Tutorial: ITI1100

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					Tutorial: ITI1100

  Dewan Tanvir Ahmed
     SITE, UofO




                       1
                       Decoders
Decoder - logic circuit that activates an output that corresponds
        to a binary number on the input (set of inputs).


       General Decoder Diagram




                       Demo
                                                                    2
                                     Decoder
•   A n-to-m decoder
                                 n
    – a binary code of n bits = 2 distinct information
                                n
    – n input variables; up to 2 output lines
    – only one output can be active (high) at any time




                                                         3
Three-line-to 8-line (or 1-of-8) decoder




                                           4
                           Decoder (cont..)
•   Expansion
    – two 3-to-8 decoder: a 4-to-16 deocder
    – a 5-to-32 decoder?




                                              5
                             Decoder (cont..)
– each output = a minterm
– use a decoder and an external OR gate to implement any Boolean function of n input
  variables
– A full-adder
    • S(x,y,x)=S(1,2,4,7)
    • C(x,y,z)= S(3,5,6,7)




                                                                                       6
                       Lab-3
Something like this:




                               7
            BCD to 7-Segment Display
              Design Requirements

 X3
                                                   a
                                    a

 X2           BCD to 7              b        f     g     b
                                    c

 X1           Segment               d
                                             e           c
                                    e

 X0           Decoder               f

                                    g              d




Design the logic circuitry that will drive a seven segment LED
 display and will be able to represent numbers from 0 to 9



                                                                 8
    Possible numbers and their representation on
                 7 segment display
      a                           a               a                                 a

f         b           b           g       b       g   b f       g       b       f   g

e             c       c       e                       c                 c               c

      d                           d               d                                 d

                  a           a                   a                 a

          f       g                   b       f   g   b     f       g       b


          e               c           c e             c                     c

                  d                               d
                                                                                        9
                    Truth Table
X3   X2   X1   X0     a   b   c   d   e   f   g
0    0    0    0      1   1   1   1   1   1   0
0    0    0    1      0   1   1   0   0   0   0
0    0    1    0      1   1   0   1   1   0   1
0    0    1    1      1   1   1   1   0   0   1
0    1    0    0      0   1   1   0   0   1   1
0    1    0    1      1   0   1   1   0   1   1
0    1    1    0      1   0   1   1   1   1   1
0    1    1    1      1   1   1   0   0   0   0
1    0    0    0      1   1   1   1   1   1   1
1    0    0    1      1   1   1   0   0   1   1
1    0    1    0      x   x   x   x   x   x   x
1    0    1    1      x   x   x   x   x   x   x
1    1    0    0      x   x   x   x   x   x   x
1    1    0    1      x   x   x   x   x   x   x
1    1    1    0      x   x   x   x   x   x   x
1    1    1    1      x   x   x   x   x   x   x


                                                  10
                   Signal b implementation

       X1X0
                                   b = f(X3, X2, X1, X0) =
X3X2          00    01   11   10


        00    1     1    1    1
                                        X1’X0’
        01    1     0    1    0       + X1X0

                                      + X2’
        11    X     X    X    X


        10    1     1    X    X



       X3


       X2


       X1                                        b

       X0
                                                             11
                    Signal c implementation


       X1X0
                                       c = f(X3, X2, X1, X0) =
X3X2          00        01   11   10


       00     1         1    1    0
                                            X1’+
       01     1         1    1    1       + X0

                                          + X2
       11     X         X    X    X


       10     1         1    X    X


                   X3


                   X2


                   X1


                   X0                       c
                                                                 12
                       7 segment display




• All the anode segments are connected together
• Power must be applied externally to the anode connection that is common
  to all the segments
• By applying the ground to a particular segment (i.e. a,b,g etc..), the
  appropriate segment will light up


                                                                       13
              7 segment common anode




• A resistor should be added in order to limit the current through
  LED
• The current to light the active LED is sink by the logic component,
  which is preferable
                                                                        14
                       7 segment display




•   All the cathode of the LED are connected together
•   The common connection must be grounded and power must be applied to
    appropriate segment in order to illuminate that segment
•   The current to light the active LED is generated by the logic component,
    which generates the logic 1

                                                                               15
                  BCD to 7 Segment Decoder/Drivers

•   Common-anode : requires VCC , LED ON when
    Output is LOW.

•   Common-cathode : NO VCC , LED ON when
    Output is HIGH.

•   TTL and CMOS devices are normally not used to
    drive the common-cathode display directly
    because of current (mA) requirement. A buffer
    circuit is used between the decoder chips and
    common-cathode display




                                                     16
                             7447 TTL IC
•   Real world example of BCD
    to 7 segment decoder
•   Outputs of the decoder are
    active low and a common
    anode 7 segment display is
    used




                                           17
                Lab: BCD to 7 Segment Decoder/Drivers

(a) BCD-to-7-segment
    decoder/driver
    driving a common-
    anode 7-segment
    LED display;

(b) segment patterns
    for all possible
    input codes.




                                                        18
               Multiplexers (Data Selectors)
•   A multiplexer (MUX) selects one of multiple input signals and passes it to the
    output.
•   The basic two input multiplexer
•   The four input multiplexer
•   The eight input multiplexer




                                                                                     19
                Multiplexers (Data Selectors)
•   A multiplexer (MUX)
    selects 1 out of N input
    data sources and
    transmits the selected
    data to a single output




                                                20
  Multiplexers
Two-input multiplexer




                        21
             Multiplexers
          Four-input multiplexer




Four-input multiplexer - using sum of products logic



                                                       22
        Multiplexers
Eight-input multiplexer: The 74151




                                     23
  Multiplexers
Eight-input multiplexer




                          24
Multiplexers (cont..)




                        25
         Boolean function implementation
– MUX: a decoder + an OR gate
   n
– 2 -to-1 MUX can implement any Boolean function of n input variable
– a better solution: implement any Boolean function of n+1 input variable
    • n of these variables: the selection lines
    • the remaining variable: the inputs




                                                                            26
                  Multiplexers (cont..)
– Example: F(A,B,C)=S(1,3,5,6)




                                          27
                   Multiplexers (cont..)
•   Procedure:
    – assign an ordering sequence of the input variable
    – the leftmost variable (A) will be used for the input lines
    – assign the remaining n-1 variables to the selection lines w.r.t. their corresponding
      sequence
    – list all the minterms in two rows (A' and A)
    – circle all the minterms of the function
    – determine the input lines




                                                                                     28
                     Multiplexers (cont..)
•   An example: F(A,B,C,D)=S(0,1,3,4,8,9,15)




                                               29
                                 Exercise
•   Try to build an inverter using 2-1 MUX
•   Try to build XOR gate using 4-1 MUX




                                             30
      Lab: Multiplexers




Four-input multiplexer - using sum of products logic



                                                       31
Thank You!




             32

				
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