Please pay special attention to part C $1.$ Consider the combinational circuit shown in figure below:

a$.(10$ points$)$ Derive the Boolean expressions for T$1$ through T$4.$ Derive the Boolean expressions for outputs F$1$ and F$2$ as a function of the four inputs $($A$,$ B$,$ C$,$ D$).$

b$.(10$ points$)$ List the truth table with $16$ binary combinations of the four input variables. Then list the binary values for T$1$ through T$4$ and outputs F$1$ and F$2$ in the table.

c$.(20$ points$)$ Plot the output Boolean functions obtained in part $($b$)$ on K$-$maps and show that the simplified Boolean expressions are equivalent to the ones obtained in part $($a$).$