Consider the Input$/$Output Table below. $($ It is the truth table for an unknown statement form that is a combination of the inputs p$,$ q$,$ and r$.)$

Input output

p q r s

$1110$

$1101$

$1011$

$1000$

$0111$

$0100$

$0010$

$0001$

a$)$ Find a disjunctive normal form $($a DNF$)$ involving the input variables p$,$ q$,$ and r that will produce those output S values. $($Assume that $1=$ True, $0=$ False.$)$

b$)$ Construct a combinational digital circuit corresponding to that DNF$,$ using AND, OR$,$ and NOT gates $($only$).$ give me a picture of the image