٢       Q٣ Q3
                              ٠           ١     ٠     ٠        ٠       ١
                              ١           ١     ١     ٠        ٠       ١
                              ٢           ١     ١     ١        ٠       ١
                              ٣           ١     ١     ١        ١       ٠      Four flip-flops will have
                              ٤           ٠     ١     ١        ١       ٠      eight output states.
                              ٥           ٠     ٠     ١        ١       ٠
                              ٦           ٠     ٠     ٠        ١       ٠
                              ٧           ٠     ٠     ٠        ٠       ١

                                                         
                                           Repeat Sequence


                                         K‫א‬‫א‬E١٠J ٤F
                                                                                                                  
                                                                                 
    ،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                                      
    F‫א‬‫א‬‫א‬‫א‬‫א‬
          
    ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬KEE٩J ٤F
EF٣١J ٤‫א‬‫א‬‫א‬،‫א‬
                                                                  KE١٠J ٤F(٢ × ٤ flip-flops = ٨)




                                                               -١٣٣-
         ‫א‬‫א‬J ‫א‬‫א‬‫א‬                         ‫٧٤١ א‬                                       ‫א‬
             ‫א‬‫א‬‫א‬‫א‬                        ‫א‬                           ‫א‬‫א‬



                                                                                            Counters‫א‬‫א‬‫א‬١٠J ٤
                       
   ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
   ،(binary bits)‫א‬‫א‬‫א‬K‫א‬
   ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
   ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K(clock input)‫א‬‫א‬
   ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                                                      K‫א‬‫א‬
   ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                             
  K(Synchronous Counters ) ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬(Asynchronous Counters)
   ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                                 
   ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬
   K(Master Clock)‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬
    
   ،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                        K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
         Asynchronous Binary-Up Counters ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬١J ١٠J ٤
         
   K‫א‬‫א‬‫א‬EF٣٢J ٤
                                                                        
   ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬J-K
                                                                        
   K‫א‬‫א‬‫א‬‫א‬‫א‬
                                        
   ‫א‬‫א‬،(High)‫א‬J,K‫א‬
             
   K‫א‬‫א‬(Negative edge)(Toggle)
‫א‬(Q)‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
   ‫א‬(٤-bit word)‫א‬‫א‬Q٣,Q٢,Q١,Q٠‫א‬KEF٣٢J ٤
   ‫א‬‫א‬‫א‬ ٠٠٠٠‫א‬‫א‬
   FF٠‫א‬‫א‬KE١١J ٤F‫א‬‫א‬‫א‬‫א‬
                      K(MSB)‫א‬(Q٣)FF٣‫א‬‫א‬(LSB)(Q٠)
                                                                                                                    


                                                              - ١٣٣ -
          ‫א‬‫א‬‫א‬                                                      ‫٧٤١ א‬                                                 ‫א‬
        ‫א‬‫א‬‫א‬‫א‬                                              ‫א‬                                     




                                 FF٠                                    FF١                               FF٢                          FF٣
                            J          Q                            J          Q                     J          Q                 J          Q
                                           0                                    1                                   2                            3
          Clock
          Input                 CK                                      CK                               CK                           CK

                            K                                       K                                 K                            K




                                                    Q                                 Q                                 Q                                Q
                                                        0                              1                                    2                                3


                                                                                               EF


                                                            ١   ٢   ٣    ٤    ٥   ٦   ٧    ٨    ٩    ١٠ ١١ ١٢ ١٣ ١٤ ١٥ ١٦ ١٧




                                                            ٠
                                               Q٠


                                               Q١           ٠


                                               Q٢           ٠


                                               Q٣           ٠

                                                                                              EF

          K‫א‬‫א‬‫א‬‫א‬E٣٢J ٤F

،(Clock input)‫א‬‫א‬‫א‬(FF٠)‫א‬‫א‬
،‫א‬‫א‬‫א‬ (Toggle)Q٠‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬KEF٣٢J ٤Q٠‫א‬
        
‫א‬K‫א‬"٠""١"‫א‬‫א‬‫א‬ "١""٠"Q٠
Q٠،FF١‫א‬‫א‬‫א‬Q٠‫א‬
                                                 
Q٢‫א‬Q١K(Toggle)Q١‫א‬
                                                                 KQ٣‫א‬Q٢،
                                                                                                                                                     
                                                                               -١٣٤-
           ‫א‬‫א‬‫א‬                               ‫٧٤١ א‬                            ‫א‬
        ‫א‬‫א‬‫א‬‫א‬                        ‫א‬                  



                                               ‫א‬‫א‬              ‫א‬
                                         Q٣      Q٢      Q١      Q٠
                                          ٠       ٠       ٠      ٠       ٠
                                          ٠       ٠       ٠      ١       ١
                                          ٠       ٠       ١      ٠       ٢
                                          ٠       ٠       ١      ١       ٣
                                          ٠       ١       ٠      ٠       ٤
                                          ٠       ١       ٠      ١       ٥
                                          ٠       ١       ١      ٠       ٦
                                          ٠       ١       ١      ١       ٧            Cycle Repeats
                                          ١       ٠       ٠      ٠       ٨
                                          ١       ٠       ٠      ١       ٩
                                          ١       ٠       ١      ٠      ١٠
                                          ١       ٠       ١      ١      ١١
                                          ١       ١       ٠      ٠      ١٢
                                          ١       ١       ٠      ١      ١٣
                                          ١       ١       ١      ٠      ١٤
                                          ١       ١       ١      ١      ١٥
                                                                                                    
                                                 Binary Count
                  K‫א‬‫א‬‫א‬‫א‬‫א‬E١١J ٤F

                                            The Maximum Count (N) of a Counter ‫א‬•
‫א‬‫א‬‫א‬،E١١J ٤F‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬،[‫א‬‫א‬(١)‫א‬]٠٠٠١‫א‬‫א‬‫א‬
]٠٠١١‫א‬‫א‬‫א‬‫א‬‫א‬،[‫א‬‫א‬(٢)‫]א‬٠٠١٠‫א‬
                                                              
                                                                               
‫א‬‫א‬‫א‬‫א‬K‫א‬،[‫א‬‫א‬(٣)
          W‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬
       N = 2 n − 1 
                                                                                                     W
             (N = maximum count before cycle repeats) ‫א‬‫א‬‫א‬ = N
        (n = number of flip-flops in the counter circuit)‫א‬‫א‬‫א‬‫א‬‫א‬ = n
                                                                                                               
