2's Complement Subtraction Examples

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Home > College Algebra calculators > 2's Complement Subtraction example

2's Complement Subtraction example ( Enter your problem )

( Enter your problem )

Examples

Other related methods

1. 1's Complement Subtraction
(Previous method)

3. 7's Complement Subtraction
(Next method)

1. Examples

Method : 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.

1. Find Subtraction of 110 and 101 using 2's complement method

Here A = 110, B = 101.
Find A - B = ? using 2's complement
First find 2's complement of B = 101

Note : 2's complement of a number is 1 added to it's 1's complement number.
1's complement of 101 is



	1	1	1
-	1	0	1

	0	1	0

Now add 1 : 010 + 1 = 011

Now Add this 2's complement of B to A

1	1
	1	1	0
+	0	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`

The left most bit of the result is called carry and it is ignored.
So answer is 001

2. Find Subtraction of 10110 and 11101 using 2's complement method

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

This material is intended as a summary. Use your textbook for detail explanation.
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