Implement $y=!$a$!$be $+ad+bd+cd+cd!$e $(6$ points for each input, $+1$ bonus for all $4$ correct$)$ by using a $4$:$1$ multiplexer and as few other gates as possible.

Input selector bits $($choose $2)=$ a $q,$ b $q,$ C $q,$ d $q,$ e $q,$

Diagram $=4$:$1$ selector switch $($mux$)$

Data inputs from left, control inputs $(S)$ from bottom, output to right

For Selector bits $($in alphabetical order$)=00,$ input equation $=$

For Selector $=0$

For Selector $=10$

For Selector $=11$ : $$

Example$/$explanation: if you choose a and $b$ as your selector bits, complete the minterms for $!a!b(00$ case$),!$ab $(01),$ a$!$b $(10),$ and ab $(11),$ using functions of $(c,d,e--$ it's essentially a Shannon decomp. problem. Some choices of selector variables may result in simpler circuits than others.