Question $2(30$ points$)$ Consider the clocked sequential circuit which has one JK flip$-$flor

a$)(9$ points$)$ Derive the flip$-$flop input, state and output equations of the circuit.

b$)(8$ points$)$ Derive the state table of the circuit.

c$)(8$ points$)$ Derive the state diagram of the circuit.

d$)(5$ points$)$ Determine the type of the sequential circuit. Justify your answer.

Note: Be careful with the notation used in the flip$-$flop input, state, and output equations. Use the notation shown in the classes; otherwise, your equations will not be understandable and will be considered wrong.