                                                                                                               
                                                         -١٣٥-
          ‫א‬‫א‬‫א‬                             ‫٧٤١ א‬                            ‫א‬
        ‫א‬‫א‬‫א‬‫א‬                     ‫א‬                  



                                    W‫א‬EF٣٢J ٤‫א‬‫א‬‫א‬‫א‬
                  N = 2n − 1
                      = 24 − 1
                      = 16 − 1
                      = 1510 (11112 )
                                                     The Modulus (MOD) of a counter‫א‬‫א‬‫א‬•
‫א‬(MOD)(Modulus of a counter)‫א‬‫א‬‫א‬
MODEF٣٢J ٤‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬
‫א‬١١١١٠٠٠٠(١٦)‫א‬‫א‬(١٦)
                                    W‫א‬‫א‬‫א‬MODKE١١J ٤F
                                                                                                 
                 MOD = ٢n
                 MOD = modulus of the counter
                 n   = number of flip-flops in the counter circuit
                                                                                                            
                W‫א‬‫א‬‫א‬‫א‬‫א‬EF٣٢J ٤‫א‬‫א‬‫א‬‫א‬
                                                                                                            
                   MOD = 2 n
                             = 24
                             = 16
                                             The Frequency Division of a counter ‫א‬‫א‬•
EF٣٢J ٤‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬(frequency divider)‫א‬‫א‬
‫א‬‫א‬،٢‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
              
،‫א‬٢‫א‬K٢‫א‬‫א‬
،‫א‬٢‫א‬٢‫א‬
٤‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                           
‫א‬‫א‬‫א‬‫א‬EF٣٢J ٤

                                                      -١٣٦-
           ‫א‬‫א‬‫א‬                             ‫٧٤١ א‬                                  ‫א‬
         ‫א‬‫א‬‫א‬‫א‬                     ‫א‬                        



                                                                                                 
،٢‫א‬‫א‬‫א‬‫א‬‫א‬،KQ١ ‫א‬
‫א‬،٨‫א‬،٤‫א‬‫א‬‫א‬‫א‬
                     W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬١٦
                                                                                                        
                  Division Factor = ٢n E‫א‬F
                  N = number of flip-flops in the counter circuit

                   The Propagation Delay Time (tp) of a counter‫א‬‫א‬•
‫א‬‫א‬،(Ripple counter)‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                    
K‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬
                                                                                    
‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬
                                K‫א‬‫א‬‫א‬‫א‬
                                                                            
E‫א‬‫א‬‫א‬F‫א‬‫א‬‫א‬،
‫א‬‫א‬K١٠٠٠٠١١١‫א‬‫א‬‫א‬‫א‬
                                                                                     
                                                          
٠١١١‫א‬‫א‬ (٤ Flip-Flops × ١٠ns) 40ns 10ns (tp)‫א‬
‫א‬‫א‬(counting speed)‫א‬K١٠٠٠
                                               
‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                               W‫א‬‫א‬‫א‬
                      1 × 10 9
                   f=
                       n× tp
                                                                                                             W
                  f = upper clock pulse frequency limit
                  n = number of flip-flops in the counter circuit
                  tp= propagation delay time of each flip-flop in nanoseconds

        Asynchronous Binary Down Counters‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬٢J ١٠J ٤
           
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K"١"
                                                    
‫א‬EF٣٣J ٤‫א‬K‫א‬"١"‫א‬

                                                       -١٣٧-
            ‫א‬‫א‬‫א‬                                                        ‫٧٤١ א‬                                                          ‫א‬
          ‫א‬‫א‬‫א‬‫א‬                                                ‫א‬                                             



 Q ‫א‬KJ-K‫א‬‫א‬‫א‬‫א‬
                                          K‫א‬‫א‬‫א‬Q‫א‬‫א‬
‫א‬KEF٣٣J ٤‫א‬‫א‬‫א‬Q‫א‬‫א‬‫א‬
                     
Q٣,Q٢,Q١,Q٠(RESET)‫א‬‫א‬‫א‬‫א‬
 Q ‫א‬LowQ‫א‬‫א‬‫א‬‫א‬K٠٠٠٠
FF٣,FF٢,FF١‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K١١١١
                                                       
‫א‬High‫א‬‫א‬‫א‬J,K‫א‬‫א‬KHigh
                           K‫א‬‫א‬‫א‬(Toggle)
      
                                                        Q
                                                             0
                                                                                                Q
                                                                                                 1
                                                                                                                                    Q
                                                                                                                                        2
                                                                                                                                                                    Q
                                                                                                                                                                        3
           HIGH
                                    FF٠                                     FF١                                      FF٢                             FF٣

                                J          Q                             J             Q                         J          Q                    J          Q
                                               0                                        1                                       2                               3
             Clock
              Input                 CK                                       CK                                      CK                              CK

                                 K         Q                             K             Q                         K          Q                    K          Q
                                              0                                        1                                       2                               3

                                                                                                    E F
  
                                                         ١       ٢   ٣       ٤     ٥   ٦    ٧   ٨      ٩    ١٠ ١١ ١٢ ١٣ ١٤ ١٥ ١٦
                                                    ١٧
                                        Clock
                                         Input

                                                         ٠
                                              Q٠

                                                         ٠
                                              Q١


                                               Q٢        ٠
  
                                               Q٣        ٠
                                                                                                          EF

                K‫א‬‫א‬‫א‬‫א‬E٣٣J ٤F

"٠"Q٠‫א‬،FF٠‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                            
‫א‬‫א‬"٠""١" Q 0 ‫א‬‫א‬،"١"

                                                                                   -١٣٨-
          ‫א‬‫א‬‫א‬                         ‫٧٤١ א‬                              ‫א‬
        ‫א‬‫א‬‫א‬‫א‬                 ‫א‬                    



‫א‬"٠""١"Q١‫א‬،FF١‫א‬‫א‬
‫א‬"٠""١" Q1 ‫א‬‫א‬K"٠""١" Q1
                                                                                K‫א‬،FF٢
                                                                                               
