Subtraction in Binary | Mathematics for JAMB PDF Download

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 are involved here, we may sometimes need to subtract 0 from 1. In such cases, we use the concept of borrowing as we do in an arithmetic subtraction. A binary number is expressed with a base-2. For example, a binary number is written as101₂

Rules of Binary Subtraction

There are some rules in which binary numbers are subtracted. They are,

How To Do Binary Subtraction?

Decimal or base-10 numbers can be expressed as binary numbers. Binary numbers are used in computers to represent data since they understand only binary digits, 0 and 1. Let us understand how to subtract binary numbers with the example shown below.
Case i) - Binary subtraction without borrowing
Subtract 100₂ from 1111₂ .Here number 4 is represented in binary as 100₂ and number 15 is represented as 1111₂.
Step 1: Arrange the numbers as shown in the figure below.

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 1011₂.

Step 3: The decimal equivalent of 1011₂ is 11. Hence the difference is correct.

Case ii) Binary subtraction with borrowing

Subtract 101₂ from 1001₂. Here number 5 is represented in binary as 101₂and number 9 is represented as 1001₂. Step 1: Arrange the numbers as shown below.

Step 2: Follow the binary subtraction rules to subtract the numbers. In this subtraction, first, 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). This is equal to 0. Similarly, we move on to the next higher order digit and subtract (0 - 0), which is 0. In 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.

Step 3: Therefore the dfference of 1001₂ and 101₂ is 100₂. To verify this, let us find the decimal equivalent of 100₂, which is 4, Therefore, 9 - 5 = 4.

Binary Subtraction Using 1's Complement

The 1's complement of a number is obtained by interchanging every 0 to 1 and every 1 to 0 in a binary number. For example, the 1's complement of the binary number 110₂ is 001₂. To perform binary subtraction using 1's complement, please follow the steps mentioned below.

• Step 1: Find the 1's complement of the subtrahend, which means the second number of subtraction.
• Step 2: Add it with the minuend or the first number.
• Step 3: If there is a carryover left then add it with the result obtained from step 2.
• Step 4: If there are no carryovers, then the result obtained in step 2 is the difference of the two numbers using 1's complement binary subtraction.

Let us understand this with an example. Subtract 110010₂ - 100101₂ using 1's complement. Here the binary equivalent of 50 is 110101₂ and the binary equivalent of 37 is 100101₂.

Step 1: Find out the 1's complement of the subtrahend (37), which is 011010₂.
Step 2: Add it with the minuend(50), which is 110010₂.
Step 3: Arrange the numbers as follows and add them.

Step 4: The left-most digit 1 is a carryover of this addition. Since there is a carryover we add it with the result, which is 001100₂.

Therefore, the result is 1101₂. Also, the difference of 50 - 37 is 13. The binary equivalent of 13 is 1101₂.