$($d$)$ Using K maps obtain the minimum SOP expressions for $V,W,Y,$ and $Z.$

$V=$

$W=$

$Y=$

$Z=$

$($e$)$ Realize the circuit using a minimum two$-$level NAND$-$gate circuit. $($Submit a file with a maximum size of $1$ MB$.$ Your submission be graded by your instructor after the due date based on its accuracy. Your grade may change.$)$

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$($f$)$ Realize the circuit using a PLA. $($Specify the PLA table. Enter your answers as comma$-$separated lists. Use the following as necessary: $0$ and $1.)$

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