Q$1.$ A digital logic circuit is shown in Fig. $1.$

Fig. $1$

$($a$)$ Write a Boolean logic function to describe the relationship between the inputs $\backslash ($ X$,$ Y$,$ Z $\backslash )$ and the output $\backslash ($ F $\backslash ).$

$10\backslash \%$

$($b$)$ Draw the Karnaugh map and the truth table of the logic circuit.

$\backslash [$

$30\backslash \%$

$\backslash ]$

$($c$)$ Express the logic function as a sum of minterms and as a product of maxterms, using the shorthand format.

$\backslash [$

$20\backslash \%$

$\backslash ]$

$($d$)$ Simplify the above function using the Karnaugh map, and implement it with twolevel NAND gate circuits. NOT gates can be used if needed.