7's Complement Subtraction Example 1256

4. Find Subtraction of 1256 and 2702 using 7's complement

Solution:

7's complement subtraction steps :

1. At first, find 7'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 7's complement of the sum is the final result and it is negative.

Here A = 1256, B = 2702.
Find A - B = ? using 7's complement
First find 7's complement of B = 2702

Note : 7's complement of a number is obtained by subtracting all bits from 7777

Step-1: 7's complement of 2702 is obtained by subtracting each digit from 7777



	7	7	7	7
-	2	7	0	2

	5	0	7	5

Step-2: Now Add this 5075 to 1256

		1	1
	1	2	5	6
+	5	0	7	5

	6	3	5	3

Step by step solution of 1256 + 5075 = 6353

Write the numbers, so that each digit lines up vertically


	1	2	5	6
+	5	0	7	5

Step-1 :
`=6_8+5_8`
`=6_10+5_10`
`=11_10`
`=8xx1+3`
`=13_8`
Write the 3 in the sum place and carry the 1 to the next carry place

			1
	1	2	5	6
+	5	0	7	5

				3

Step-2 :
`=1+5_8+7_8`
`=1+5_10+7_10`
`=13_10`
`=8xx1+5`
`=15_8`
Write the 5 in the sum place and carry the 1 to the next carry place

		1	1
	1	2	5	6
+	5	0	7	5

			5	3

Step-3 :
`=1+2_8+0_8`
`=1+2_10+0_10`
`=3_10`
`=3_8`
Write the 3 in the sum place

		1	1
	1	2	5	6
+	5	0	7	5

		3	5	3

Step-4 :
`=1_8+5_8`
`=1_10+5_10`
`=6_10`
`=6_8`
Write the 6 in the sum place

		1	1
	1	2	5	6
+	5	0	7	5

	6	3	5	3

Here there is no carry, answer is - (7's complement of the sum obtained 6353)

Note : 7's complement of a number is obtained by subtracting all bits from 7777

Step-1: 7's complement of 6353 is obtained by subtracting each digit from 7777



	7	7	7	7
-	6	3	5	3

	1	4	2	4

So answer is -1424

This material is intended as a summary. Use your textbook for detail explanation.
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4. Example 1256 - 2702