Hex Calculator

Perform hexadecimal arithmetic and convert between hex, decimal, binary, and octal number systems.

Hexadecimal Operations

Number 1 (Hex):

Operation:

Number 2 (Hex):

Calculation Results

Hexadecimal

base 16

Decimal

base 10

Binary

base 2

Octal

base 8

💡 Hex System: Hexadecimal uses 16 symbols: 0-9 and A-F. Each hex digit represents 4 binary bits, making it ideal for representing binary data compactly.

What is Hexadecimal?

Hexadecimal (base-16) is a number system that uses 16 symbols: 0-9 and A-F. It's widely used in computing because it provides a human-friendly representation of binary-coded values. Each hex digit represents exactly 4 binary bits (a nibble).

Hexadecimal Digits

Hex	Decimal	Binary	Octal
0	0	0000	0
1	1	0001	1
2	2	0010	2
3	3	0011	3
4	4	0100	4
5	5	0101	5
6	6	0110	6
7	7	0111	7
8	8	1000	10
9	9	1001	11
A	10	1010	12
B	11	1011	13
C	12	1100	14
D	13	1101	15
E	14	1110	16
F	15	1111	17

Hex Arithmetic Operations

Hex Addition

Example: 1A + 2B = 45

Step 1: A (10) + B (11) = 21 decimal = 15 hex
Write 5, carry 1
Step 2: 1 + 2 + 1 (carry) = 4
Result: 45

Hex Subtraction

Example: 2B - 1A = 11

Step 1: B (11) - A (10) = 1
Step 2: 2 - 1 = 1
Result: 11

Why Hexadecimal Matters

Memory Addresses: Computer memory addresses are typically shown in hex.
Color Codes: Web colors use hex (e.g., #FF5733 = orange).
MAC Addresses: Network device identifiers use hex.
Character Encoding: Unicode and ASCII use hex codes.
Debugging: Programmers use hex to read raw memory dumps.

Hex to Decimal Conversion

To convert hex to decimal, multiply each digit by 16 raised to the power of its position (from right, starting at 0):

1A (hex) = (1 × 16¹) + (A × 16⁰)
= (1 × 16) + (10 × 1)
= 16 + 10 = 26 (decimal)

References

Khan Academy. "Hexadecimal Numbers." 2026.
GeeksforGeeks. "Hexadecimal Arithmetic." 2026.