🔢 Number Base Converter
Convert numbers simultaneously between Decimal, Hexadecimal, Octal, and Binary bases.
Computer Science Numeral Systems
Digital systems operate on binary code (0s and 1s). Decimal is standard base-10 human counting. Hexadecimal (base-16) and Octal (base-8) offer compact ways for programmers and engineers to represent raw binary byte streams. All four fields above are live at once: type into any one of them and the other three rewrite themselves, so you can work in whichever direction the problem arrives in.
Hexadecimal earns its place because the arithmetic lines up exactly. One hex digit covers four bits, so two digits describe one byte with nothing left over — which is why colours are written #FF8800, memory addresses appear as 0x7FFE, and a byte is read as a tidy pair rather than eight loose ones and zeros. Octal packs three bits per digit and now survives mainly in Unix file permissions, where 755 is really three sets of read, write and execute bits.
Conversion here runs on arbitrary-precision integers, so values far beyond the range of ordinary JavaScript numbers convert exactly — 64-bit identifiers, hashes and large bitmasks keep every digit instead of silently rounding once they pass about 9 quadrillion. Whole numbers only, positive or negative; fractional values and floating-point bit patterns are outside what this converter handles.