Finding 2’s compliment

1. Write down the binary number: Make sure it has a fixed number of bits (e.g., 8 bits).
2. Invert the digits: Change every 0 to 1 and every 1 to 0. This is known as taking the one’s complement of the number.
3. Add one to the result: This final step gives you the two’s complement of the original binary number.

Example

Let’s find the two’s complement of the 8-bit binary number 00101100.

1. Write down the binary number:

00101100

1. Invert the digits (one’s complement):

11010011

1. Add one to the inverted number:

11010011 + 1 = 11010100

So, the two’s complement of 00101100 is 11010100.

Explanation

• Original binary number: 00101100
• One’s complement: 11010011 (inverted digits)
• Add 1: When you add 1 to 11010011, you get 11010100.

This result (11010100) is the two’s complement of the original binary number 00101100.