                                       ‫א‬‫א‬               ‫א‬
                                    Q٣    Q٢     Q١       Q٠
                                    ١     ١      ١        ١       ١٥
                                    ١     ١      ١        ٠       ١٤
                                    ١     ١      ٠        ١       ١٣
                                    ١     ١      ٠        ٠       ١٢
                                    ١     ٠      ١        ١       ١١
                                    ١     ٠      ١        ٠       ١٠
                                    ١     ٠      ٠        ١        ٩
                                    ١     ٠      ٠        ٠        ٨              Cycle Repeats
                                    ٠     ١      ١        ١        ٧
                                    ٠     ١      ١        ٠        ٦
                                    ٠     ١      ٠        ١        ٥
                                    ٠     ١      ٠        ٠        ٤
                                    ٠     ٠      ١        ١        ٣
                                    ٠     ٠      ١        ٠        ٢
                                    ٠     ٠      ٠        ١        ١
                                    ٠     ٠      ٠        ٠        ٠
                                                                                               
                                           Binary Count
                    K‫א‬‫א‬‫א‬‫א‬‫א‬E١٢J ٤F

(١٥)١٠ = ١١١١Q٣,Q٢,Q١,Q٠‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                          
‫א‬‫א‬‫א‬‫א‬KE١٢J ٤F‫א‬‫א‬‫א‬
                                      
‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬
 FF٠‫א‬‫א‬،EF٣٣J ٤‫א‬
Q٣,Q٢,Q١‫א‬،‫א‬Q٠‫א‬،‫א‬‫א‬
                                                                   
              K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬




                                                  -١٣٩-
             ‫א‬‫א‬‫א‬                                   ‫٧٤١ א‬                                   ‫א‬
           ‫א‬‫א‬‫א‬‫א‬                        ‫א‬                            



                                        ‫א‬‫א‬‫א‬L‫א‬‫א‬‫א‬‫א‬‫א‬٣J ١٠J ٤
   Asynchronous Binary Up/Down Counters
  ‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
  Q‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                              K Q ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
L‫א‬E٣٤J ٤F
                                      K UP / DOWN ‫א‬‫א‬AND-OR
                                                                                                                                

                             Q                           Q                                  Q                                   Q
                                 0                        1                                     2                                   3
    HIGH

                 FF٠                            FF١                             FF٢                                 FF٣
                   Q                               Q                              Q                                   Q
            J            0                    J     1                      J            2                      J            3
 Clock
                CK                             CK                              CK                                  CK
 Input

            K        Q                        K     Q                      K        Q                          K        Q
                         0                           1                                  2                                   3
   UP/DOWN control




                                       K‫א‬‫א‬‫א‬‫א‬E٣٤J ٤F

                                                                                                                   
  ‫א‬AND‫א‬‫א‬،High‫א‬ UP / DOWN ‫א‬‫א‬
  ‫א‬‫א‬‫א‬‫א‬Q،(Enabled)‫א‬
  ‫א‬‫א‬،‫א‬‫א‬‫א‬،‫א‬
  ‫א‬‫א‬‫א‬‫א‬‫א‬،Low‫א‬ UP / DOWN
 (Enabled)‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬(Disabled)‫א‬
                                   
  ‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬ Q 
                                                                                                          K‫א‬




                                                              -١٤٠-
         ‫א‬‫א‬‫א‬                                                 ‫٧٤١ א‬                                                     ‫א‬
      ‫א‬‫א‬‫א‬‫א‬                                          ‫א‬                                        



Asynchronous Decade (MOD ١٠) Counters ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬٤J ١٠J ٤


‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬EF٣٥J ٤
                                                                                                                      K(MOD-١٠)‫א‬‫א‬
                                                                                                                                                 
       HIGH                                                                                                                                             
                           FF٠                               FF١                                     FF٢                          FF٣

                      J          Q
                                     0
                                                        J              Q
                                                                        1
                                                                                             J               Q
                                                                                                                 2
                                                                                                                             J          Q
                                                                                                                                            3           
       Clock
       Input              CK                                CK                                   CK                              CK
                                                                                                                                                        
                      K                                  K                                       K                            K
                           CLR                               CLR                                     CLR                          CLR
                                                                                                                                                        

                                         Q                                   Q                                       Q                          Q
                                                                                                                                                        
                                             0                                1                                          2                          3
                                                                                  E F
                                                                                                                                                        
                                                             ١     ٢     ٣   ٤    ٥      ٦   ٧       ٨   ٩
                                                        ١٠
                                                 Clock
                                                 Input
                                                                                                                                                        
                                                             ٠
                                                   Q٠                                                                                                   
                                                             ٠
                                                   Q١
                                                                                                                                                        
                                                   Q٢        ٠
                                                                                                                                                        
                                                   Q٣        ٠
                                                                                                                                                        
                                                 CLR


                                                                                 EF
                                                                                                                                                        

           K‫א‬‫א‬‫א‬‫א‬E٣٥J ٤F

                                                                                                                                                




                                                                         -١٤١-
          ‫א‬‫א‬‫א‬                        ‫٧٤١ א‬                             ‫א‬
        ‫א‬‫א‬‫א‬‫א‬                ‫א‬                   



‫א‬E٩F١٠٠١E٠F٠٠٠٠‫א‬‫א‬‫א‬
‫א‬‫א‬EF٣٥J ٤‫א‬‫א‬
                                                                                    KE١٣J ٤F
‫א‬‫א‬١٠F١١١١ ١٠١٠‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬E CLR F‫א‬‫א‬‫א‬‫א‬NAND ‫א‬E١٥
‫א‬‫א‬KQ٣‫א‬‫א‬Q١‫א‬‫א‬‫א‬K‫א‬
                                                      
،High‫א‬Q٣,Q١E‫א‬‫א‬١٠F١٠١٠‫א‬
‫א‬K‫א‬ (CLEAR)Low NAND‫א‬
‫א‬(inactive) CLR ‫א‬EF٣٥J ٤‫א‬
‫א‬KHigh‫א‬Q٣,Q١‫א‬‫א‬‫א‬‫א‬K١٠٠١٠٠٠٠
‫א‬‫א‬‫א‬‫א‬(CLEAR)،Q٣،Q١‫א‬
E١٣J ٤F‫א‬‫א‬‫א‬‫א‬‫א‬K CLR ‫א‬‫א‬
                  K‫א‬٩‫א‬٠‫א‬‫א‬،‫א‬‫א‬
                                                                                             

