Objective:

Derive a truth table and sum$-$of$-$products representation for the function describing the operation

of the $4-$channel multiplexor shown in P&H Fig B$\mathrm{.}5\mathrm{.}10($above$).$

Please produce the following:

A truth table $($ASCII format$)$ for this function

A Sum$-$of$-$Products representation for this function. In your Sum$-$of$-$products

representation, please use the following $C++$ conventions for describing boolean

operations:

$!A=$ NOT $(A)$

$A$&&$B=$A AND $B$

$A||B=A$ OR B

Precedence:

NOT has highest precedence

Assume AND and OR have equal precedence: use parentheses as

needed to indicate the order of operations

Hints:

We are interested in the truth table ONLY for the inputs to the multiplexor.

In your writeup, please identify the inputs clearly. E$.$g$.,$ The output from the AND gate is labeled as A$,$ the output from the OR gate is labeled B$,$ and so forth.

Unlike the previous problem for the two$-$input mux where S $($the selector$)$ was binary, here S is a $4-$valued thing, so you need to figure out how to map from a $4-$valued thing into a form suitable for use in a truth table.