Binary to Decimal Converter

Number the bits from 0 on the right. Each 1 bit is worth 2 raised to its position; add those values together. For 101101 the 1 bits are at positions 5, 3, 2, and 0, so the value is 32 + 8 + 4 + 1 = 45. Type a binary number above and the decimal value updates as you type.

Divide the number by 2 and write down the remainder (0 or 1), then keep dividing the quotient by 2 until it reaches 0. The remainders read from the last one to the first are the binary digits: 156 becomes 10011100. Press Swap above, or set From to Decimal and To to Binary.

Computers use two’s complement: invert every bit of the positive value and add 1. In 8 bits, 100 is 0110 0100, so −100 is 1001 1011 + 1 = 1001 1100. The leftmost bit is the sign bit. Enter a negative decimal number and pick a width in the two’s complement panel to see the stored pattern.

Four bits (a nibble) map to exactly one hexadecimal digit, and eight bits make a byte, so grouping by four makes long values easier to read and to check against hex. Spaces and underscores in your input are ignored, so you can paste 1001_1100 or 1001 1100.

An unsigned value n needs ⌊log₂ n⌋ + 1 bits, so 255 needs 8 bits and 256 needs 9. Signed values need one extra bit for the sign. The converter shows the bit length of every result and flags an overflow when the value does not fit in the width you choose.