Page 50 - Digital Electronics by harish

2.1.4 Subtraction using complement methods

The number to be subtracted (subtrahend) is converted into 1‟s complement form or 2‟s
complement form to represent it as a negative number. Then it will be added to the first
number (minuend).

Minuend
+ Complement of Subtrahend
Difference

Binary subtraction using 1’s complement method

The following steps are used to subtract a number using 1‟s complement method

1) Find the 1‟s complement of the subtrahend.
2) Add the 1‟s complement with the minuend.
3) If there is any carry:
a. Add the carry (ie. add 1) to the result
b. The result is a positive number.
4) If there is no carry:
a. Find the 1‟s complement of the result.
b. The result is a negative number.

Example 1 : Subtract 100101 from 101100

Here, the minuend is 101100
And the subtrahend is 100101

101100
- 100101
Difference

The 1‟s complement of subtrahend 100101 is 011010. This should be added to the minuend.

Minuend 101100
Add 1‟s complement of + 011010
Subtrahend
1 000110 There is a carry 1.
Add Carry + 1
+ 000111 Result is positive.

Answer : + (111) 2

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