At One Place

Number base converter

Convert between binary, octal, decimal, hexadecimal and any base from 2 to 36.

How it works

Converts a number between any two bases from 2 to 36, showing binary, octal, decimal and hex simultaneously.

Base 36 is the practical ceiling because it uses all ten digits plus all twenty-six letters. Beyond that there are no conventional symbols left.

Hexadecimal is used in computing because the conversion to binary is trivial: each hex digit maps to exactly four bits, with no arithmetic. Octal does the same for three bits, which is why Unix file permissions are written in octal — each digit is exactly one read/write/execute triple.

The bit width is shown alongside, since that is usually the reason for converting. A value that needs 33 bits will not fit in a 32-bit integer, and that is the kind of thing this is used to check.

This tool runs entirely in your browser. Nothing you enter is sent to a server, logged or stored, and the page keeps working with the network disconnected.

Common questions

Why does computing use hexadecimal?
Each hex digit is exactly four bits, so converting to and from binary needs no arithmetic — just substitution.
Why are Unix permissions in octal?
Each octal digit is exactly three bits, matching the read, write and execute triple for owner, group and others.
What is the highest base?
Base 36 in common use, because that exhausts the ten digits and twenty-six letters. Higher bases need invented symbols.

Related pages

Sources

  1. Calculated on this page — At One Place

How these figures are compiled and checked