4. Find Subtraction of 1256 and 2702 using 8's complementSolution:8's complement subtraction steps :
1. At first, find 8'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 8's complement of the sum is the final result and it is negative.
Here A = 1256, B = 2702.
Find A - B = ? using 8's complement
First find 8's complement of B = 2702
Note : 8's complement of a number is 1 added to it's 7's complement number.
Step-1: 7's complement of 2702 is obtained by subtracting each digit from 7
Step-2: Now add 1 :
5075 + 1 = 5076
Step-3: Now Add this 5076 to 1256
Step by step solution of 1256 + 5076 = 6354
Write the numbers, so that each digit lines up vertically
Step-1 :
`=6_8+6_8`
`=6_10+6_10`
`=12_10`
`=8xx1+4`
`=14_8`
Write the 4 in the sum place and carry the 1 to the next carry place
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
Step-3 :
`=1+2_8+0_8`
`=1+2_10+0_10`
`=3_10`
`=3_8`
Write the 3 in the sum place
Step-4 :
`=1_8+5_8`
`=1_10+5_10`
`=6_10`
`=6_8`
Write the 6 in the sum place
Here there is no carry, answer is - (8's complement of the sum obtained 6354)
Note : 8's complement of a number is 1 added to it's 7's complement number.
Step-1: 7's complement of 6354 is obtained by subtracting each digit from 7
Step-2: Now add 1 :
1423 + 1 = 1424
So answer is -1424
This material is intended as a summary. Use your textbook for detail explanation.
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