Question

I want a one line code to check whether a given integer is of form 2ⁱ – 2^j or NOT. (using bitwise operators)

Answer 1

As AndreyT says, the answer can be found in Hacker’s Delight:

Use the following formula to turn off the rightmost contiguous string of 1-bits (e.g., 01011000 ⇒ 01000000):

((x | (x – 1)) + 1) & x

This may be used to see if a nonnegative integer is of the form 2^j – 2^k for some j ≥ k ≥ 0; apply the formula followed by a 0-test of the result.

(was debating whether to post this, as it’s a homework question, but as AndreyT already mentioned it and it’s easily Googlable, I figure it’s more helpful to quote directly; I’ll let the questioner deal with the ethical implications of accepting help on the homework, and I expect that if his answer depends on this, he will write up the explanation of how it works himself)