1's Complement Subtraction Example 10100

4. Find Subtraction of 10100 and 11010 using 1's complement

Solution:

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 = 10100, B = 11010.
Find A - B = ? using 1's complement
First find 1's complement of B = 11010

Note : 1's complement of a number is obtained by subtracting all bits from 11111

Step-1: 1's complement of 11010 is obtained by subtracting each digit from 11111



	1	1	1	1	1
-	1	1	0	1	0

	0	0	1	0	1

Step-2: Now Add this 00101 to 10100

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

	1	1	0	0	1

Step by step solution of 10100 + 00101 = 11001

Write the numbers, so that each digit lines up vertically


	1	0	1	0	0
+	0	0	1	0	1

Step-1 :
`=0_2+1_2`
`=0_10+1_10`
`=1_10`
`=1_2`
Write the 1 in the sum place


	1	0	1	0	0
+	0	0	1	0	1

					1

Step-2 :
`=0_2+0_2`
`=0_10+0_10`
`=0_10`
`=0_2`
Write the 0 in the sum place


	1	0	1	0	0
+	0	0	1	0	1

				0	1

Step-3 :
`=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

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

			0	0	1

Step-4 :
`=1+0_2+0_2`
`=1+0_10+0_10`
`=1_10`
`=1_2`
Write the 1 in the sum place

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

		1	0	0	1

Step-5 :
`=1_2+0_2`
`=1_10+0_10`
`=1_10`
`=1_2`
Write the 1 in the sum place

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

	1	1	0	0	1

Here there is no carry, answer is - (1's complement of the sum obtained 11001)

Note : 1's complement of a number is obtained by subtracting all bits from 11111

Step-1: 1's complement of 11001 is obtained by subtracting each digit from 11111



	1	1	1	1	1
-	1	1	0	0	1

	0	0	1	1	0

So answer is -00110

This material is intended as a summary. Use your textbook for detail explanation.
Any bug, improvement, feedback then Submit Here

4. Example 10100 - 11010