$($a$)($i$)$ A multiplexer is called a data selector while a de$-$multiplexer is called a data

distributor. Explain in simple language what these means

$($ii$)$ the figure below is a multiplexer, by following the signals on appropriate lines,

Show the logic or logic code that must be exhibited on data selector lines for the data

on lines D$2$ and D$4$ to route to the output. Hence write down the logic equation for

these routing.

Prove that when the data selector reads $S1=0$ and $S2=1,$ gate $3$ is open to route the

data D$3$ while all the other gates are closed

What does the designation $4-$to$-1$ mean?