This reminds me of an assignment we had in one of my CpE classes. We had to implement a whole bunch of interesting operations using a limited set of operators and in as few operations as possible. Favorites:

Absolute value of a signed it:

a= x >> 32

return (a + x)^a

Swap values of two ints without a temporary int:

a^=b

b^=a

a^=b

! operator (boolean not) without any boolean operators:

int a = x | (~x +1);

int b = a >> 31;

return b + 1;

There were a ton of interesting problems. Made for a great assignment.