5. Find Subtraction of 1101110 and 1010101 using 1's complementSolution: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 = 1101110, B = 1010101.
Find A - B = ? using 1's complement
First find 1's complement of B = 1010101
Note : 1's complement of a number is obtained by subtracting all bits from 1111111
Step-1: 1's complement of 1010101 is obtained by subtracting each digit from 1111111
Step-2: Now Add this 0101010 to 1101110
| 1 | | 1 | 1 | 1 | | |
| 1 | 1 | 0 | 1 | 1 | 1 | 0 |
| + | 0 | 1 | 0 | 1 | 0 | 1 | 0 |
|
| 1 | 0 | 0 | 1 | 1 | 0 | 0 | 0 |
Step by step solution of 1101110 + 0101010 = 10011000
Write the numbers, so that each digit lines up vertically
Step-1 :
`=0_2+0_2`
`=0_10+0_10`
`=0_10`
`=0_2`
Write the 0 in the sum place
Step-2 :
`=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
Step-3 :
`=1+1_2+0_2`
`=1+1_10+0_10`
`=2_10`
`=2xx1+0`
`=10_2`
Write the 0 in the sum place and carry the 1 to the next carry place
Step-4 :
`=1+1_2+1_2`
`=1+1_10+1_10`
`=3_10`
`=2xx1+1`
`=11_2`
Write the 1 in the sum place and carry the 1 to the next carry place
Step-5 :
`=1+0_2+0_2`
`=1+0_10+0_10`
`=1_10`
`=1_2`
Write the 1 in the sum place
Step-6 :
`=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 | 1 | 1 | | |
| 1 | 1 | 0 | 1 | 1 | 1 | 0 |
| + | 0 | 1 | 0 | 1 | 0 | 1 | 0 |
|
| | 0 | 1 | 1 | 0 | 0 | 0 |
Step-7 :
`=1+1_2+0_2`
`=1+1_10+0_10`
`=2_10`
`=2xx1+0`
`=10_2`
Write the 10 in the sum place
| 1 | | 1 | 1 | 1 | | |
| 1 | 1 | 0 | 1 | 1 | 1 | 0 |
| + | 0 | 1 | 0 | 1 | 0 | 1 | 0 |
|
| 1 | 0 | 0 | 1 | 1 | 0 | 0 | 0 |
The left most bit (1) of the result (10011000) is called carry and add it to the rest part of the result (0011000)
So answer is 0011001
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