zlacker

For base 2/16 this is pretty easy if you use assembly, because most ISAs have instructions to count the leading zeros, so for eg. aarch64 to get length of hex integer (assuming you're not trying to do anything weird like signed hex - negative numbers will always be max width this way):

  hlen:
        // int hlen(uint64_t x)
        // takes an integer, returns length of hex string
        mov     x9,     #16             // max width
        clz     x0,     x0              // count binary leading zeros
        cmp     x0,     #64
        lsr     x0,     x0,     #2      // 4 bits per hex digit
        sub     x0,     x9,     x0
        cinc    x0,     x0,     eq      // if num = 0, add 1
        ret

Decimal requires looping (well, only ~20 comparisons needed for 64-bit so maybe that could be unrolled but same thing either way), so it's simpler to just use high level.