$(15$ points$)$ Convert the following numbers:

$(247\mathrm{.}25{)}_{10}q,$

$(2$A$3$B$.$C$2){?}_{16}$cdots$---1$

$(247{)}_{8}q,18$

$12$

$10$

$.2)(20$ points$)$ Implement the following functions with $($a$)$ PAL, and $($b$)$ with PLA.

$o.F_1(A,B,C,D)=m(0,2,7,10)+d(12,15)$

$0,F_2(A,B,C,D)=m(2,4,5)+d(6,7,8,10)$

$(15$ points$)$ Show how to construct a $321$ mux using only $41$ Mux$($s$)$

$(15$ points$)$ Realize the output functions shown below using a $3-$to$-8$ decoder and the appropriate logic gates.

$f_1(a,b,c)=ab+b^{\text{'}}c$

$f_2(a,b,c)=(a+b^{\text{'}}+c)(a^{\text{'}}+b)$

$(15$ Points$)$ Use the Quine$-$McCluskey method to simplify the following function

$F(a,b,c,d,e)={\displaystyle \underset{?}{\overset{?}{}}}m(1,3,10,11,14,15,17,19,26)$

$(20$ points$)$ Implement the circuit described below using JK flip$-$flops and gates

$\backslash$table$[[$Current$,,,],[$State$,$Input,$\backslash$table$[[$Next$],[$State$]],$Output$],[$A$,0,$B$,0],[$A$,1,$A$,0],[$B$,0,$B$,0],[$B$,1,$C$,0],[$C$,0,$D$,0],[$C$,1,$A$,0],[$D$,0,$B$,0],[$D$,1,$C$,1]]$