Number Base Converter
Convert a number between binary, octal, decimal, hexadecimal, or any base from 2 to 36.
Why different number bases exist
Decimal (base 10) is the everyday counting system, built around having 10 fingers. Binary (base 2) is fundamental to computing since digital circuits represent two states naturally. Hexadecimal (base 16) is widely used in programming as a compact, human-readable shorthand for binary, since each hex digit represents exactly four binary digits. Octal (base 8) sees less common use today but historically appeared in some computing contexts.
Every base system follows the same underlying logic — each digit position represents a power of the base, just like each decimal digit position represents a power of 10 (ones, tens, hundreds, and so on).
Where you'll encounter different bases
Hexadecimal shows up constantly in web development (color codes like #FF5733), programming (memory addresses, error codes), and networking (MAC addresses). Binary is fundamental to how computers store and process all data at the hardware level, and understanding it helps when working with bitwise operations or low-level programming.
This calculator supports the four most common bases directly through the dropdown, and the underlying conversion logic actually works for any base from 2 to 36 if you need something less common.
Frequently asked questions
Why is hexadecimal used instead of just binary in programming?
Hexadecimal is far more compact and easier for humans to read than long binary strings, while still converting cleanly to binary (each hex digit equals exactly 4 binary digits), making it a practical shorthand.
What happens if I enter an invalid digit for the selected base?
The calculator will flag the input as invalid — for example, entering a '9' while converting from binary (which only uses 0 and 1) isn't a valid binary digit and won't produce a result.