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

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

$1.$ Find the minimum Sum of Products $($SOP$)$ form from the Karnaugh map.

$2.$ Find the minimum Product of Sums $($POS$)$ form from the Karnaugh map for the complement of $F.$

$3.$ Draw the circuit diagram for the boolean formula using AND, OR$,$ and

NOT gates.

$4.$ Draw the circuit diagram using only NAND gates.

$5.$ Implement $F$ using a decoder.

$6.$ Implement $F$ using an $8-$to$-1$ Multiplexer.