Number Base Converter

Because hex is compressed binary: each hex digit is exactly one nibble (4 bits), so a byte is always two hex digits and the translation is mechanical — 0xFD is 1111 1101, readable at a glance once you know 16 patterns. Writing 0xFF3A21 beats writing 24 binary digits, and unlike decimal, the bit structure stays visible. That's why colors, memory addresses, and byte dumps are hex.

Repeatedly divide the decimal number by 2, keeping each remainder: the remainders, read bottom-to-top, are the binary digits. It works because each division peels off the lowest bit (the remainder is whether the number is odd). The tool prints every division so you can copy the work onto homework — and the same method converts to any base by dividing by that base instead.

They're the prefixes programming languages use to mark a literal's base: 0x for hex, 0b for binary, 0o for octal (all from C-family conventions, now in Python, JavaScript, Rust, and most modern languages). 0x10 is sixteen, not ten. The converter accepts them on input and includes them in copies so pasted values mean the same thing in code.

Almost exclusively Unix file permissions: chmod 755 is octal, where each digit packs three permission bits (read/write/execute) for owner, group, and others — a place where base-8 genuinely fits the data. Beyond that, octal is mostly historical. The chmod calculator decodes those permission digits specifically.