                                       ‫א‬‫א‬              ‫א‬
                                    Q٣   Q٢     Q١       Q٠
                                    ٠    ٠      ٠        ٠        ٠
                                    ٠    ٠      ٠        ١        ١
                                    ٠    ٠      ١        ٠        ٢
                                    ٠    ٠      ١        ١        ٣
                                    ٠    ١      ٠        ٠        ٤
                                    ٠    ١      ٠        ١        ٥
                                    ٠    ١      ١        ٠        ٦          Cycle Repeats
                                    ٠    ١      ١        ١        ٧
                                    ١    ٠      ٠        ٠        ٨
                                    ١    ٠      ٠        ١        ٩
                                          Binary Count                                                  

                        K‫א‬‫א‬‫א‬‫א‬‫א‬E١٣J ٤F




                                                 -١٤٢-
             ‫א‬‫א‬‫א‬                                        ‫٧٤١ א‬                                              ‫א‬
           ‫א‬‫א‬‫א‬‫א‬                                ‫א‬                              



(MOD-١٠)٩٠‫א‬‫א‬‫א‬‫א‬
            1
(           
              ) Q٣‫א‬،‫א‬‫א‬‫א‬
           10
                                                            .(Clock input)‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬(Digital Voltmeter)‫א‬‫א‬ ،(Digital clocks)‫א‬‫א‬‫א‬
                                                                                                 K(Frequency Counter)‫א‬
                         Synchronous Binary Counters ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬٥J ١٠J ٤
AND‫א‬J-K‫א‬‫א‬EF٣٦J ٤
‫א‬‫א‬(MOD-١٦) (٤-bit)‫א‬‫א‬‫א‬‫א‬
                                                          
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬EF‫א‬‫א‬
                                         
‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬(Triggered)
     K‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬
                                                                                                                                 
                                                     Q                        Q                           Q                              Q
                                                         0                     1                              2                              3


                         HIGH
                                                                                   A                              B
                                       FF٠                       FF١                        FF٢                            FF٣

                                 J           Q               J          Q              J          Q                   J          Q
                                                 0                       1                            2                              3
                                      CK                         CK                        CK                             CK


                   Clock          K                          K                         K                              K
                   Input
            
                         K‫א‬‫א‬‫א‬E٣٦J ٤F

FF٠‫א‬‫א‬J,K‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                       
‫א‬(Toggle)‫א‬،High‫א‬
  Low‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                                    K‫א‬LowHighHigh



                                                                      -١٤٣-
                   ‫א‬‫א‬‫א‬                                      ‫٧٤١ א‬                                            ‫א‬
                 ‫א‬‫א‬‫א‬‫א‬                              ‫א‬                                



      ‫א‬‫א‬٢‫א‬‫א‬‫א‬ FF١‫א‬‫א‬J,K‫א‬
                                                                
      FF١‫א‬‫א‬Q١‫א‬،Low‫א‬Q٠‫א‬‫א‬KFF٠
      Q١‫א‬،High‫א‬Q٠‫א‬(No change)
                                                                                                                        K(Toggle)
      AND(A)‫א‬‫א‬ FF٢‫א‬‫א‬J,K‫א‬
             
      ،High AND(A)‫א‬Q٠ = Q١ = High‫א‬KQ٠,Q١
                                        K‫א‬‫א‬FF٢‫א‬‫א‬(Enable) ‫א‬‫א‬
                                                                                                  
      ‫א‬AND(B)‫א‬‫א‬FF٣‫א‬‫א‬J,K‫א‬
      AND(B)‫א‬High‫א‬Q٢,Q١,Q٠‫א‬KQ٢,Q١,Q٠
                                                                                            
                                                         K‫א‬FF٣‫א‬‫א‬ ‫א‬‫א‬High
                                   Synchronous Counters Advantages ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ٦J ١٠J ٤
      (Ripple counters)‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
      ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬
                                                 KEF٣٣J ٤‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬EF٣٢J ٤
      ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                    
      ‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬K‫א‬
                                                                    
‫א‬‫א‬K ‫א‬‫א‬‫א‬
      ‫א‬‫א‬‫א‬‫א‬ (Propagation-delay time)
                                                                            K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
     ‫א‬‫א‬‫א‬‫א‬
                                                                    
      ‫א‬‫א‬F‫א‬‫א‬‫א‬ ،‫א‬‫א‬‫א‬
                                                                     
      ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬KE
                                                                         
      ‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬
                              
      ‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬
         K‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬




                                                                         -١٤٤-
         ‫א‬‫א‬‫א‬                     ‫٧٤١ א‬                              ‫א‬
       ‫א‬‫א‬‫א‬‫א‬             ‫א‬                    



                                                                
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                       
‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬
                                                         W‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                                            
       tp = Single (flip-flop) tp + Single (AND-gate) tp



                                            
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                                            
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                                            
                                            
                                            
                                            
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                                                -١٤٥-
          ‫א‬‫א‬‫א‬                              ‫٧٤١ א‬                           ‫א‬
        ‫א‬‫א‬‫א‬‫א‬                      ‫א‬                



                                                 
                                                      
                
‫א‬‫א‬‫א‬‫א‬S-R‫א‬‫א‬(Q)‫א‬‫א‬E١
‫א‬‫א‬‫א‬(negative edge trigger)‫א‬‫א‬
        K‫א‬‫א‬Q=٠‫א‬‫א‬‫א‬K


          CK



             S



             R


‫א‬‫א‬‫א‬‫א‬D‫א‬‫א‬‫א‬(Q)‫א‬‫א‬E٢
K‫א‬‫א‬‫א‬(positive edge trigger)‫א‬‫א‬
                       K‫א‬‫א‬Q=٠‫א‬‫א‬‫א‬
                                                                                                           

            CK




               D


‫א‬‫א‬‫א‬‫א‬JK‫א‬‫א‬(Q)‫א‬‫א‬E٣
‫א‬K‫א‬‫א‬‫א‬(negative edge trigger)‫א‬‫א‬
                                   K‫א‬‫א‬Q=٠‫א‬‫א‬
                                                                                                           

                                                       -١٤٦-
          ‫א‬‫א‬‫א‬                         ‫٧٤١ א‬                              ‫א‬
        ‫א‬‫א‬‫א‬‫א‬                 ‫א‬                    




             CK
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                 J
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‫א‬‫א‬‫א‬‫א‬T‫א‬‫א‬‫א‬(Q)‫א‬‫א‬E٤
‫א‬‫א‬‫א‬(negative edge trigger)‫א‬‫א‬
        K‫א‬‫א‬Q=٠‫א‬‫א‬‫א‬K


