5. Find Subtraction of 31421 and 7253 using 7's complementSolution: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 = 31421, B = 07253.
Find A - B = ? using 7's complement
First find 7's complement of B = 07253
Note : 7's complement of a number is obtained by subtracting all bits from 77777
Step-1: 7's complement of 07253 is obtained by subtracting each digit from 77777
Step-2: Now Add this 70524 to 31421
Step by step solution of 31421 + 70524 = 122145
Write the numbers, so that each digit lines up vertically
Step-1 :
`=1_8+4_8`
`=1_10+4_10`
`=5_10`
`=5_8`
Write the 5 in the sum place
Step-2 :
`=2_8+2_8`
`=2_10+2_10`
`=4_10`
`=4_8`
Write the 4 in the sum place
Step-3 :
`=4_8+5_8`
`=4_10+5_10`
`=9_10`
`=8xx1+1`
`=11_8`
Write the 1 in the sum place and carry the 1 to the next carry place
Step-4 :
`=1+1_8+0_8`
`=1+1_10+0_10`
`=2_10`
`=2_8`
Write the 2 in the sum place
Step-5 :
`=3_8+7_8`
`=3_10+7_10`
`=10_10`
`=8xx1+2`
`=12_8`
Write the 12 in the sum place
The left most bit (1) of the result (122145) is called carry and add it to the rest part of the result (22145)
So answer is 22146
This material is intended as a summary. Use your textbook for detail explanation.
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