I want to be able to take, as input, a character pointer to a number in base 2 through 16 and as a second parameter, what base the number is in and then convert that to it’s representation in base 2. The integer can be of arbitrary length. My solution now does what the atoi() function does, but I was curious purely out of academic interest if a lookup table solution is possible.
I have found that this is simple for binary, octal, and hexadecimal. I can simply use a lookup table for each digit to get a series of bits. For instance:
0xF1E —> (F = 1111) (1 = 0001) (E = 1110) —> 111100011110
0766 —> (7 = 111) (6 = 110) (6 = 110) —> 111110110
1000 —> ??? —> 1111101000
However, my problem is that I want to do this look up table method for odd bases, like base 10. I know that I could write the algorithm like atoi does and do a bunch of multiplies and adds, but for this specific problem I’m trying to see if I can do it with a look up table. It’s definitely not so obvious with base 10, though. I was curious if anyone had any clever way to figure out how to generate a generic look up table for Base X -> Base 2. I know that for base 10, you can’t just give it one digit at a time, so the solution would likely have to lookup a group of digits at a time.
I am aware of the multiply and add solution but since these are arbitrary length numbers, the multiply and add operations are not free so I’d like to avoid them, if at all possible.
You will have to use a look up table with an input width of
mbasebsymbols returningnbits so thatfor positive integers
b,nandm. So ifbis not a power of two, there will be no (simple) look up table solution.I do not think that there is a solution. The following example with base 10 illustrates why.
Changing the last digit from 6 to 5 will flip all bits.
And almost the same will hold if you process the input starting from the end. Changing the first digit from 6 to 5 flips a significant number of bits.