Implementing logical negation with only bitwise operators (except !)

Question

~ & ^ | + << >> are the only operations I can use

Before I continue, this is a homework question, I've been stuck on this for a really long time.

My original approach: I thought that !x could be done with two's complement and doing something with it's additive inverse. I know that an xor is probably in here but I'm really at a loss how to approach this.

For the record: I also cannot use conditionals, loops, ==, etc, only the functions (bitwise) I mentioned above.

For example:

!0 = 1
!1 = 0
!anything besides 0 = 0

Answer 1

Assuming a 32 bit unsigned int:

(((x>>1) | (x&1)) + ~0U) >> 31

should do the trick