Question $6$

A control system is required for an industrial process that will turn off an output when the four sensors detect the following conditions:

sensor D is activated $($on$)$

sensors A and C are activated $($on$)$

sensors B and C are activated $($on$)$

$($a$)$ draw the truth table

$($b$)$ write the standard sum$-$of$-$product $($SOP$)$ expression for the truth table.

$($c$)$ design a digital circuit that will implement the SOP using an AND$-$OR gate network with inverters.