         CK



             T


                                 
‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬٥٥٥‫א‬‫א‬(f)‫א‬‫א‬ E٥
                                          KC = ٠{١µf‫א‬،RB = ٣kΩ‫א‬RA = ١٠kΩ

‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬٥٥٥‫א‬‫א‬ E٦
                                                      KC = ٠{٠١µf‫א‬،ΩRA = ١٢kΩ‫א‬




                                                  -١٤٧-
                                                ‫א‬‫א‬‫א‬
                                             ã¹]<gè…‚jÖ]æ<ËÖ]<Üé×Ãj×Ö<íÚ^ÃÖ]<퉉ö¹]
                                                 ‫א‬‫א‬‫א‬‫א‬




                             ‫א‬
                         ‫א‬‫א‬
 ‫א‬‫א‬




٥


                                   - ١٣٣ -
 ‫א‬‫א‬                  ‫٧٤١ א‬                               ‫א‬
‫א‬‫א‬            ‫א‬                     



                        ‫א‬‫א‬‫א‬
                                  
                                       W‫א‬‫א‬
                       K‫א‬‫א‬‫א‬ •
                         K‫א‬‫א‬‫א‬‫א‬ •
                           K‫א‬‫א‬‫א‬ •
                                                K‫א‬‫א‬‫א‬ •
                          K‫א‬‫א‬‫א‬ •




                                  - ١٤٨ -
             ‫א‬‫א‬                           ‫٧٤١ א‬                                 ‫א‬
            ‫א‬‫א‬                     ‫א‬                       



                                                                          Introduction١J ٥
                
    ‫א‬K،‫א‬‫א‬‫א‬‫א‬‫א‬
    ‫א‬(fuse–programmable) ‫א‬‫א‬‫א‬
      
   K‫א‬‫א‬‫א‬(Customer)‫א‬
    ‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬(fusible links)‫א‬
                                                      
    K‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬
                                                                      W‫א‬‫א‬
          (The Programmable Logic Array (PLA))‫א‬‫א‬‫• א‬
           (The Programmable Array Logic (PAL))‫א‬‫א‬                   •
         (The Programmable Logic Sequencer (PLS))‫א‬‫א‬‫• א‬
                                                  ‫א‬‫א‬‫• א‬
            (Erasable Programmable Logic Device (EPLD))
    ‫א‬‫א‬‫א‬ ‫א‬ (F)
(FPLA, FPAL, ….)
                                                                      K(Field Programmable Logic Devices)
           Basic Programmable Logic Devices ‫א‬‫א‬‫א‬٢J ٥
PLDJ ‫א‬‫א‬‫א‬‫א‬E١J ٥F‫א‬
            
    ‫א‬،‫א‬‫א‬‫א‬‫א‬K(٢-input/٤-output)
    (noninverting Buffer)‫א‬‫א‬‫א‬‫א‬
                                                                           K(Inverting Buffer)‫א‬
                                                                      
    A,B ‫א‬‫א‬‫א‬‫א‬‫א‬High  AND‫א‬
‫א‬‫א‬AND‫א‬‫א‬،E١J ٥F‫א‬
                                                    
    ‫א‬،‫א‬،(Product Lines)
    ‫א‬K‫( א‬A B, AB, AB and AB) 
    (fusible link)OR‫א‬‫א‬
                                   .PLDJ ‫א‬‫א‬(×)‫א‬‫א‬،E١J ٥F
                                                                                                                

                                                       - ١٤٩ -
 ‫א‬‫א‬                          ‫٧٤١ א‬                                        ‫א‬
‫א‬‫א‬                 ‫א‬                                 



              Inputs                        
                                            
        A              B
                                            
                                                                  Fusible
                                                                   Link
                                            
          A       A    B    B               
                                    ٠  ×                 ×         ×         ×            AB

                                    ١          ×         ×           ×       ×            AB

                                    ٢           ×            ×         ×         ×        AB
                                            
                                    ٣                 ×        ×          ×        ×       AB
                                            
                                            
                                            
                                                Q3           Q2        Q1        Q0
                                            
                                                              Outputs
                                            
             KPLD‫א‬‫א‬‫א‬E١J ٥F
                                            
                                            
                                A       B       High Out
                                ٠       ٠        AND ٠
                                ٠       ١        AND ١
                                ١       ٠        AND ٢
                                ١       ١        AND ٣

                                            
     KE١J ٥F‫א‬AND‫א‬‫א‬E١J ٥F
                                            

                                            - ١٥٠ -
        ‫א‬‫א‬                          ‫٧٤١ א‬                              ‫א‬
       ‫א‬‫א‬                    ‫א‬                    



‫א‬‫א‬‫א‬،E١J ٥F‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬PLDs J ‫א‬K‫א‬
                                                                                      
                                                                          
‫א‬‫א‬E١J ٥F‫א‬‫א‬E٢J ٥FK‫א‬‫א‬‫א‬
                                                                                             K‫א‬
                Inputs                           
                                                 
          A                       B
                                                                                             
                                                                                             
                                                                                             
      A       A               B       B                                                      
                                          ٠           ×        ×      ×        ×         AB

                                          ١           ×        ×      ×        ×         AB

                                                      ×        ×      ×        ×         AB
                                                                                             
                                          ٢
                                                                                             
                                          ٣           ×        ×      ×        ×         AB
                                                                                             
                                                                                             
                                                       I٣
                                                                                             
                                                      Q3       Q2    Q1      Q0              
                                                                                             
                                                                Outputs
                                                                                             
               KPLD‫א‬‫א‬E٢J ٥F                        
                                                                                             
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬
          
AND ‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬،
                                       
‫א‬،‫א‬‫א‬‫א‬
 OR ‫א‬‫א‬‫א‬K‫א‬‫א‬
                                                                 
K(fusible link)‫א‬(×’s)‫א‬‫א‬

                                                 - ١٥١ -
          ‫א‬‫א‬                             ‫٧٤١ א‬                                 ‫א‬
        ‫א‬‫א‬                        ‫א‬                       



  ×’s‫א‬‫א‬‫א‬،OR, AND‫א‬‫א‬
                                                                                                     K‫א‬
K‫א‬‫א‬PLD ‫א‬‫א‬‫א‬‫א‬
 (Q٠,Q١,Q٢,Q٣)A,B‫א‬E٣J ٥F
                                            KE٢J ٥F‫א‬،PLD‫א‬
                                                                                                    
                   Inputs                             
                                                                                                     
              A                    B
                                                                                                     
                                                                                                     
                                                                                                     
