log(num_options)/log(2)

So for a 8 character digits-only value, num_options is 10^8, so log(power(10, 8))/log(2) = 30 bits. This means both 30 bits needed to store the value and 30 bits of security. It also works for octal or hexadecimal: just replace log(2) with log(n), like log(16) for hexadecimal.