Consider the combinational logic circuit illustrated below:

a$)$ Derive Boolean expressions from $T1$ to $T4.$ Evaluate outputs $F$ and $F2$ as a function of $4$ inputs.

b$)$ Give the truth table with $16$ binary combinations for the $4$ input variables. List the binary values from $T1$ to $T2$ and the outputs $F1$ and F$2.$

c$)$ Put the Boolean outputs obtained in b$)$ into a Karnaugh table and show that the simplified Boolean expressions are equivalent to those obtained in a$).$