$1.$ Sequential circuits: Counters

$($a$)(5$ points$)$ What is the difference between a synchronous and asynchronous counter?

$($b$)(15$ points$)$ Implement a synchronous $2-$bit Gray Code UP$-$DOWN counter using D flip$-$flops as follows $($i$.$e a counter that counts $00011110)$

i$.$ Specify the counter sequence and draw the state diagram

ii$.$ Derive the next state table from the state diagram

iii. Develop the transition table from the excitation table of the D$-$flip flops

iv$.$ Obtain the logical expression for each flip$-$flop input

v$.$ Implement the sequential counter.

$[$Hint:$]$ You can use a mode selector $\backslash ($ M $\backslash )$ such that you have a UP$-$count when $\backslash ($ M$=0\backslash )$ and a DOWN$-$count when $\backslash ($ M$=1\backslash ).$

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