Binary, Octal, Decimal, Hex

Computers think in binary, humans think in decimal, and hex sits in the middle as the compromise everyone actually uses day to day — one hex digit maps cleanly onto four binary digits, so converting between them is mechanical once you've done it a few hundred times. This tool skips the mechanical part: type into any field and the others update live.

Why hex won

Nobody chose hexadecimal because it's elegant — they chose it because a byte is 8 bits, and 8 bits splits perfectly into two 4-bit nibbles, and each nibble maps to exactly one hex digit (0–F). So a byte is always exactly two hex characters, no remainder, no awkward rounding. That's the whole reason memory addresses, colour codes, MAC addresses and SHA hashes are all written in hex — it's the most compact way to write binary data that a human can still read without their eyes glazing over.

Numbers you'll recognise once you've seen them

• FF hex = 255 decimal = 11111111 binary — the max value of a single byte, shows up constantly (subnet masks, RGB colour channels, byte overflow bugs)
• #FF5733 in CSS is just three bytes in a row: R=255, G=87, B=51
• chmod 755 is octal, and it's really 111 101 101 in binary — owner gets everything, group and others get read+execute
• IPv6 addresses and MAC addresses are both written in hex for the same reason colour codes are — compact, byte-aligned, easy to eyeball for obvious typos

Where octal still shows up

Octal feels like a fossil from old Unix systems, and mostly it is — except for file permissions, where it's still the standard way to specify them, and the occasional legacy protocol spec that predates hex becoming the default. If you're not doing sysadmin work, you can probably go your whole career without touching base 8 again outside of chmod.