Problem $3$: $(16$ marks$)$ Combinational Circuit Optimization

Assume that $F\frac{?}{b}=ar(W+x+Y)+WxZ+WxPZ+\frac{W}{b}ar((x+Y+Z))$

a$.(2$ marks$)$ Obtain the truth table of $F.$

b$.(2$ marks$)$ Represent F as a sum of miterms ${}_m(dots)$ and product of maxterms $M(...)$

Assume that you have the previous $F$ with the following don't care

a$.(2$ marks$)$ Find all prime implicants.

b$.(2$ marks$)$ Find all essential prime implicants

c$.(2$ marks$)$ Optimize $F.$

d$.(2$ marks$)$ Find $F$ cost in terms of GN by finding L and G first.

e$.(2$ marks$)$ Draw the lowest$-$cost two$-$level AND$-$OR block diagram of F $.$

f$.(2$ marks$)$ Convert your logic diagram using NANDS and inverters.

$\backslash$table$[[$W$,$X$,$Y$,$Z$,$F$],[,,,,],[,,,,],[,,,,],[,,,,],[,,,,],[,,,,],[,,,,],[,,,,],[,,,,],[,,,,],[,,,,],[,,,,],[,,,,],[,,,,],[,,,,],[,,,,],[,,,,],[,,,,],[,,,,]]$