Consider the following truth table. $($Refer to the image$)$

Also consider the following $1-$bit ALU that performs AND, OR$,$ and addition on a and $b.($Refer to image$)$

Note that one can select between three values using the Operation select line to the Result multiplexor. Assume that the Ainvert and Binvert signals can be asserted or deasserted and that the CarryIn signal can be deasserted or taken from the CamOut of the preceding $1-$bit ALU. The value of a NOR $b$ can be obtained by asserting Ainvert and Binvert and selecting an AND operation.

$($a$)$ Describe how the value of a NEW $b$ can be obtained. $(10$ points$)$

$($b$)$ Describe how the value of a XOR $b$ can be obtained. $(10$ points$)$