Number Base Converter
Convert between Binary, Octal, Decimal, and Hexadecimal — all four at once
| Base | Value |
|---|---|
| Binary (Base 2) | 11111111 |
| Octal (Base 8) | 377 |
| Decimal (Base 10) | 255 |
| Hexadecimal (Base 16) | FF |
Frequently Asked Questions
Converting between binary, octal, decimal, and hexadecimal number systems means re-expressing the same underlying quantity using a different base (radix) — the value doesn't change, only how many symbols are available per digit and what each digit position is worth, which is why the same quantity looks completely different written in each system.
Why the same number looks so different across bases
A number system's base determines how many unique digit symbols exist (binary uses 2, octal uses 8, decimal uses 10, hexadecimal uses 16 — the extra 6 symbols in hex conventionally represented as A through F) and what each digit position represents (each position's place value is the base raised to that position's power, rather than always being a power of 10 as in decimal). This is why the same underlying quantity requires vastly different digit counts to represent across bases — binary needs many more digits than decimal for the same value, since each binary digit position carries much less place value than each decimal digit position. None of this changes the actual quantity being represented; it's purely a different notation for identical values, the same way "5" and "five" represent the same quantity in different notations.
A worked example
A number that looks compact in hexadecimal expands to a visibly longer string of digits in binary, purely because binary's base-2 place values pack far less information per digit than hexadecimal's base-16 place values — both representations describe the exact same underlying quantity, just using dramatically different digit counts to do so.
How this connects to your other technical calculations
Hexadecimal specifically shows up constantly in computing and networking contexts — for IP addressing specifically, the IP Subnet Calculator works with binary-derived address math, and for encoding arbitrary data into a different character representation entirely (not a numeric base conversion), the Base64 Encoder/Decoder handles a related but conceptually distinct kind of representation conversion.
Common mistakes
Assuming a number's digit sequence carries the same meaning across different bases — reading a hexadecimal number's digits as if they were decimal, for instance — produces a completely wrong value, since the same digit sequence represents a different quantity depending on which base it's actually expressed in; always confirm which base a given number is written in before interpreting or converting it.