A Johnson counter is a shift register where the inverted output of the last flip$-$flop is fed to the

input of the first flip$-$flop. Consider a $4-$bit Johnson counter with an initial state of $0000.$

$($a$)$ What is the sequence of states of the counter starting from $0000?$

$($b$)$ Draw the full state table of a $4-$bit Johnson counter. Name the four state bits as $D_3,D_2,D_1,$

and $D_0.$

$(8$ marks$)$

$($c$)$ Draw the full state diagrams of a $4-$bit Johnson counter.

$(6$ marks$)$