Binary to Decimal Converter

Multiply each digit by two raised to its position, counting from zero on the right, then add the results. So 1011 is 8 + 0 + 2 + 1 = 11. The doubling method is faster in practice: start at the left, double the running total and add the next digit.

It surfaces whenever a value overflows, a bitmask is used for permissions, or a colour is packed into an integer. A file permission of 755 is three sets of three bits — read, write, execute — which only makes sense in binary.

Two to the power of the bit count, minus one. Eight bits reach 255, sixteen reach 65,535, and thirty-two reach 4,294,967,295 — which is why unsigned 32-bit counters wrap at roughly 4.3 billion.