Question

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Bitwise and in place of modulus operator

Can someone explain the rationale that makes both expressions equivalents? I know it only works because 64 is a power of two, but how can I logically or mathematically go from division to bitwise and?

Answer 1

The operation x % 64 returns the remainder when x is divided by 64, which (assuming x>0) must be a number between 0 and 63. Let’s look at this in binary:

63_dec = 0011 1111_b
64_dec = 0100 0000_b

You can see that the binary representation of any multiple of 64 must end with 6 zeroes. So the remainder when dividing any number by 64 is the original number, with all of the bits removed except for the 6 rightmost ones.

If you take the bitwise AND of a number with 63, the result is exactly those 6 bits.