          A       A            B       B                                                             
                                               ٠                           ×        ×         AB 

                                               ١          ×         ×                         AB 

                                               ٢                                    ×        AB 
                                                                                                     
                                               ٣                    ×                        AB
                                                                                                     
                                                                                                     
                                                          ٣         ٢      ١        ٠
                                                                                                     
                                                                                                     
                                                                                                     
                                                                               Q 0 = A B + AB
                                                                        Q1 = AB             
                                                                 Q 2 = AB + AB              
                                                          Q 3 = AB                          
                                                                                                     
                  KPLD‫א‬‫א‬E٣J ٥F 



                                                      - ١٥٢ -
          ‫א‬‫א‬                                   ‫٧٤١ א‬                                      ‫א‬
        ‫א‬‫א‬                              ‫א‬                            



                                
Q٣ ‫א‬،٣OR ‫א‬١،٣،٤(blowing fuses)‫א‬‫א‬
                   
،٢ OR ‫א‬١،٣‫א‬‫א‬KAB = ٠١  High 
٢،٣،٤‫א‬‫א‬KAB = ١١ AB = ٠١ High Q٢ ‫א‬
                  
‫א‬KAB = ٠٠HighQ١‫א‬،١OR‫א‬
                        
  High Q٠‫א‬،٠‫א‬٢،٤‫א‬‫א‬
                                                                                               KAB = ١٠AB = ٠٠
                                                                                                                 
                                                                                                                 
                                             ‫א‬                           ‫א‬

                                            A        B          Q٣        Q٢     Q١      Q٠
                                  AB        ٠        ٠          ٠         ٠          ١    ١
                                  AB        ٠        ١          ١         ١          ٠    ٠
                                  AB        ١        ٠          ٠         ٠          ٠    ١
                                  AB        ١        ١          ٠         ١          ٠    ٠

                                                            
                   KE٣J ٥F‫א‬‫א‬‫א‬E٢J ٥F
                                                            
‫א‬‫א‬ ‫א‬PLD ‫א‬
                                                                                                  
 XOR ‫א‬(Programmable Output Polarity fuse)
‫א‬‫א‬‫א‬‫א‬،E٤J ٥F
                                 K(blown)(Intact)‫א‬
Low XOR ‫א‬‫א‬‫א‬،‫א‬‫א‬
                                       
XOR ‫א‬‫א‬‫א‬،‫א‬‫א‬K‫א‬‫א‬‫א‬
                                                              
                                       K‫א‬‫א‬‫א‬ High
                                                                 KE٣J ٥F‫א‬‫א‬



                                                            - ١٥٣ -
       ‫א‬‫א‬                              ‫٧٤١ א‬                              ‫א‬
      ‫א‬‫א‬                     ‫א‬                       



                                                                                                
                                                                                                
                                                               ×
                                                                                                
                                                               ×
                                                                                                
                                                                                                
                                                                                                
                                                                                                
                              Polarity                                                          
                                 Fuse
                                                                                                
                                                       Output                                   
                                                                                                
                        KPLD‫א‬‫א‬E٤J ٥F
                                                                                                
                                                                                                
                Polarity FuseE‫א‬F                    XOR's Operation

                        Intact E‫א‬F           Will not invert E‫א‬F
                   Blown E‫א‬F                  Will invert E‫א‬F
                                              
              K‫א‬‫א‬‫א‬E٣J ٥F
                                              
                The Programmable Logic Array (PLA) ‫א‬‫א‬‫א‬٣J ٥
                                           
،‫א‬‫א‬‫א‬‫א‬
(٢-bit outputs)(٨-bit inputs) PLD
                          K (٢٥٦) ‫א‬‫א‬(١٢)
K(PLA)‫א‬‫א‬،‫א‬
      
 PLA ‫א‬‫א‬E٥J ٥F‫א‬PLA‫א‬‫א‬‫א‬
OR  AND 
                                                              K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                   - ١٥٤ -
          ‫א‬‫א‬                              ‫٧٤١ א‬                                    ‫א‬
        ‫א‬‫א‬                         ‫א‬                          



                                                                                                         
                                     I٣   I٢   I١   I٠   

                                                         
                                                         
                                 × ×× × × ×× ×               ×      ×     ×     ×
                                 × × × × × ×× ×               ×      ×     ×     ×
                                 × ×× × × ×× ×               ×      ×     ×     ×
                                 × × × × × ×× ×               ×      ×     ×     ×
                                                         
                                 × × × × × ×× ×               ×      ×     ×     ×
                                 × × × × × ×× ×              ×      ×     ×     ×
                                 × × × × × ×× ×               ×      ×     ×     ×
                                 × × × × × ×× ×                     ×           ×
                                                              ×            ×
                                 × × × × × ×× ×              ×      ×     ×     ×
                                 × × × × × ×× ×               ×      ×     ×     ×
                                 × × × × × ×× ×              ×      ×     ×     ×
                                 × ×× × × ×× ×               ×      ×     ×     ×
                                 × × × × × ×× ×               ×      ×     ×     ×
                                 × × × × × ×× ×              ×      ×     ×     ×
                                 × × × × × ×× ×              ×      ×     ×     ×
                                 × × × × × ×× ×               ×      ×     ×     ×
                                                         
                                                         
                                                                     O٣     O٢ O١ O٠
                                                  
                                KPLA‫א‬‫א‬‫א‬E٥J ٥F
                                                  
                                                         
                   The Programmable Array Logic (PAL)‫א‬‫א‬ ٤J ٥
ANDEPLAF‫א‬‫א‬‫א‬
                                 
 PLA ‫א‬‫א‬K‫א‬‫א‬OR 
   
K‫א‬‫א‬،،‫א‬‫א‬‫א‬‫א‬
 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
OR AND،PAL ‫א‬
                            KE٦J ٥FE‫א‬F
                                                         - ١٥٥ -
        ‫א‬‫א‬                               ‫٧٤١ א‬                              ‫א‬
       ‫א‬‫א‬                      ‫א‬                       



                                               
                                  I٣ I٢   I١   I
                                                ٠

                                                          OR 

                                              
                                 × ×× × × ×××
                                 × ×× × × × × ×
                                 × × × × × × ××
                                 × ×× × × ×××
                                 × ×× × × × × ×
                                 × ×× × × ×××
                                 × ×× × × ×××
                                 × ×× × × ×× ×
                                 × ×× × × ×××
                                 × ×× × × × × ×
                                 × ×× × × ×××
                                 × ×× × × ×××
                                 × ×× × × × × ×
                                 × ×× × × ×××
                                 × ×× × × ×××
                                 × ×× × × ×× ×
                                              
