OK, I'm trying to figure this out but I cannot remember how to do the math
behind it.

If I have a series such as
1
2
4
8
16
32
64
128

and I add any combination of these numbers together (4 + 16 = 20) the only
way I can come up with the number 20 is by adding 4 and 16.  Now how do I do
this in reverse?  If I know the sum is 81, how do I determine that the
numbers that make up this sum are 1 + 16 + 64?

Thanks to anyone with the solution.