100 LearnersLast updated on July 28th, 2025
Subtraction of Hexadecimal Numbers
The mathematical operation of finding the difference between two hexadecimal numbers is known as the subtraction of hexadecimal numbers. This process is essential in digital computing and helps solve problems involving hexadecimal arithmetic operations.
What is Subtraction of Hexadecimal Numbers?
Subtracting hexadecimal numbers involves a process similar to decimal subtraction but with base 16. It requires borrowing from higher significant digits when the minuend is smaller than the subtrahend in a given column.
Hexadecimal numbers consist of:
Digits: These include 0-9 and letters A-F, representing values from 0 to 15.
Operators: For subtraction, the operator is the minus (-) symbol.
How to do Subtraction of Hexadecimal Numbers?
When subtracting hexadecimal numbers, students should follow these steps:
Borrowing: If a digit in the minuend is smaller than the corresponding digit in the subtrahend, borrow from a higher digit.
Convert to Decimal: Convert the hexadecimal numbers to decimal if necessary, perform the subtraction, and convert back to hexadecimal.
Simplifying result: Write the result in hexadecimal form, ensuring that each digit is between 0 and F.
Methods to do Subtraction of Hexadecimal Numbers
The following methods are used for subtraction of hexadecimal numbers:
Method 1: Direct Subtraction
Perform the subtraction directly by comparing each column starting from the right, borrowing as necessary, similar to decimal subtraction.
Example: Subtract 1A3 from 2B5
Step 1: Start from the rightmost digit.
Step 2: Borrow from the left when necessary.
Step 3: Compute the difference.
Answer: 112
Method 2: Convert and Subtract
Convert the hexadecimal numbers to decimal, perform the subtraction, and convert the result back to hexadecimal.
Example: Subtract C4 from 1F6 Decimal Conversion: 1F6 (502) - C4 (196)
Subtract: 502 - 196 = 306
Hexadecimal Conversion: 306 = 132
Answer: 132
Properties of Subtraction of Hexadecimal Numbers
Subtraction in hexadecimal arithmetic has the following properties:
- Subtraction is not commutative Changing the order of the numbers changes the result, i.e., A - B ≠ B - A.
- Subtraction is not associative Rearranging the numbers in subtraction changes the outcome. (A − B) − C ≠ A − (B − C)
- Subtraction requires borrowing When a digit in the minuend is smaller, borrowing from the next higher digit is necessary.
- Subtracting zero leaves the number unchanged Subtracting zero from any hexadecimal number results in the same number: A - 0 = A.
Tips and Tricks for Subtraction of Hexadecimal Numbers
Here are some tips to efficiently perform hexadecimal subtraction:
Tip 1: Be familiar with borrowing in base 16.
Tip 2: Remember hexadecimal values: A=10, B=11, C=12, D=13, E=14, F=15.
Tip 3: Use conversion for complex problems: Convert to decimal, perform subtraction, convert back.
Forgetting to borrow
Students often forget to borrow in base 16. Always check if the minuend digit needs borrowing.
Mistake 1
Misinterpreting hexadecimal values
Ensure you correctly interpret hexadecimal digits as their respective decimal values (A=10 to F=15).
Mistake 2
Misalignment in subtraction
Ensure digits are aligned properly, with corresponding significant places matched.
Mistake 3
Leaving results in decimal
Always convert the result back to hexadecimal if you used decimal conversion for calculations.
Mistake 4
Ignoring leading zeros
Remove unnecessary leading zeros in the final hexadecimal result for clarity.
Mistake 5
Examples of Subtraction of Hexadecimal Numbers
Subtract 4B from 7E
33
Problem 1
Using direct subtraction, 7E (126) - 4B (75) = 126 - 75 = 51 Convert back to hexadecimal: 51 = 33
Subtract A2 from F3
Explanation
51
Problem 2
Using direct subtraction, F3 (243) - A2 (162) = 243 - 162 = 81 Convert back to hexadecimal: 81 = 51
Subtract 56 from B7
Explanation
61
Problem 3
B7 (183) - 56 (86) = 183 - 86 = 97 Convert back to hexadecimal: 97 = 61
Subtract 1A3 from 2B5
Explanation
112
Problem 4
2B5 (693) - 1A3 (419) = 693 - 419 = 274 Convert back to hexadecimal: 274 = 112
Subtract C4 from 1F6
Explanation
132
Yes, subtraction can be performed directly, but borrowing must be done in base 16 where necessary.
1.Is subtraction commutative in hexadecimal?
2.What are hexadecimal digits?
3.What is the first step in subtracting hexadecimal numbers?
4.What methods are used for subtracting hexadecimal numbers?
5.How can children in Vietnam use numbers in everyday life to understand Subtraction of Hexadecimal Numbers?
6.What are some fun ways kids in Vietnam can practice Subtraction of Hexadecimal Numbers with numbers?
7.What role do numbers and Subtraction of Hexadecimal Numbers play in helping children in Vietnam develop problem-solving skills?
8.How can families in Vietnam create number-rich environments to improve Subtraction of Hexadecimal Numbers skills?
Common Mistakes and How to Avoid Them in Subtraction of Hexadecimal Numbers
Subtraction in hexadecimal can be challenging, leading to common mistakes. Awareness of these errors can help avoid them.
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.
