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Problem: 2's complement subtraction 10110-11101 [ Calculator, Method and examples ]

Solution:
Your problem -> 2's complement subtraction 10110-11101

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.
1's complement of 11101 is
 1 1 1 1 1 - 1 1 1 0 1 0 0 0 1 0

Now add 1 : 00010 + 1 = 00011

Now Add this 2's complement of B to A

 1 1 1 0 1 1 0 + 0 0 0 1 1 1 1 0 0 1

Hints : (Move mouse over the steps for detail calculation highlight)
 Step-1=0+1=0+1=1=2xx0+1=1_2:. Sum=1 Step-2=1+1=1+1=2=2xx1+0=10_2:. Sum=0 and carry=1 Step-3=1+1+0=1+1+0=2=2xx1+0=10_2:. Sum=0 and carry=1 Step-4=1+0+0=1+0+0=1=2xx0+1=1_2:. Sum=1 Step-5=1+0=1+0=1=2xx0+1=1_2:. Sum=1

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.
1's complement of 11001 is
 1 1 1 1 1 - 1 1 0 0 1 0 0 1 1 0

Now add 1 : 00110 + 1 = 00111
So answer is -00111

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