BINARY ADDITION

Binary additions ais accomplished in a manner similar to that in the decimal number system. RULES:

1. 0+0=02. 0+1=13. 1+0=14. 1+1=105. 1+1+1=11

EXAMPLE:

10111010 +

10101

BINARY SUBTRACTION:Binary subtraction involves four basic rules which must be understood before

performing subtraction of larger binary members.

RULES:1. 0-0=02. 1-0=13. 1-1=04. 10-1=1

COLUMN BY COLUMN SUBTRACTION:To subtract large a binary numbers, we follow the same established system as

with the decimal numbers.

EXAMPLE:Subtract 1 0 1 0 from 1 1 0 0

1 1 0 01 0 1 0 _

0 0 1 0

1’s COMPLEMENT:

The 1’s complement of a binary number is the number that results when we change each 0 to a 1,and each 1 to a 0.

EXAMPLE:(a) The 1’s complement of 1 0 0 1. is 0 1 1 0

1’s Complement Subtraction:In 1’s complement subtraction the 1’s complement of the subtrahend is added to the minuend.Subtract 1 1 0 1 from 1 0 1 0

EXAMPLE:

1 1 0 1 11 0 0 1 0 +

1 0 1 1 0 1 1

+ 0 1 1 1 0

2’s COMPLEMENT :

The 2’s complement of a binary number is obtained by adding 1 to its 1’s complement .

FORMULA:2’s complement = 1’s complement +1

Ex:Number 2’s complement

1 1 1 0 0001+1=0010

0 0 0 1 1110+1=1111

2’s COMPLEMENT SUBTRACTION:In the 2’s complement subtraction as in the 1’s complement subtraction,

The 2’s complement of the subtrahend is added to the minuend, but the end-around Carry if generated, is disregared.

EXAMPLE:

1 1 1 0 1 1 +

1 0 1 0

{ discard in the carry 1}

9’s COMPLEMENT AND 10’s COMPLEMENT:

In the 9’s complement is found by subtracting each decimal digit from 9

9 9 9 9 6 2 9 1 _

3 7 0 8

{ the 9’s complement of 6 2 9 1 }

The 10’s complement of a decimal integer is 1 greater then the 9’s complement

10’s complement = 9’s complement +1

EXAMPLE;

9 9 9 9 6 2 9 1 _

3 7 0 8 +1=3709