Number Systems: Binary, Octal, Decimal and Hexadecimal
Computers juggle several number systems, and they're really just different "bases" for writing the same value. Understanding how they relate ties a lot of computing concepts together.
The four bases
- Decimal (base 10) — digits 0–9, what humans use.
- Binary (base 2) — digits 0–1, what computers use internally.
- Octal (base 8) — digits 0–7, used in file permissions.
- Hexadecimal (base 16) — digits 0–F, the compact shorthand for binary.
How they connect
The number fifteen is 15 (decimal), 1111 (binary), 17 (octal), F (hex) — same value, different bases. Hex and octal exist mainly because they map cleanly onto binary (1 hex digit = 4 bits, 1 octal digit = 3 bits), making long binary readable.
Convert between any of them
Our free converters cover every pair — see our guides on binary, hexadecimal and octal, or jump straight to tools like decimal to binary and decimal to hex.
Bottom line
Binary, octal, decimal and hex are just different bases for the same numbers. Decimal is for humans, binary is for machines, and hex/octal are readable shortcuts for binary. See them as one idea in four costumes and computing makes more sense.
