For the Boolean functions in Q$3)$ to Q$4)$ you are going to find a simplified Product of Sums expression using the

following steps:

$($a$)$ Construct the truth table.

$($b$)$ Write the function as a product of maxterms.

$($c$)$ Draw the Karnaugh Map.

$($d$)$ Write down all prime implicants for $F^{\text{'}}($complement of $F).$

$($e$)$ Mark essential prime implicants. Indicate the minterm$($s$)$ that make them essential.

$($f$)$ Find a simplified POS expression for $F$ using prime implicants $($hint: $F=(F^{\text{'}}{)}^{\text{'}}).$

$($g$)$ Calculate literal cost $($L$)$ and gate input cost $($G$).$

$($h$)$ Implement using AND, OR gates.

$($i$)$ Implement using two$-$level NOR gates.

Q$3),F(w,x,y,z)=wx{z}^{\text{'}}+w{x}^{\text{'}}{y}^{\text{'}}+wx{y}^{\text{'}}+x{y}^{\text{'}}{z}^{\text{'}}$

Q$4),F(x,y,z)=(xo+y^{\text{'}})z+xy$