Binary to decimal converter

Write the place values over the bits, starting with 1 on the right and doubling to the left. Then add the place values that sit over a 1.

128 + 32 + 16 + 4 + 2 = 182, so 10110110 is 182. Spaces between groups of four (1011 0110) only help reading; the converter ignores them, along with _ and a 0b prefix.

Faster in your head for long numbers: start at 0, and for each bit from the left, double the running total and add the bit. You never need to know the place values.

bits:  1  0  1  1  0  1  1  0
total: 0×2+1 = 1
       1×2+0 = 2
       2×2+1 = 5
       5×2+1 = 11
      11×2+0 = 22
      22×2+1 = 45
      45×2+1 = 91
      91×2+0 = 182

This is also how parsers read numbers in any base: multiply the total by the base, add the next digit.

Computers store signed integers in two’s complement. In an N-bit value the top bit is worth -2^(N-1) instead of +2^(N-1); every other bit keeps its usual value. In 8 bits the top place is -128:

Shortcut: if the top bit is 1, the signed value is the unsigned value minus 2^N. 251 - 256 = -5. The converter shows both readings for 8, 16, 32, 64 and 128 bits.

Bits after the point are worth ½, ¼, ⅛ and so on. 101.101 is 4 + 1 + ½ + ⅛ = 5.625. Every binary fraction ends in decimal, because each place is a power of ½. The other way round is not true: decimal 0.1 never ends in binary.

// JavaScript
parseInt('10110110', 2)        // 182
0b10110110                     // 182 (literal)
BigInt('0b' + bits)            // exact for any length

# Python
int('10110110', 2)             # 182
int('0b1011_0110', 0)          # 182, prefix and underscores allowed

// Go
n, _ := strconv.ParseInt("10110110", 2, 64)   // 182

# Bash
echo $((2#10110110))           # 182

Going the other way? Use decimal to binary. For hex, use hex to decimal, and for bits that encode text, the binary to text translator.

Every 8-bit value with its unsigned and signed (two’s complement) decimal value.