A positional numeral string has meaning only together with its base. The rightmost digit multiplies base⁰, the next base¹, then base², and so on. That rule works unchanged from binary base 2 through alphanumeric base 36; only the allowed digit alphabet grows.
Expand a value into powers of its base
Hexadecimal FF uses digit value 15 twice: 15 × 16¹ + 15 × 16⁰ = 240 + 15 = 255. Binary 11111111 adds powers 2⁷ through 2⁰ and reaches the same decimal integer. Conversion changes the representation, not the mathematical value.
The base limits the alphabet
Digit symbols map in order: 0–9 have values 0–9 and a–z have values 10–35. Base 2 permits only 0 and 1; base 16 ends at f; base 36 reaches z. A symbol equal to or above the base is invalid, so 2 cannot appear in binary and g cannot appear in hexadecimal.
Accumulate left to right
Repeatedly multiplying the accumulated value by the source base and adding the next digit is Horner-style evaluation of the same power expansion. For FF: start 0, obtain 15, then 15 × 16 + 15 = 255. It needs no floating-point powers and works exactly with BigInt.