# Computer_Arthimatics

Document Sample

```					     Computer
Fundamentals
Lecture 3 :Computer Arithmetic
2

Objectives
   After completing this module you will be able to:
 Perform basic arithmetic operations using
binary number system
 Explain the use of special memory locations in
CPU to keep track of the status of last
operation
 Signed and Unsigned Integers
 Sign-Magnitude

Computer Fundamentals (101)   Lecture 03 - Computer Arithmetic   © Sri Lanka Institute of Information Technology
3

Lecture Outline
   Binary Subtraction
   Number Representation
   Overflow & Underflow

Computer Fundamentals (101)   Lecture 03 - Computer Arithmetic   © Sri Lanka Institute of Information Technology
4

 0 + 0 = 0
 0 + 1 = 1
 1 + 0 = 1
 1 + 1 = 0, and carry 1 to the next more significant bit
 1 + 1 + 1 = 1, and carry 1 to the next more significant bit

Computer Fundamentals (101)   Lecture 03 - Computer Arithmetic   © Sri Lanka Institute of Information Technology
5

     101               5                             00011010 +                     26
+ 101              +5                             00001100                       12

1010                   10                      00100110                         38

Exercise
00010011 + 19                                        10001 + 11101
00111110 62

Computer Fundamentals (101)        Lecture 03 - Computer Arithmetic   © Sri Lanka Institute of Information Technology
6

1.     10001 + 11101 = ?
2.     1110 + 1111 = ?
3.     101101 + 11001 = ?
4.     10111 + 110101 = ?
5.     1011001 + 111010 = ?
6.     11011 + 1001010 = ?

Computer Fundamentals (101)   Lecture 03 - Computer Arithmetic   © Sri Lanka Institute of Information Technology
7

Computer Fundamentals (101)   Lecture 03 - Computer Arithmetic   © Sri Lanka Institute of Information Technology
8

Binary Subtraction
Rules of Binary Subtraction
 0 - 0 = 0
 0 - 1 = 1, and borrow 1 from the next more
significant bit
 1 - 0 = 1
 1 - 1 = 0

   Just like subtraction in any other base
Minuend                        10110
Subtrahend                     -10010
Difference                     00100

Computer Fundamentals (101)   Lecture 03 - Computer Arithmetic   © Sri Lanka Institute of Information Technology
9

Binary Subtraction
   And when a borrow is needed. Note that the borrow
gives us 2 in the current bit position.

   Try out these subtractions: Exercise: 2
0 2
00110011                                                    51
 00100101     37             - 00010110                                                   22
- 00010001 - 17
00010100      20             00011101                                                   29
Computer Fundamentals (101)   Lecture 03 - Computer Arithmetic   © Sri Lanka Institute of Information Technology
10

Binary Subtraction(Contd.)

Computer Fundamentals (101)   Lecture 03 - Computer Arithmetic   © Sri Lanka Institute of Information Technology
11

Binary Subtraction - Examples
   1011011 − 10010 = ?
   100010110 − 1111010 = ?
   1010110 − 101010 = ?
   101101 − 100111 = ?
   1000101 − 101100 = ?
   1110110 − 1010111 = ?

Computer Fundamentals (101)   Lecture 03 - Computer Arithmetic   © Sri Lanka Institute of Information Technology
12

Computer Fundamentals (101)   Lecture 03 - Computer Arithmetic   © Sri Lanka Institute of Information Technology
13

Overflow & Underflow
   Overflow
 Occurs when the result of an operation is too large to
store in the location allocated.
0 1100 12
0 0110 06
1 0010 18
   Underflow
   Occurs when the result of an operation is too small to
store in the location allocated.

Computer Fundamentals (101)   Lecture 03 - Computer Arithmetic   © Sri Lanka Institute of Information Technology
14

format)
1001 0110 +
1111 1001
11000 1111

   Since we have only 8 bit format the result has no
place to appear.
   Thus it generates an OVERFLOW.
   Unless we handle them we get wrong results.

Computer Fundamentals (101)   Lecture 03 - Computer Arithmetic   © Sri Lanka Institute of Information Technology
15

(Contd.)
 In the CPU there are special places to hold
these two important information.
 In computer processors the Carry flag
(usually indicated as the C Flag/ C bit) is a
single bit in a system status (flag) register
 It is used to indicate when an arithmetic
carry or borrow has been generated out of
the most significant bit position.

Computer Fundamentals (101)   Lecture 03 - Computer Arithmetic   © Sri Lanka Institute of Information Technology
16

 In computer processors, the oVerflow
flag (sometimes called V flag/ V bit) is
usually a single bit in a system status
register
 It is used to indicate when an arithmetic
overflow has occurred in an operation.
 These places in the CPU can be accessed
through a program.
   This means that when we design a program we need to
first have an understanding of the extent of the data
format that we are going to handle.

Computer Fundamentals (101)   Lecture 03 - Computer Arithmetic   © Sri Lanka Institute of Information Technology
17

Unsigned and Signed Integers
   Unsigned Integers : Unsigned integer is
either positive or zero value of an
integer.
   Example : The number of integers between
0 and + 127

   Signed Integer: signed integer is either
negative value or positive value of
the integer.
   Example : The number of integers between
- 128 and + 127

Computer Fundamentals (101)   Lecture 03 - Computer Arithmetic   © Sri Lanka Institute of Information Technology
18

Unsigned and Signed integers (Contd.)

Computer Fundamentals (101)   Lecture 03 - Computer Arithmetic   © Sri Lanka Institute of Information Technology
19

Sign-Magnitude
Sign-Magnitude Representation
    There are many schemes for representing
negative integers with patterns of bits.
     One scheme is sign-magnitude. It uses one bit
(usually the leftmost) to indicate the sign.
   "0“ - indicates a positive integer
   "1“ - indicates a negative integer

The rest of the bits are used for the magnitude
of    the number.
Eg. -2410 is represented as: 1001 1000

Computer Fundamentals (101)     Lecture 03 - Computer Arithmetic   © Sri Lanka Institute of Information Technology
20

Sign-Magnitude
 Sign-Magnitude Representation
Sign Bit
0000 1001          1000 1001
+9                                                -9

 Problem: two values for zero
0000 0000              1000 0000
 8-bit number can represent from
-127 (1111 1111) to +127 (0111 1111)

Computer Fundamentals (101)     Lecture 03 - Computer Arithmetic   © Sri Lanka Institute of Information Technology
21

Number Representation
001011                    +01011
001110                    +01110
+11001                               011001

001011                     +01011
100110                     -00110
+00101                               000101

Computer Fundamentals (101)   Lecture 03 - Computer Arithmetic   © Sri Lanka Institute of Information Technology
22

Number Representation
001011                         +01011
110110                    +    -10110
-01011                               101011
Subtraction
001011                          +01011
001001                        - +01001
+00010                              000010

Computer Fundamentals (101)        Lecture 03 - Computer Arithmetic   © Sri Lanka Institute of Information Technology
23

Thank You
Next Lecture

Lecture 04: Complimentary Arithmetic

Computer Fundamentals (101)   Lecture 03 - Computer Arithmetic   © Sri Lanka Institute of Information Technology

```
DOCUMENT INFO
Shared By:
Categories:
Tags:
Stats:
 views: 1 posted: 4/13/2012 language: English pages: 23