2. Find Subtraction of 10110 and 11101 using 1's complementSolution:1's complement subtraction steps :
1. At first, find 1'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 1 is added to the result.
4. If there is no carry over, then 1's complement of the sum is the final result and it is negative.
Here A = 10110, B = 11101.
Find A - B = ? using 1's complement
First find 1's complement of B = 11101
Note : 1's complement of a number is obtained by subtracting all bits from 11111
Step-1: 1's complement of 11101 is obtained by subtracting each digit from 11111
Step-2: Now Add this 00010 to 10110
Step by step solution of 10110 + 00010 = 11000
Write the numbers, so that each digit lines up vertically
Step-1 :
`=0_2+0_2`
`=0_10+0_10`
`=0_10`
`=0_2`
Write the 0 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 - (1's complement of the sum obtained 11000)
Note : 1's complement of a number is obtained by subtracting all bits from 11111
Step-1: 1's complement of 11000 is obtained by subtracting each digit from 11111
So answer is -00111
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