$($a$)$ Write the truth table and draw the circuit represented by

$F=(A+B+C+D^{\text{'}})(A^{\text{'}}+B^{\text{'}}+C^{\text{'}})+D^{\text{'}}(A+B+C)+D^{\text{'}}$

$($b$)$ Write the equivalent min term and max term expressions.

$($c$)$ Use K$-$map to find the simplest sum of product expressions. Use K$-$map of the complement to find the simplest of product of sums expression for $F.$

$($d$)$ Draw a circuit in terms of AND, NOT and OR gates.

$($e$)$ Change it into a circuit with NOR $($NAND$)$ gates.

$($f$)$ Implement $F$ with a $4-16$ decoder

$($g$)$ Implement $F$ with two $3-8$ decoders

$($h$)$ Implement $F$ with a $16-1$ multiplexer