Binary to Decimal Converter: Exact, Any Length

1. Type or paste the binary number. A 0b prefix is accepted, and spaces or underscores between groups of bits are ignored, so 1111 1111, 0b1111_1111 and 11111111 are the same value.
2. Read the decimal value at the top. A leading minus sign is kept, so -1010 gives −10.
3. If the bits are a signed machine integer, read the Two's complement row instead and choose the width of 8, 16, 32 or 64 bits. Or switch From to two's complement to decode the pattern as a signed number.

Each binary digit is worth twice the digit to its right. Reading from the right, the places are worth 1, 2, 4, 8, 16, 32, 64, 128 and so on. To convert, add the place values where the bit is 1. For 101101, that is 32 + 8 + 4 + 1 = 45.

A quicker method by hand is to start with 0 and, for each bit from the left, double the running total and add the bit. For 101101: 1, 2, 5, 11, 22, 45. The converter does the same with arbitrary-precision integers, so a 128-bit or 1,000-bit value is exact rather than rounded the way a calculator's floating-point number would be.

The same bits can mean different numbers. As an unsigned value, 11111111 is 255. Read as an 8-bit two's complement integer, the way most processors store signed bytes, it is −1. The converter shows both, so you can pick the one that matches the program or datasheet you are reading.