How to find 1’s and 2’s Complement with Shortcut | Lesson 14 | Digital Electronics | Learning Monkey

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Electronics

Here we will try to understand How to find 1’s and 2’s Complement with Shortcut.

Here is the discussion on how to find the 9’s and 10’s complement of a decimal number.

How to find 1’s and 2’s Complement

Steps to find the 1’s Complement

Every bit of the given binary number should be subtracted from 1.

Steps to find the 2’s Complement

Add 1 to the 1’s complement of the given number.

Let’s try to find the 1’s and 2’s complement of the following binary numbers.

1. 110100101

2. 1000100

Example 1:

110100101

To find the 1’s complement of the above number we have to subtract every bit of the number from 1 and the result is as shown in the image below.

Similarly, to find the 2’s complement we have to ADD 1 to the above 1’s complement result and the result of adding is as shown in the image below.

Example 2:

1000100

To find the 1’s complement of the above number we have to subtract every bit of the number from 1 and the result is as shown in the image below.

Similarly, to find the 2’s complement we have to ADD 1 to the above 1’s complement result and the result of adding is as shown in the image below.

Shortcut Method to find 1’s and 2’s complement:

1’s Complement Shortcut Method:

Complement each bit of a given number.

The complement of 0 is 1 and the complement of 1 is 0.

Complementing 110100101 is 001011010.

Similarly, Complementing 1000100 is 0111011.

2’s Complement Shortcut Method:

Complement every bit after finding the first 1 in the given number from the LSB.

Example 1:

110100101

The first 1 is obtained in the 0th position of the given number.

After finding the first 1 all the bits have to be complemented and before that, we have to use the bits as they are.

The result of the 2’s complement shortcut method is as shown in the image below.

Example 2:

The result of the 2’s complement shortcut method is as shown in the images below.

The first 1 is obtained in the 2nd positions of the given number.

After finding the first 1 all the bits have to be complemented and before that, we have to use the bits as they are.

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