$5.($a$)(5$ points$)$ State three differences between synchronous and asynchronous counters.

$($b$)(15$ points$)$ Implement a synchronous $2-$bit binary DOWN counter using J$-$K flip flops as follows $($i$.$e a counter that counts $\backslash (32103\backslash$ldots $\backslash ))$

$($a$)$ Specify the counter sequence and draw the state diagram

$($b$)$ Derive the next state table from the state diagram

$($c$)$ Develop the transition table from the excitation table of the J$-$K$-$flip flop

$($d$)$ Using K$-$map minimize the min$-$terms of each outputs and obtain the logical expression for each output function

$($e$)$ Implement the sequential counter.