Math Tool

Number Base Converter

Convert numbers between decimal (base 10), hexadecimal (base 16), binary (base 2), and octal (base 8) instantly. Type in any field and all other bases update automatically. Supports positive integers up to 2⁵³.

Decimal Base 10 · digits 0–9

Hexadecimal Base 16 · digits 0–9, A–F

Binary Base 2 · digits 0–1

Octal Base 8 · digits 0–7

Number Systems Explained

Decimal (Base 10)

The number system humans use daily. Uses digits 0–9. Each position represents a power of 10. Example: 255 = 2×100 + 5×10 + 5×1.

Hexadecimal (Base 16)

Uses digits 0–9 and letters A–F. Each hex digit represents exactly 4 bits. Widely used in programming, color codes, memory addresses, and cryptographic hashes.

Binary (Base 2)

The fundamental language of computers. Uses only 0 and 1. Every piece of data in a computer is ultimately stored and processed as binary. Each digit is called a bit.

Octal (Base 8)

Uses digits 0–7. Each octal digit represents exactly 3 bits. Used in Unix/Linux file permissions (e.g., chmod 755) and some legacy computing systems.

Common Use Cases

Hex colors — CSS color #FF5733 is three hex pairs: R=255, G=87, B=51
Memory addresses — debuggers and hex editors display addresses in hexadecimal
File permissions — Unix chmod uses octal: 755 = rwxr-xr-x
Bitwise operations — understanding binary is essential for bitwise AND, OR, XOR, and shift operations
Network masks — subnet masks like 255.255.255.0 are easier to understand in binary
ASCII codes — character codes are often shown in decimal and hex simultaneously
Cryptography — hash values and keys are displayed in hexadecimal

Quick Reference Table

Dec	Hex	Binary	Octal

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