Binary to Decimal Converter

Each binary digit represents a power of 2, starting from the rightmost digit (2⁰=1). Multiply each digit by its place value and add them up: binary 1010 = (1×8) + (0×4) + (1×2) + (0×1) = 10 in decimal.

Repeatedly divide the decimal number by 2, recording the remainder each time, until you reach 0 — then read the remainders from bottom to top. This calculator does that conversion automatically in either direction.

Hexadecimal (base 16) is commonly used in computer science for representing memory addresses, color codes (like #FF5733), and binary data more compactly, since each hex digit represents exactly 4 binary bits.

Octal (base 8) was historically common in computing (Unix file permissions like 755 are octal) since it's a simple grouping of binary digits (3 bits per octal digit), though it's less common than hex in modern use.

Computers represent negative integers using two's complement: invert all the bits of the positive value and add 1. Enable "Signed (two's complement)" and choose a bit width to interpret your binary or hex input as a signed value — for example, 11111011 in 8-bit two's complement equals −5 in decimal.