                                                                                                  
                              AND
                                                                   O٣    O٢   O١     O٠           
                                                                                                  
                                 KPAL‫א‬‫א‬‫א‬E٦J ٥F
                                                                                                  
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬PLA‫א‬
                     K،‫א‬
                                                                                                  
                                                                                                  




                                                     - ١٥٦ -
         ‫א‬‫א‬                                ‫٧٤١ א‬                                     ‫א‬
        ‫א‬‫א‬                          ‫א‬                          



                The Programmable Logic Sequencer (PLS)‫א‬‫א‬‫א‬٥J ٥
‫א‬‫א‬‫א‬(PLS)‫א‬‫א‬‫א‬
      
‫א‬،‫א‬‫א‬K‫א‬
   K‫א‬‫א‬‫א‬‫א‬‫א‬،(Input and output registers)

                                                          ‫א‬‫א‬‫א‬٦J ٥
 Erasable Programmable Logic Device (EPLD)
‫א‬(PLDs)‫א‬‫א‬‫א‬
،‫א‬K(blowing their internal fuses)‫א‬‫א‬‫א‬‫א‬
                                                 
‫א‬،‫א‬
         
‫א‬K‫א‬‫א‬‫א‬‫א‬PLD‫א‬
            
K ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬(erase)‫א‬
                  K،‫א‬‫א‬‫א‬




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                                                        - ١٥٧ -
        ‫א‬‫א‬                               ‫٧٤١ א‬                               ‫א‬
       ‫א‬‫א‬                      ‫א‬                       



                                              
Q٠,Q١,Q٢,Q٣A, B‫א‬PLD‫א‬‫א‬ E١
                                                                     K‫א‬


                              ‫א‬                                 ‫א‬

                         A             B       Q٣              Q٢           Q١     Q٠
                         ٠             ٠        ٠               ١           ١       ١
                         ٠             ١        ١               ١           ٠       ٠
                         ١             ٠        ٠               ١           ٠       ١
                         ١             ١        ١               ٠           ٠       ٠



‫א‬‫א‬Q٠,Q٣‫א‬‫א‬‫א‬‫א‬‫א‬ E٢
                                                                                         K‫א‬
                                                                                                            
                                            KPLA‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ E٣
                                                                                                            
                                                                                                            
                                                                                                  



                                 
                                                                                                            
                                                                                                            



                                                     - ١٥٨ -
 ‫א‬                            ‫٧٤١ א‬                                     ‫א‬
                                    ‫א‬                           



                                     ‫א‬

      ‫א‬                                                            ‫א‬
                                                                              
                                                          ‫א‬‫א‬W‫א‬‫א‬
                                                               ‫א‬‫א‬‫א‬
       ٢                                                                 ١J ١
            ٣                                            ‫א‬‫א‬‫א‬٢J ١
            ٤                                           ‫א‬‫א‬‫א‬٣J ١
            ٦                        ‫א‬‫א‬‫א‬‫א‬‫א‬٤J ١
            ٦         ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬١J ٤J ١
            ٧                 ‫א‬‫א‬‫א‬‫א‬‫א‬٢J ٤J ١
            ٩                       ‫א‬‫א‬‫א‬‫א‬‫א‬٥J ١
          ١٠                                 ‫א‬‫א‬‫א‬‫א‬٦J ١
          ١٠                                                  ‫א‬‫א‬١J ٦J ١
          ١٠                                                 ‫א‬‫א‬٢J ٦J ١
          ١١                               ‫א‬‫א‬‫א‬‫א‬‫א‬٧J ١
          ١٢                                          ‫א‬‫א‬‫א‬‫א‬٨J ١
          ١٣                                             ‫א‬‫א‬١J ٨J ١
          ١٣                                           ‫א‬‫א‬٢J ٨J ١
          ١٤                                           ‫א‬‫א‬٣J ٨J ١
          ١٤                          ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬٩J ١
          ١٥                                         ‫א‬‫א‬‫א‬١٠J ١
          ١٥                    ‫א‬‫א‬‫א‬‫א‬١J ١٠J ١
          ١٦                     ‫א‬‫א‬‫א‬‫א‬٢J ١٠J ١
          ١٦    ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬١J ٢J ١٠J ١
 ‫א‬                              ‫٧٤١ א‬                                        ‫א‬
                                      ‫א‬                              



        ١٦              ‫א‬‫א‬‫א‬‫א‬‫א‬٢J ٢J ١٠J ١
        ١٨                 ‫א‬‫א‬‫א‬‫א‬‫א‬ ٣J ١٠J ١
        ١٩                     ‫א‬‫א‬‫א‬‫א‬‫א‬٤J ١٠J ١
        ١٩                     ‫א‬‫א‬‫א‬‫א‬‫ א‬٥J ١٠J ١
        ٢٠                             ‫א‬‫א‬‫א‬‫א‬٦J ١٠J ١
        ٢٠                                               ‫א‬‫א‬١J ٦J ١٠J ١
        ٢٢                                  ‫א‬‫א‬‫א‬٢J ٦J ١٠J ١
        ٢٣                                    ‫א‬‫א‬‫א‬‫א‬١١J ١
        ٢٣                      ‫א‬‫א‬‫א‬‫א‬١J ١١J ١
        ٢٣                   ‫א‬‫א‬‫א‬‫א‬٢J ١١J ١
             ‫א‬‫א‬‫א‬‫א‬‫א‬١J ٢J ١١J ١
        ٢٣
                                                                          ‫א‬‫א‬
        ٢٤     ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬٢J ٢J ١١J ١
        ٢٥                     ‫א‬‫א‬‫א‬‫א‬٣J ١١J ١
        ٢٦            ‫א‬‫א‬‫א‬‫א‬‫א‬ ٤J ١١J ١
        ٢٧            ‫א‬‫א‬‫א‬‫א‬‫ א‬٥J ١١J ١
        ٢٨           ‫א‬‫א‬‫א‬‫א‬‫א‬ ٦J ١١J ١
        ٢٩           ‫א‬‫א‬‫א‬‫א‬‫א‬ ٧J ١١J ١
        ٢٩                ‫א‬‫א‬‫א‬‫א‬‫א‬٨J ١١J ١
        ٢٩                        ‫א‬‫א‬‫א‬‫א‬١J ٨J ١١J ١
        ٣٠                       ‫א‬‫א‬‫א‬‫א‬٢J ٨J ١١J ١
 ‫א‬              ‫٧٤١ א‬                                          ‫א‬
                      ‫א‬                               




