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.
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Sources
- Calculated on this page — At One Place