Number Base Converter

How it works

Changing base changes the notation, not the number. The value we write 255 in decimal is 11111111 in binary, 377 in octal and FF in hexadecimal — four labels for one quantity. The conversion works by repeated division by the target base, collecting remainders. Computers work in binary because a transistor has two stable states, but binary is unreadable for humans: eight bits is already an unmemorable string. Hexadecimal solves that by packing exactly four bits into one digit, so a byte becomes two characters, and 255 — the largest value a byte can hold — becomes the tidy FF. That four-bits-per-digit relationship is why hex appears everywhere near hardware: colour codes, memory addresses, MAC addresses, error codes and file signatures. Octal, grouping three bits, survives mainly in Unix file permissions.