We're Going to Look at Some Ways in Which Binary

We're going to look at some ways in which binary arithmetic can be unexpectedly useful. For this problem, all numbers will be 8-bit, signed, and in 2's complement.
(a) For x = 8, compute x & (−x). (& here refers to bitwise-and, and − refers to arithmetic negation.)
(b) For x = 36, compute x & (−x).
(c) Explain what the operation x & (−x) does.
(d) In some architectures (such as the PowerPC), there is an instruction adde rX=rY,rZ, which performs the following:
rX = rY + rZ + CA
where CA is the carry flag. There is also a negation instruction, neg rX=rY which performs:
rX = 0 - rY
Both adde and neg set the carry flag. gcc (the GNU C Compiler) will often use these instructions in the following sequence in order to implement a feature of the C language:
neg r1=r0 adde r2=r1,r0
Explain, simply, what the relationship between r0 and r2 is (Hint: r2 has exactly two possible values), and what C operation it corresponds to. Be sure to show your reasoning.