Q$1)$ For the Boolean function $F(A,B,C,D)=(0,1,2,3,7,8,10)+{}_d(5,6,11,15)$

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 SOP expression for F using prime implicants.

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

f$)$ Implement using two$-$level NAND gates.