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Free online tools to generate, calculate, convert, format, transform, and de/en-code.
 

Base Calculator

Convert numbers between different bases: Binary (2), Octal (8), Decimal (10), Hexadecimal (16), and custom bases.

Enter a Number

Binary: 0-1 | Octal: 0-7 | Decimal: 0-9 | Hex: 0-9, A-F | Bases up to 36: 0-9, A-Z

Number Systems Explained

Common Bases

  • Binary (Base 2): Uses digits 0-1. Foundation of digital computing
  • Octal (Base 8): Uses digits 0-7. Common in computing
  • Decimal (Base 10): Uses digits 0-9. Standard human counting
  • Hexadecimal (Base 16): Uses 0-9, A-F. Common in programming

How It Works

  • Each position represents a power of the base
  • Rightmost position is base0 = 1
  • Next position is base1
  • And so on, moving left

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

Examples

Binary Octal Decimal Hexadecimal
1010 12 10 A
11111111 377 255 FF
100000000 400 256 100

Use Cases

Programming

  • Color codes (hex)
  • Memory addresses
  • Bit manipulation
  • File permissions (octal)

Computing

  • IP addresses
  • Binary operations
  • Character encoding
  • Data representation

Education

  • Number theory
  • Computer science
  • Digital electronics
  • Mathematics

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