Binary to Decimal Converter

Binary is base 2: each digit (bit) is worth twice the one to its right. To convert to decimal, multiply each bit by its power of two and add them up. For 11010110: 1×128 + 1×64 + 0×32 + 1×16 + 0×8 + 1×4 + 1×2 + 0×1 = 214. Only the 1-bits contribute, so in practice you add up the place values of the ones. The step-by-step table below the result shows this expansion for the number you enter.

It helps to remember the powers of two: 1, 2, 4, 8, 16, 32, 64, 128 for one byte, then 256, 512, 1024 and so on. Eight bits give 0–255, sixteen give 0–65,535 and thirty-two give 0–4,294,967,295. A byte of all ones, 11111111, is 255; a 1 followed by n zeros is 2ⁿ.

Input can contain spaces or underscores between groups (1101 0110, 0b1101_0110) and a leading minus sign. The number is treated as an unsigned magnitude — if your bits are a signed two's complement value, use the number base converter, which shows the signed interpretation at 8, 16, 32 and 64 bits. Conversion uses BigInt, so bit strings of any length are exact.