Last updated on July 28th, 2025
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.
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.
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.
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
Subtraction in hexadecimal arithmetic has the following properties:
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.
Students often forget to borrow in base 16. Always check if the minuend digit needs borrowing.
Using direct subtraction, 7E (126) - 4B (75) = 126 - 75 = 51 Convert back to hexadecimal: 51 = 33
Subtract A2 from F3
51
Using direct subtraction, F3 (243) - A2 (162) = 243 - 162 = 81 Convert back to hexadecimal: 81 = 51
Subtract 56 from B7
61
B7 (183) - 56 (86) = 183 - 86 = 97 Convert back to hexadecimal: 97 = 61
Subtract 1A3 from 2B5
112
2B5 (693) - 1A3 (419) = 693 - 419 = 274 Convert back to hexadecimal: 274 = 112
Subtract C4 from 1F6
132
Subtraction in hexadecimal can be challenging, leading to common mistakes. Awareness of these errors can help avoid them.
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.
: She loves to read number jokes and games.