Consider the function $F(W,x,Y,Z)=(1,2,3,6,13,15),$ where $W$ is the MSB and $Z$ is the LSB$.$

The don't care function $D=(5,7,8,9,11,12,14).$ Answer the following questions:

a$)$ Write the truth table of $F.$

b$.$ 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$)$ Write a Verilog code for the logic expression of $"F"$ found in part $($b$)$ using structural representation.

d$)$ Write and simulate the Verilog code in part $($c$)$ using Vivado. Take screenshots of your code, test bench code and your simulation results. Label the inputs and outputs clearly on the screenshots. Hint: you must use the first $5$ input combinations from the truth table in your testbench to verify your code.

e$)$ 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.

f$)$ Write a Verilog code for the logic expression of $"F"$ found in part $($e$)$ using the $$assign$"$ statement.

g$)$ Write and simulate the Verilog code in part $($f$)$ using Vivado. Take screenshots of your code, test bench code and your simulation results. Label the inputs and outputs clearly on the screenshots. Hint: you must use the first $5$ input combinations from the truth table in your testbench to verify your code.

h$)$ Do the simulation results in parts $($d$)$ and $($g$)$ match? Explain your answer.