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.