How to Subtract Binary Numbers

Binary subtraction is the process of subtracting binary numbers. Binary numbers include only 0 and 1. The process of binary subtraction is the same as the arithmetic operation of subtraction that we do with numbers. Since only 0 and 1 involved here, we may sometimes need to subtract 0 from 1. In such cases, we use the concept of borrowing as in an arithmetic subtraction. A binary number is expressed with a base-2. For example, a binary number is written as 101₂

Rules of Binary Subtraction

The binary subtraction is performed like decimal subtraction, the rules for binary subtraction are:

There are two cases for subtract binary numbers :-

1- Binary subtraction with borrowing

2- Binary subtraction without borrowing

Binary subtraction with borrowing

Let us take an example for explanation this case;

Example: Subtract the binary numbers 101 from 1001.

Here the decimal equivalent of 101 is 5, and 1001 is 9.

Step 1: Arrange the numbers as shown below.

1001

- 101

________

Step 2: Use the rules of binary subtraction to subtract 101 from 1001.

Let us Subtract the numbers starting from the right and move to the next higher-order digit. The first step is to subtract (1−1), which is equal to 0. Similarly, We move on to the next higher-order digit and subtract (0–0), which is equal to 0. The next step, we have to subtract (0–1), so we borrow a 1 from the next higher-order digit. Therefore, the result of subtracting (0–1) is 1.

1001

- 101

_________

100

Step 3: The difference of 101 from 1001 is 100.

To verify this, check the decimal equivalent of 100, which is 4 and 9 – 5 = 4. Hence the answer is correct.

Binary subtraction without borrowing

Let us take an example for explanation this case;

Example: Subtract the binary numbers 100 from 111.

Here number 4 is represented in binary as 100₂ and number 7 is represented as 111₂.

Step 1: Arrange the numbers as shown in the figure below.

111

- 100

__________

011

Step 2: Follow the binary subtraction rules to subtract the numbers. In this subtraction, we do not encounter the subtraction of 1 from 0. Hence, the difference is 011₂.

111

- 100

__________

011

Step 3: The decimal equivalent of 011₂ is 3. Hence the difference is correct.

Let us take another example with "Logic Kit" app this app is very easy and so good in these subjects of number systems. Download This app from the app store for iOS devices click here.

1- Open the app

2- Choose More Arithmetic

3- Select the base 2

4- write your equation you need to solve

5- You see the solution then click on show steps