$1.$ Find the boolean expression for the given digital circuit at the bottom. $(25$ points$)2.$ Simplify and implement a function F$($A$,$B$,$C$,$D$)=$ & $(0,2,5,7,10,13,15)$ with don't$-$care conditions d$($A$,$B$,$C$,$D$)=$ & $(4,8,14)$ using the Karnaugh map method and logic gates. Design the required circuit. $(25$ points$)3.$ Design the necessary circuit for the given function F$($A$,$ B$,$ C$,$ D$)=(1,3,4,11,12,13,14,15)$ using an $8$x$1$ MUX and the minimum number of logic gates. $(25$ points$)$