Hex Calculator
Perform arithmetic operations in Hexadecimal number system. Enter two hexadecimal numbers and select an operation.
About Hex Calculator
The Hexadecimal Calculator allows you to perform addition, subtraction, multiplication, and division operations directly in the hexadecimal number system without converting to decimal first.
How the Hexadecimal Calculator Works
A hexadecimal calculator performs arithmetic operations on base-16 numbers. Hexadecimal uses digits 0–9 and letters A–F (where A=10, B=11, C=12, D=13, E=14, F=15). Hex arithmetic carries at 16 instead of 10. This calculator accepts two hex values, performs the selected operation (+, −, ×, ÷), and returns the result in hexadecimal.
- Enter two hexadecimal numbers (digits 0–9 and A–F)
- Select an operation: addition, subtraction, multiplication, or division
- The result is displayed in hexadecimal format
Hexadecimal Arithmetic Rules
Addition: Add digit values. If sum ≥ 16, write (sum − 16) and carry 1.
Example: A + 7 = 10 + 7 = 17 → write 1, carry 1
Subtraction: If top digit < bottom digit, borrow 16 from next column.
Example: 3 − 8 → borrow to get 19 − 8 = B (11)
Multiplication: Multiply digit values, carry quotient when product ≥ 16.
Division: Long division in base-16.
Worked Example: FF + 1
FF (255 in decimal)
+ 1 (1 in decimal)
----
Column 0: F + 1 = 15 + 1 = 16 → write 0, carry 1
Column 1: F + carry 1 = 15 + 1 = 16 → write 0, carry 1
Column 2: carry 1
Result: 100₁₆ = 256₁₀
Verification: 255 + 1 = 256 ✓
Technical Details
Hexadecimal arithmetic is essential in low-level programming, memory address calculations, and color manipulation. When working with memory offsets, programmers frequently add hex addresses: a base address of 0x1000 plus an offset of 0x2F gives 0x102F. In CSS color math, adjusting brightness involves hex addition/subtraction on RGB channels. This calculator performs integer arithmetic with floor division. Input is case-insensitive — "ff" and "FF" are treated identically.
Frequently Asked Questions
What is FF + FF in hex?
FF + FF = 1FE. In decimal: 255 + 255 = 510, and 510 in hex is 1FE.
How do you subtract hex numbers?
Subtract digit by digit from right to left. If a digit in the top number is smaller than the bottom, borrow 16 from the next column. For example, 100 − 1 = FF (256 − 1 = 255).
Why is hex used for memory addresses?
Because each hex digit represents exactly 4 bits, making it compact and directly mappable to binary. A 32-bit address is just 8 hex digits (e.g., 0x7FFF0000), compared to 32 binary digits.
What is hex multiplication used for?
Hex multiplication appears in computing when calculating memory sizes (e.g., 0x400 × 0x400 = 0x100000, which is 1024 × 1024 = 1,048,576 bytes = 1 MB) and in cryptographic hash computations.