$5.$

For the Boolean function $F$ represented in the truth table:

a$)$ write the sum$-$of$-$products $($SOP$)$ Boolean expression $($i$.$e$.,$ where are

the $1\text{'}$s are in the $F$ column, $F\frac{?}{b}=ar\frac{A}{b}ar\frac{B}{b}ar(C)D\frac{+}{b}ar\frac{A}{b}ar(B)\frac{C}{b}ar(D)+$cdots

b$)$ draw the unsimplified circuit for this SOP expression, and determine

the number of gate delays and circuit complexity $($# gates $+$ # inputs into

those gates$)$

c$)$ using a K$-$map $($or the identities of Boolean algebra$),$ simplify this

function $F$ as much as you can

d$)$ draw the simplified circuit for your answer in part $($c$),$ and determine

the number of gate delays and circuit complexity $($# gates $+$ # inputs into

those gates$)$ of this circuit