How to do Binary Subtraction The Easy Way || Lesson 11 || Digital Electronics || Learning Monkey ||

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Here we will try to understand How to do Binary Subtraction The Easy Way.

Here is the discussion on Binary Addition.

The basic rules of binary subtraction.

1 – 0 = 1, 1 – 1 =0, 0 – 0 = 0, 0 – 1 = 1.

We try to solve the following examples.

1. 1111 – 10

2. 1000 – 11

3. 1001 – 10

Example 1:

1111 – 10

Here we will apply the basic rules and start our subtraction from 0th position.

The result after the subtraction of the bits at the 0th position is as shown below.

Similarly, based on the basic rules we will subtract the bits in the remaining positions.

The result of the subtraction is as shown in the image below

Example 2:

1000 – 11

Here we will apply the basic rules and start our subtraction from 0th position.

The subtraction of the bits from the 0th position is 0 – 1 which is not possible.

Because we have to subtract the bigger number from a smaller number.

In order to do the subtraction, we have to borrow from the next highest position.

For example, if the 1st position is not having 1 we have to go to the next highest position.

If we consider our example we have to borrow from the 1 in the 3rd position.

The borrow happens based on the positional weight.

To have a better-understanding consider the image below.

In the above binary subtraction, we have to borrow from the 1 in the 3rd position whose positional weight is 8.

Now 8 will be borrowed by the 0 in the 2nd position.

The value 8 can be considered as 4 + 4.

Now a 4 will be borrowed by the 0 in the 1st position.

The value of 4 can be considered as 2 + 2.

Now a 2 will be borrowed by the 0 in the 0th position.

Now subtract 1 from 2 in the 0th position after borrow.

2 – 1 = 1.

Therefore 0 – 1 = 1.

The complete process of borrow is done as shown in the image below.

Similarly, We will subtract the bits in the 1st position as per the borrows obtained.

The result is as shown in the image below.

Similarly, we will do the subtraction of the bits in the 2nd and the 3rd position.

In the second position, the positional weight is 4.

1 – 0 = 1, 1 in 2nd position means the positional weight is 4.

In the third position, 1 has been borrowed so the value in the third position is 0.

0 – 0 = 0.

The result of the subtraction is as shown in the image below.

Example 3:

1001 – 10

Based on the discussion above the result of the subtraction is as shown in the image below.

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