b$)$ Implement the below function using a $1$:$8$ demultiplexer and any logic gates.

Q$1$ Mux

a$)$ Given the below four$-$input boolean function

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

Define the inputs $x0,x1,x2,x3$ to implement the function $F(A,B,C,D)$ using $2$:$1$

multiplexers and NOT gates. Only $1,0,A,B,C,D,A^{\text{'}},B^{\text{'}},C^{\text{'}},$ and $D^{\text{'}}$ are allowed.

$A^{\text{'}}$