Binary to Decimal Converter

Binary is base 2. Each digit, or bit, is either 0 or 1, and each position is worth twice the position to its right. From the right, the place values are 1, 2, 4, 8, 16, 32, 64 and 128 for the eight bits of a byte, and they keep doubling after that. A bit that is 1 contributes its place value to the total and a bit that is 0 contributes nothing.

So to go from base 2 to base 10, add the place values of the 1 bits. For 101101 the 1s sit in the 32, 8, 4 and 1 positions, so the value is 32 + 8 + 4 + 1 = 45. For 1100100 they sit at 64, 32 and 4, giving 100. There's a left-to-right shortcut too: start at 0, and for each bit double the running total and add the bit. For 101101 that goes 1, 2, 5, 11, 22, 45.

A few patterns help with checking. A run of n ones is 2^n - 1, so 11111111 is 255, the largest value of a byte, and sixteen ones is 65,535. A 1 followed by n zeros is 2^n, so 10000000 is 128. Leading zeros don't change anything: 00101101 is still 45. Network engineers use this daily, because an IPv4 address is four bytes: 11000000.10101000.00000001.00000001 is 192.168.1.1.

The converter reads binary as an unsigned whole number. Hardware and most programming languages store negative integers in two's complement, where the leftmost bit carries a negative weight. Read as a signed 8-bit value, 11111111 is -128 + 127 = -1 rather than 255, so you need to know the bit width and whether the value is signed. There's no length limit here: values are parsed with BigInt, so a 64-bit or 128-bit string converts exactly.