$($a$){?}^{**}$ Derive the Boolean expressions for $T_1$ through $T_4.$ Evaluate the outputs $F_1$ and $F_2$ as

a function of the four inputs.

$($b$)$ 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$)$ Plot the output Boolean functions obtained in part $($b$)$ on maps and show that the

simplified Boolean expressions are equivalent to the ones obtained in part $($a$).$

Obtain the simplified Boolean expressions for output $F$ and $G$ in terms of the input vari$-$

ables in the circuit of Fig. P$4\mathrm{.}2.$