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Number Base Converter

Convert between Binary, Octal, Decimal, and Hexadecimal
Decimal
Base 10
Binary
Base 2
Octal
Base 8
Hexadecimal
Base 16
Enter a decimal number (0-9)

Enter a number to convert between bases.

Number Systems Guide

Number Base Systems

Binary (Base 2)

Uses only digits 0 and 1. Each position represents a power of 2.

Example: 1011₂ = 1×2³ + 0×2² + 1×2¹ + 1×2⁰ = 8 + 0 + 2 + 1 = 11₁₀

Octal (Base 8)

Uses digits 0-7. Each position represents a power of 8.

Example: 17₈ = 1×8¹ + 7×8⁰ = 8 + 7 = 15₁₀

Decimal (Base 10)

The standard number system we use daily. Uses digits 0-9.

Example: 123₁₀ = 1×10² + 2×10¹ + 3×10⁰ = 100 + 20 + 3

Hexadecimal (Base 16)

Uses digits 0-9 and letters A-F (where A=10, B=11, C=12, D=13, E=14, F=15).

Example: 2F₁₆ = 2×16¹ + 15×16⁰ = 32 + 15 = 47₁₀

Common Uses

  • Binary: Computer memory, digital circuits, Boolean logic
  • Octal: Unix file permissions, compact binary representation
  • Decimal: Everyday counting, mathematics, finance
  • Hexadecimal: Color codes, memory addresses, MAC addresses
Quick Reference
Dec Bin Oct Hex
0 0 0 0
1 1 1 1
8 1000 10 8
10 1010 12 A
15 1111 17 F
16 10000 20 10
255 11111111 377 FF
Hex Letters
A = 10
B = 11
C = 12
D = 13
E = 14
F = 15

Number Bases

Different number systems are used in computing and mathematics. Understanding how to convert between them is essential for programming and digital electronics.

Base Prefixes
Binary Prefix: 0b (e.g., 0b1010)
Octal Prefix: 0o (e.g., 0o12)
Hexadecimal Prefix: 0x (e.g., 0xA)
Related Tools
Scientific Calculator Roman Numeral Calculator Percentage Calculator
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Number Systems:

Did You Know?

Computers use binary (base 2) internally because digital circuits can easily represent two states: on (1) and off (0). All data in computers is ultimately stored as binary!