What is the best way to find the # of binaries for 00000011?

it really works just like base-10: you are simply counting how many of the base^x there are in each number position. in base 10 we count by 1s, 10s, 100s, etc, those are simply powers of 10: 10^0, 10^1, 10^2 etc. the highest we can go in a position is the base minus 1, so 9 in base 10. once you have 9 10s for example, you can't have any more 10s without needing a 100. base 2 works the exact same. each position is a power of 2 this time though, so we count by 1s, 2s, 4s, 8s, 16s etc, and the highest we can count in a position is 1 (base of 2 minus 1), so once we have a 1 in a position we can't have any more without needing the next highest position. so 011 is three, if we want four, well we have a 4s position, so we put a 1 there and 0s for the 2s and 1s, we don't need those to count to 4 when we already have a 4, so 4 is 100. 100 in binary is simply saying 0 1s, 0 2s, and 1 4, or 2^2.