Binary to Decimal Converter
Convert between binary, decimal, octal and hexadecimal instantly — with the working shown.
Step by step
11012 = 1310
- 1 × 23 = 8
- 1 × 22 = 4
- 1 × 20 = 1
Total = 13
This binary to decimal converter translates a number between binary, decimal, octal and hexadecimal at the same time. Type into any field and the other three update immediately, so you can go binary to decimal, decimal to binary, or hex to binary without switching tools. Very large values are supported using arbitrary-precision arithmetic, so nothing overflows at 32 bits.
Converting binary to decimal is a matter of positional weights. Each digit represents a power of two, starting at 20 on the right. So 1101 is (1×8) + (1×4) + (0×2) + (1×1) = 13. The working shown below the fields spells out this expansion for the current value, which makes the tool genuinely useful for homework and for anyone learning number systems rather than just wanting the answer.
Hexadecimal is the shorthand programmers use because one hex digit maps exactly to four binary digits — F is 1111. That's why colour codes, memory addresses and byte dumps are written in hex. Octal groups three bits at a time and still shows up in Unix file permissions. All conversion here is client-side JavaScript: free, instant, and nothing is uploaded.