Orpheus

Binary, Hex and Decimal Converter

Convert between bases, one number per line.

Options

Auto detects 0x and 0b prefixes.

Group binary in fours
Result

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A base is how many digits a system uses before it carries. Decimal has ten, binary two, hexadecimal sixteen. The number itself does not change — 255, 0xFF and 0b11111111 are the same value written three ways.

How to use Number Base Converter

  1. Paste your numbers. One per line. Prefixes 0x, 0b and 0o are detected automatically.
  2. Read all four bases. Decimal, hexadecimal, octal and binary for each input.

About converting number bases

A number base is a notation, not a property of the number. Two hundred and fifty five is the same quantity whether written 255, 0xFF or 0b11111111; only the representation changes. Computing settled on hexadecimal because sixteen is a power of two, so every hex digit corresponds exactly to four bits and a byte is always exactly two digits. That alignment is what makes hex readable as a bit pattern in a way decimal never is — 0xF0 is visibly the top four bits set, while 240 tells you nothing. Octal survives mainly in Unix permissions, where three permission bits map cleanly to one digit, which is why chmod takes numbers like 755 and 644. Its wider use faded partly because the C convention of a leading zero meaning octal produced a long tail of bugs when people wrote zero-padded decimals. The implementation detail that matters here is precision. Converting through an ordinary floating-point number loses exactness above 2^53, which quietly corrupts 64-bit identifiers, memory addresses and long bitmasks — the very things people convert bases for. Using arbitrary-precision integers avoids it entirely, and it is why the results here are exact at any size.

Frequently asked questions

Why is hexadecimal used so much in computing?
Because sixteen is a power of two, so each hex digit maps exactly to four bits. A byte is always two hex digits, which makes the notation compact and lets you read the bit pattern directly. Decimal has no such alignment.
Are very large numbers handled correctly?
Yes. Conversion uses arbitrary-precision integers rather than floating point, so a 64-bit value or a long bitmask converts exactly. Tools built on ordinary numbers silently lose precision above about nine quadrillion.
What do the 0x and 0b prefixes mean?
They are conventions marking the base: 0x for hexadecimal, 0b for binary, 0o for octal. They are notation rather than part of the number — 0xFF and 255 are the same value, written for different readers.
Why does octal still exist?
Mostly for Unix file permissions, where three bits map neatly to one octal digit — which is why chmod 755 is written that way. Outside that it has been largely displaced by hexadecimal, and a leading zero meaning octal in C caused enough bugs that later languages dropped the convention.

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