5. Find Subtraction of 1101110 and 1010101 using 2's complementSolution:2's complement subtraction steps :
1. At first, find 2'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 2's complement of the sum is the final result and it is negative.
Here A = 1101110, B = 1010101.
Find A - B = ? using 2's complement
First find 2's complement of B = 1010101
Note : 2's complement of a number is 1 added to it's 1's complement number.
Step-1: 1's complement of 1010101 is obtained by subtracting each digit from 1
Step-2: Now add 1 :
0101010 + 1 = 0101011
Step-3: Now Add this 0101011 to 1101110
| 1 | | 1 | 1 | 1 | | |
| 1 | 1 | 0 | 1 | 1 | 1 | 0 |
| + | 0 | 1 | 0 | 1 | 0 | 1 | 1 |
|
| 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 |
Step by step solution of 1101110 + 0101011 = 10011001
Write the numbers, so that each digit lines up vertically
Step-1 :
`=0_2+1_2`
`=0_10+1_10`
`=1_10`
`=1_2`
Write the 1 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 | 1 |
|
| | 0 | 1 | 1 | 0 | 0 | 1 |
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 | 1 |
|
| 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 |
The left most bit of the result (10011001) is 1, called carry and it is ignored.
So answer is 0011001
This material is intended as a summary. Use your textbook for detail explanation.
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