1’s Complement Subtraction Explained with Examples

Binary Subtraction Using 1’s Complement

In binary subtraction using the 1’s complement method, we have two symbols:

• 0 represents the positive sign
• 1 represents the negative sign

Here are the steps for binary subtraction using 1’s complement:

1. Write the 1’s complement of the subtrahend (the number we want to subtract).
2. Add the 1’s complement of the subtrahend to the minuend (the number we are subtracting from).
3. If there is a carryover in the result, add it to the least significant bit.
4. If there is no carryover, take the 1’s complement of the result to get the negative value.

Example of Using 1’s Complement

Example: Question:

(110101)2 – (100101)2

Solution:

(110101)2 = 53 in decimal (minuend)

(100101)2 = 37 in decimal (subtrahend)

Now, take the 1’s complement of the subtrahend and add it to the minuend.

1 carry

1 1 0 1 0 1

(+) 0 1 1 0 1 0

0 0 1 1 1 1

1 carry

0 1 0 0 0 0

Therefore, the solution is 010000, which is 16 in decimal.

So, (110101)2 – (100101)2 = 16 in decimal.

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