Q$2)$ For the Boolean function $F(A,B,C,D)=(1,3,5,6,7,9,10,11,14)$ find a simplified POS expression.

a$)$ Draw the Karnaugh Map.

b$)$ Write down all prime implicants.

c$)$ Mark essential prime implicants. Give your reasoning by indicating the minterm$($s$)$ that make them essential.

d$)$ Find a simplified POS expression for $F$ using prime implicants.

e$)$ Calculate literal cost $($L$)$ and gate input cost $($GI$).$

f$)$ Implement using two$-$level NOR gates.