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Problem Set #$2$: Truth Tables and Boolean Equations, Part $2$

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

I am interested in the truth table ONLY for the inputs to the multiplexor. Please identify the inputs clearly. For example, The output from the AND gate is labeled as A$,$ the out put from the OR gate is labeled B$,$ and so forth.

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.