Ok , I just worked out that every natural number can be expressed as sum of powers of 2, eg: (9 = 2^3 + 2 ^0). I am looking for an algorithm which does the splitting of natural number into powers of 2 efficiently.
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As mentioned in the comment above,
and then put a '1' wherever that list doesn't have a '0':
You can improve the speed a bit by not calculating the powers of 2, but by shifting the bit in the test pattern to the right position:
Or you can bitshift the number-under-test to the right and compare with '1' and reverse the result:
As usual, there is more than just one way to skin this particular cat...