Problem $6$: $(10$ points$)$ Determine the logic expression for a $1-$bit logic unit module whose operation for each bit position is specified by the condensed function table of Table $2.$ The inputs and output all active high. The expression will not be a standard sum of products or product of sums. Do not simply the expression.

Table $2.$ Function Table for Logic Unit Module

Problem $7$; $(10$ points$)$ Realize the $1-$bit logic unit module specified in the function table of Table $2($problem $6)$ using SSI gates and a $4$ to $1$ multiplexer. The $74153$ schematic below is a $\backslash (4\backslash$times $1\backslash )$ multiplexer with two selections $(\backslash ($ B $\backslash )($MSB$)$ to $\backslash ($ A$($L S B$)\backslash )),$ four inputs $(1$ CO to $\backslash (1\backslash$mathrm$\{$C$3\}\backslash )),$ one active high enable GN $,$ and output Y $.$ Use proper mixed logic design and clearly label the inputs and outputs of the design.