Number Base Converter
Free number base converter. Convert between binary, octal, decimal, and hexadecimal instantly. Learn how each number system works.
Base Converter
Comprehensive Guide & Practice
Master the mathematical principles, formulas, and step-by-step methods with worked examples and FAQs.
1. Number Systems Explained
A number system is a way of representing numbers using a specific set of digits. The base (or radix) tells you how many unique digits are used before the system "wraps around" to the next column.
2. Decimal (Base 10)
The number system we use every day. Uses digits 0–9. Each position is a power of 10: ones, tens, hundreds, thousands...
3. Binary (Base 2)
Used by computers. Uses only two digits: 0 and 1. Each position is a power of 2. Example: 1101₂ = 1×8 + 1×4 + 0×2 + 1×1 = 13 in decimal.
4. Hexadecimal (Base 16)
Uses digits 0–9 and letters A–F (where A=10, B=11, ... F=15). Widely used in programming and colour codes (e.g. #FF5733). Example: FF₁₆ = 15×16 + 15 = 255 in decimal.
5. Octal (Base 8)
Uses digits 0–7. Each octal digit corresponds to exactly 3 binary digits, making it useful in early computing. 377₈ = 3×64 + 7×8 + 7 = 255 in decimal.
See also: Roman Numeral Converter | Number Systems Guide | Scientific Notation