How to do Binary Addition The Easy Way || Lesson 10 || Digital Electronics || Learning Monkey ||

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Electronics

Here we will try to understand How to do Binary Addition The Easy Way.
Here is the link for Introduction to Binary Number System.
The basic rules of binary addition are 1 + 0 = 1, 0 + 0 = 0, 0 + 1 = 1, 1 + 1 = 10 (Binary representation of 2 ), 1 + 1 + 1 = 11 (Binary representation of 3 ).

Based on the following rules we will solve the following examples.
1. 1001 + 1111

2. 1101011.11 + 10110.1

3. 011111 + 101101 + 011110 + 110110

Example 1:

1001 + 1111

From the above addition, we have to add 1 + 1 the least significant bits.

1 + 1 = 10, 0 is the sum and 1 is the carry as shown in the image below.

Now we will add the bits in the 1st position which is 1 + 1 ( In the carry ) = 10.

Now we will add the bits in the 2nd position which is 1 + 1 ( In the carry ) = 10.

Now we will add the bits in the 3rd position which is 1 + 1 + 1 ( In the carry ) = 11.

Example 2:

1101011.11 + 10110.1

We will directly solve the example and the result is as shown in the image below.

Example 3:

011111 + 101101 + 011110 + 110110

This example is a bit different from the examples we have solved so far.

In this example, we will use the rules other than the basic rules.

Let’s start with the 0th position bits.

Find the sum of the bits in the 0th position which is 1 + 1 + 0 + 0 = 10 ( As we have 2 ones the sum is 10 ).

Find the sum of the bits in the 1st position which is 1 + 0 + 1 + 1 + 1 = 100 ( As we have 4 ones the sum is 100 [ Binary representation of 4 ] ).

The binary representation of 4 is 100.

The first zero is used as a sum and the 10 is used as carry ( is marked in blue ) as shown in the image above.

Now find the 2nd position which is 1 + 1 + 1 + 0 + 1 = 100 ( As we have 4 ones the sum is 100 [ Binary representation of 4 ] ).

Similarly, we will add the bits in all the remaining positions.

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