Binary to decimal converter

Binary to decimal table

The last rows are the largest 32-bit and 64-bit unsigned values. The second is past the point where ordinary JavaScript numbers start rounding; the table and the converter above both compute with BigInt, so every digit is exact.

How to convert binary to decimal

Each binary digit stands for a power of two — 1, 2, 4, 8, 16 and so on, counting from the right — so the decimal value is simply the sum of the powers where the bit is 1; the 0 bits contribute nothing. For 10101101: 2⁷ + 2⁵ + 2³ + 2² + 2⁰ = 128 + 32 + 8 + 4 + 1 = 173.

Binary and decimal side by side

The largest 16-bit value is 1111111111111111 in binary and 65535 in decimal: 16 digits against 5. A decimal digit is worth log₂ 10 ≈ 3.32 bits — not a whole ratio, so decimal and binary digits never line up and there is no digit-by-digit shortcut: the whole number has to be added up, as above. Binary is what bit masks, flags and subnet masks are reasoned in: a /24 network mask is twenty-four 1 bits followed by eight 0 bits, 255.255.255.0 once written in decimal. In JavaScript and Python source, 173 is written 0b10101101 in binary and 173 with no prefix in decimal. Paste a prefixed number into the converter and it switches to the matching base; a number with no prefix is read in the selected base — binary on this page.

Other conversions

Going the other way? Decimal to binary converter.

• Binary to octal
• Binary to hex
• Octal to decimal
• Hex to decimal

Or open the full number base converter and see a number in all four bases at once.