102 LearnersLast updated on July 28th, 2025
Subtraction of Binary Numbers
The mathematical operation of finding the difference between two binary numbers is known as binary subtraction. It is a fundamental operation in digital electronics and computer science, helping to manipulate binary data efficiently in computations and digital circuits.
What is Subtraction of Binary Numbers?
Subtracting binary numbers involves using the concept of borrowing, similar to decimal subtraction. In binary, subtraction follows specific rules due to the presence of only two digits, 0 and 1.
The process involves comparing bits and borrowing from higher-order bits when necessary. The main components of binary subtraction include:
Borrowing: A process similar to borrowing in decimal subtraction.
Binary digits: Only 0 and 1 are used in binary numbers.
Operators: The subtraction operation primarily uses the minus (-) symbol.
How to Perform Subtraction of Binary Numbers?
When subtracting binary numbers, follow these steps:
Borrow when necessary: If the current bit of the minuend is smaller than the bit of the subtrahend, borrow from the next higher bit.
Subtract bits: Subtract each bit of the subtrahend from the corresponding bit of the minuend.
Simplify result: After performing the subtraction, simplify the result by removing any unnecessary leading zeros.
Methods to Perform Subtraction of Binary Numbers
The following are the methods for binary subtraction:
Method 1: Bit-by-Bit Subtraction
Step 1: Align the numbers at the right.
Step 2: Subtract each bit, borrowing from the next bit if needed.
Step 3: Write the result for each bit from right to left.
Example:
Question: Subtract 1101 from 10100 - Align the numbers: 10100 - 1101
Step 1: Borrow from higher bits if needed.
Step 2: Perform subtraction. Answer: 01111
Method 2: Complement Method
In this method, we use the 2’s complement to perform subtraction:
Step 1: Find the 2’s complement of the subtrahend.
Step 2: Add it to the minuend.
Step 3: If there’s an overflow, discard it. Example: Subtract 1101 from 10100 using 2’s complement.
Solution:
Step 1: 2’s complement of 1101: 0011
Step 2: Add to 10100: 10100 + 0011
Result: 01111
Properties of Subtraction of Binary Numbers
In binary arithmetic, subtraction has the following properties:
- Subtraction is not commutative In subtraction, changing the order of the numbers changes the result, i.e., A - B ≠ B - A
- Subtraction is not associative Subtraction cannot be regrouped like addition. Changing the grouping alters the result. (A − B) − C ≠ A − (B − C)
- Subtraction as addition of complements Subtracting a number is equivalent to adding its complement, allowing subtraction to be performed as an addition operation. A − B = A + (−B)
- Subtracting zero from a number leaves the number unchanged Subtracting zero from any binary number results in the same binary number: A - 0 = A
Tips and Tricks for Subtraction of Binary Numbers
These tips can help make binary subtraction simpler and more efficient:
Tip 1: Pay attention to borrowing during subtraction, as it can affect the entire process.
Tip 2: For large numbers, use the complement method to simplify calculations, as it minimizes manual borrowing.
Tip 3: Visual aids, such as arranging numbers in columns, can help track borrowing and ensure accuracy.
Improper borrowing
Students sometimes forget to borrow correctly, leading to incorrect results. Always ensure that borrowing is done from the correct bit position.
Mistake 1
Misaligning bits
Ensure that binary numbers are aligned correctly, with each bit in the correct column, to avoid errors in subtraction.
Mistake 2
Forgetting to remove leading zeros
Once the subtraction is complete, remember to simplify the result by removing any unnecessary leading zeros.
Mistake 3
Ignoring overflow in complement method
When using the complement method, remember to discard any overflow bit to get the correct result.
Mistake 4
Not checking results
It's important to verify the result of subtraction by converting binary numbers to decimal to ensure accuracy.
Mistake 5
Examples of Subtraction of Binary Numbers
Subtract 101 from 1101
1000
Problem 1
Use the bit-by-bit subtraction method: ``` 1101 - 101 ``` Borrow from higher bits if needed: = 1000
Subtract 1100 from 10101
Explanation
11101
Problem 2
Perform bit-by-bit subtraction: ``` 10101 - 1100 ``` Borrow and subtract as needed: = 11101
Subtract 111 from 10010
Explanation
11011
Problem 3
Align numbers and subtract: ``` 10010 - 111 ``` Borrow where necessary: = 11011
Subtract 1011 from 11100
Explanation
10101
Problem 4
Use the complement method: 2’s complement of 1011 is 0101. Add to 11100: ``` 11100 + 0101 ``` Result: 10101
Subtract 1001 from 10110
Explanation
1101
Yes, when subtracting larger binary numbers from smaller ones, the result is negative, often represented in binary using the 2’s complement method.
1.Is subtraction commutative in binary arithmetic?
2.What are the rules for borrowing in binary subtraction?
3.What is the first step in binary subtraction?
4.What method is commonly used for binary subtraction?
5.How can children in United States use numbers in everyday life to understand Subtraction of Binary Numbers?
6.What are some fun ways kids in United States can practice Subtraction of Binary Numbers with numbers?
7.What role do numbers and Subtraction of Binary Numbers play in helping children in United States develop problem-solving skills?
8.How can families in United States create number-rich environments to improve Subtraction of Binary Numbers skills?
Common Mistakes and How to Avoid Them in Subtraction of Binary Numbers
Binary subtraction can be tricky, leading to common mistakes. Awareness of these can help prevent errors.
Hiralee Lalitkumar Makwana
About the Author
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
Fun Fact
: She loves to read number jokes and games.
