Number Systems Converter

Convert numbers between different bases: binary, decimal, octal, and hexadecimal.

Why & What

Number systems are different ways of representing numerical values. While we commonly use the decimal system (base-10) in everyday life, computers use binary (base-2), and programmers often work with hexadecimal (base-16) for convenience.

Binary (Base-2): Uses only 0 and 1. Foundation of all digital computing. Octal (Base-8): Uses 0-7. Historically used in computing. Decimal (Base-10): Uses 0-9. Our everyday system. Hexadecimal (Base-16): Uses 0-9 and A-F. Compact representation for binary data.

Number Base Concepts

Value = Σ(digit × base^position)
Each digit's value depends on its position and the base
Binary (Base-2)

Digits: 0, 1

Example: 1010₂ = 10₁₀

Octal (Base-8)

Digits: 0-7

Example: 12₈ = 10₁₀

Decimal (Base-10)

Digits: 0-9

Example: 10₁₀ = 10

Hexadecimal (Base-16)

Digits: 0-9, A-F

Example: A₁₆ = 10₁₀

Base Converter

Educational Purpose Only: This calculator is provided for learning and educational purposes. For critical applications or professional use, please verify results with appropriate professional tools and expertise.

Quick Reference Table

Decimal Binary Octal Hex
0000000
1000111
81000108
10101012A
15111117F
16100002010
25511111111377FF

Example: Converting 1010 Binary to Decimal

Step-by-Step Conversion

Binary: 1010

Position values (right to left): 2³, 2², 2¹, 2⁰ = 8, 4, 2, 1

Calculation: (1×8) + (0×4) + (1×2) + (0×1) = 8 + 0 + 2 + 0 = 10

Limitations & Disclaimer

Important Limitations
  • This converter handles positive integers only.
  • Very large numbers may lose precision due to JavaScript limitations.
  • Maximum safe integer: 9,007,199,254,740,991 (2⁵³ - 1).
  • For educational purposes only.