Number Base Converter

What a Base Actually Changes

Only the notation. The quantity is identical whichever base you write it in: decimal 255, binary 11111111 and hexadecimal FF all describe the same number of things. What changes is how many symbols are available before you need another column.

Why Computers Use Binary

A circuit is reliably either on or off, and two states map exactly onto two digits. Every larger structure, from an integer to a video frame, is built from those. Binary is unreadable at length for people, though, which is where hexadecimal comes in.

Hexadecimal Is Compressed Binary

Sixteen is two to the fourth, so one hex digit stands in for exactly four binary digits with no arithmetic needed. 1111 becomes F, and 11111111 becomes FF. That is why colour codes, memory addresses and byte dumps are written in hex rather than binary: it is four times shorter and converts back mechanically.

Converting by Hand

To go from decimal, divide repeatedly by the target base and read the remainders bottom to top. To come back, multiply each digit by its place value and add. 1011 in binary is 8 plus 0 plus 2 plus 1, which is 11.

Common Questions