2. Find Subtraction of 10110 and 11101 using 2's complementSolution:2's complement subtraction steps :
1. At first, find 2's complement of the B(subtrahend).
2. Then add it to the A(minuend).
3. If the final carry over of the sum is 1, then it is dropped and the result is positive.
4. If there is no carry over, then 2's complement of the sum is the final result and it is negative.
Here A = 10110, B = 11101.
Find A - B = ? using 2's complement
First find 2's complement of B = 11101
Note : 2's complement of a number is 1 added to it's 1's complement number.
Step-1: 1's complement of 11101 is obtained by subtracting each digit from 1
Step-2: Now add 1 :
00010 + 1 = 00011
Step-3: Now Add this 00011 to 10110
Step by step solution of 10110 + 00011 = 11001
Write the numbers, so that each digit lines up vertically
Step-1 :
`=0_2+1_2`
`=0_10+1_10`
`=1_10`
`=1_2`
Write the 1 in the sum place
Step-2 :
`=1_2+1_2`
`=1_10+1_10`
`=2_10`
`=2xx1+0`
`=10_2`
Write the 0 in the sum place and carry the 1 to the next carry place
Step-3 :
`=1+1_2+0_2`
`=1+1_10+0_10`
`=2_10`
`=2xx1+0`
`=10_2`
Write the 0 in the sum place and carry the 1 to the next carry place
Step-4 :
`=1+0_2+0_2`
`=1+0_10+0_10`
`=1_10`
`=1_2`
Write the 1 in the sum place
Step-5 :
`=1_2+0_2`
`=1_10+0_10`
`=1_10`
`=1_2`
Write the 1 in the sum place
Here there is no carry, answer is - (2's complement of the sum obtained 11001)
Note : 2's complement of a number is 1 added to it's 1's complement number.
Step-1: 1's complement of 11001 is obtained by subtracting each digit from 1
Step-2: Now add 1 :
00110 + 1 = 00111
So answer is -00111
This material is intended as a summary. Use your textbook for detail explanation.
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