        ٣١                                                        
                               ‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬
        ٣٥                                         ‫א‬‫א‬‫א‬
        ٣٦                                                     ١J ٢
        ٣٦                             ‫א‬‫א‬٢J ٢
        ٣٧                                       AND‫א‬٣J ٢
        ٤٠                                         OR‫א‬ ٤J ٢
        ٤٢                              E‫א‬F NOT ‫א‬٥J ٢
        ٤٢                                      NAND ‫א‬٦J ٢
        ٤٤                                       NOR ‫א‬٧J ٢
        ٤٥                       E‫א‬F‫ א‬OR ‫א‬٨J ٢
        ٤٧                    E‫א‬F‫ א‬NOR ‫א‬٩J ٢
        ٤٨                               ‫א‬‫א‬‫א‬١٠J ٢
        ٥٠                     ‫א‬‫א‬‫א‬١١J ٢
        ٥١         ‫א‬‫א‬‫א‬‫א‬١٢J ٢
        ٥٢            ‫א‬‫א‬١٣J ٢
        ٥٤             ‫א‬‫א‬‫א‬١٤J ٢
        ٥٥    ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬١٥J ٢
        ٥٨                                                     
                              ‫א‬‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬
        ٦١                                         ‫א‬‫א‬‫א‬
        ٦٢                                                  ١J ٣
        ٦٢                                   ٣J ٢
        ٦٤            NOR , NAND‫א‬‫א‬‫א‬‫א‬٣J ٣
        ٦٥            NAND‫א‬‫א‬١J ٣J ٣
 ‫א‬                             ‫٧٤١ א‬                                         ‫א‬
                                     ‫א‬                               



        ٦٦                             NOR‫א‬‫א‬٢J ٣J ٣
                                      
             ،NAND‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬٤J ٣
        ٦٧
                                                                                NOR
        ٦٧                  NAND‫א‬‫א‬‫א‬١J ٤J ٣
        ٦٩                           NOR‫א‬‫א‬‫א‬٢J ٤J ٣
        ٧٢                                                         ٥J ٣
        ٧٣                                    ‫א‬‫א‬‫א‬٦J ٣
        ٨١                                             ‫א‬‫א‬‫א‬‫א‬٧J ٣
        ٨١                                            ‫א‬‫א‬‫א‬١J ٧J ٣
        ٨٢                                            ‫א‬‫א‬‫א‬٢J ٧J ٣
        ٨٥                                        ‫א‬‫א‬‫א‬٣J ٧J ٣
        ٨٧                                             ‫א‬‫א‬‫א‬٤J ٧J ٣
        ٩٠                                                                    
                                                                                         
                                              ‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬‫א‬
        ٩٢                                                          ‫א‬‫א‬‫א‬
        ٩٣                                                                  ١J ٤
        ٩٣                                                              ‫א‬٢J ٤
        ٩٨                                                 ‫א‬‫א‬S-R‫א‬٣J ٤
       ١٠١                                              D ‫א‬‫א‬‫א‬٤J ٤
       ١٠٣                                                 ‫א‬‫א‬J-K‫א‬٥J ٤
       ١٠٥                                              T ‫א‬‫א‬‫א‬٦J ٤
       ١٠٦                                                  ‫א‬–‫א‬٧J ٤
       ١١٤                                               ‫א‬‫א‬٨J ٤
       ١١٤                          ‫א‬‫א‬‫א‬‫א‬‫א‬١J ٨J ٤
       ١١٥                 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬٢J ٨J ٤
 ‫א‬                       ‫٧٤١ א‬                                       ‫א‬
                               ‫א‬                             



       ١١٦                                       ٥٥٥‫א‬‫א‬٣J ٨J ٤
       ١١٦         ‫א‬‫א‬‫א‬‫א‬٥٥٥‫א‬١J ٣J ٨J ٤
       ١١٩       ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬٢J ٣J ٨J ٤
       ١٢١                                               ‫א‬‫א‬٩J ٤
       ١٢٢                                         ‫א‬١J ٩J ٤
       ١٢٤                                        ‫א‬‫א‬٢J ٩J ٤
       ١٢٥    ‫א‬‫א‬–‫א‬‫א‬‫א‬‫א‬١J ٢J ٩J ٤
       ١٢٧     ‫א‬‫א‬–‫א‬‫א‬‫א‬٢J ٢J ٩J ٤
       ١٢٨     ‫א‬‫א‬–‫א‬‫א‬‫א‬٣J ٢J ٩J ٤
       ١٢٩             E‫א‬F‫א‬‫א‬‫א‬٤J ٢J ٩J ٤
       ١٣١                                      ‫א‬٥J ٢J ٩J ٤
       ١٣٣                                                   ‫א‬‫א‬‫א‬١٠J ٤
       ١٣٣             ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬١J ١٠J ٤
       ١٣٧               ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬٢J ١٠J ٤
       ١٤٠    ‫א‬‫א‬‫א‬L‫א‬‫א‬‫א‬‫א‬‫א‬٣J ١٠J ٤
       ١٤١                        ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬٤J ١٠J ٤
       ١٤٣                 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬٥J ١٠J ٤
       ١٤٤                          ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ٦J ١٠J ٤
       ١٤٦                                                            
                                            ‫א‬‫א‬W‫א‬‫א‬
       ١٤٨                                                   ‫א‬‫א‬‫א‬
       ١٤٩                                                          ١J ٥
       ١٤٩                      ‫א‬‫א‬‫א‬٢J ٥
       ١٥٤                              ‫א‬‫א‬‫א‬٣J ٥
       ١٥٥                                     ‫א‬‫א‬ ٤J ٥
 ‫א‬         ‫٧٤١ א‬                                    ‫א‬
                 ‫א‬                          



       ١٥٧                    ‫א‬‫א‬‫א‬٥J ٥
       ١٥٧    ‫א‬‫א‬‫א‬٦J ٥
       ١٥٨                                           
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               ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

            ‫א‬E‫א‬F‫א‬‫א‬

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posted:2/23/2012
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Description: الكترونيات صناعيه وتحكم electronic circuits &control