Q$2$

$(6$ points$)$

Consider an $8-$to$-1$ multiplexer with eight data inputs $d_0$ to $d_7,$ three select inputs $S_2,S_1,$ and $S_0,$ and one output $Y.$

a$)$ Write the logic expression for the output $Y.$

b$)$ Implement an $8-$to$-1$ multiplexer using only $2-$to$-1$ multiplexers.