Q $(100$ points$)/$ Consider the function $F(A,B,C,D)={\displaystyle \underset{?}{\overset{?}{}}}(0,1,5,6,7,8,9,10,11,13,14,15),$ where $A$ is the MSB

and $D$ is the LSB$.$ Answer the following questions:

a$)(5$ points$)$ Write the truth table of $F.$

b$)(20$ points$)$ Using K$-$map, find the most optimized version of F in the SOP form. Hint: To find the

SOP form, you need to consider the $1\text{'}$s in the K$-$map.

c$)(15$ points$)$ Write a Verilog code using structural representation for the logic expression of

$"$F$"$ found in part $($b$).$

d$)(15$ points$)$ Write a Verilog code using the "assign" statement for the logic expression of $"$F$"$

found in part $($b$).$

e$)(5$ points$)$ Explain why you believe the expression derived in part $($b$)$ is the simplest form of $"$F$."$

Discuss this in terms of the rules applied when working with K$-$maps.

f$)(20$ points$)$ Using K$-$map, find the most optimized version of F in the POS form. Hint: To find the

POS form, you need to consider the $0\text{'}$s in the K$-$map.

g$)(10$ points$)$ Write a Verilog code for the logic expression of $"F"$ found in part $(f)$ using the

"assign" statement.

h$)(10$ points$)$ Using DeMorgan's Theorem, prove that the expressions found in part $($b$)$ and part $($f$)$

are logically equivalent.