Consider the following boolean formula in $4$ variables, $A,B,C,$ and $D$ :

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

Draw the circuit diagram using only NAND gates.

Implement $F$ using a decoder.

Implement $F$ using an $8-$to$-1$ Multiplexer.