Binary (Base 2) to Decimal (Base 10) Converter

A number base, or radix, is simply how many distinct digits a counting system uses before it rolls over into a new place. Everyday decimal is base 10, using the digits 0 to 9; each position is worth ten times the one to its right. Computers work in binary — base 2, just 0 and 1 — because a switch is either on or off, and every bit is a power of two. Because long strings of bits are hard to read, programmers group them into octal (base 8, three bits per digit) or, far more commonly, hexadecimal (base 16, four bits per digit), which is why colours on the web look like #FF8800 and memory addresses are written in hex. When a base goes above ten it runs out of ordinary digits, so letters take over: A stands for 10, B for 11, and so on up to Z for 35, which is why base 36 is the largest that fits the usual 0–9 A–Z alphabet. Converting a number between bases never changes its actual value — 255, 0xFF, 0o377 and 11111111 in binary are all the same quantity, just written differently. This converter parses whatever you type in its source base into that one underlying integer and then writes it out in the base you want, using exact big-integer arithmetic so even very long binary or hexadecimal values stay precise.