P$1.$ Counter Design using FSM $(\backslash (1\backslash$times $60\backslash )$ p each $\backslash (=60\backslash )$ p$)$

A counter has a special counting sequence: $\backslash (0,5,7,1,0,5,7,1\backslash ),$ and so on$.$ Design this counter with minimal number of states.

a$)$ Draw a state diagram for the counter.

b$)$ Construct a state$-$assigned table including the next state and output.

c$)$ Draw the circuit diagram for the counter using D flip$-$flops.

d$)$ Repeat $($c$)$ using T flip$-$flops.

e$)$ Repeat $($c$)$ using JK flip$-$flops.