TProblem $3(25$ points$)$

A sequential circuit has two D flip$-$flops, as shown in the logic diagram below.

a$)$ Identify the input, output, and state bits of this FSM$.(5$ points$)$

b$)$ Derive the Boolean equations for the output and the next state bits. $(10$ points$)$

c$)$ Construct the state table and state transition table for this circuit. $(10$ points$)$

$*$taken from Logic and Computer Design Fundamentals textbook