Two sequential circuits have the form shown in Figure

Chapter 13, Problem 13.17

(choose chapter or problem)

Two sequential circuits have the form shown in Figure 13-17. The initial state of both circuits is \(Q_{2} Q_{1} Q_{0} = 000\). The two circuits perform the same function but with different timing between the input and output.

(a) Construct a state table and state graph for each circuit. (In the state graphs only include states reachable from the initial state.)

(b) Describe in words when each circuit produces Z = 1. (Hint: Consider three consecutive inputs as a 3-bit binary number with the most significant bit being sent first.)

(c) Considering the dependence of the output on the input, are the circuits Moore or Mealy circuits?

(d) Considering the timing of when Z = 1 with respect to the input, do the circuits have Mealy or Moore type timing?

Circuit 1                                                          Circuit 2

\(\begin{array}{ll} Q_{2}^{+}=Q_{2}^{\prime} Q_{0} & Q_{2}^{+}=Q_{2}^{\prime} Q_{0} \\ Q_{1}^{+}=X Q_{2}^{\prime} Q_{1}+X Q_{2}^{\prime} Q_{0}^{\prime} & Q_{1}^{+}=X Q_{1}+X Q_{0}^{\prime}+Q_{2} Q_{1} \\ Q_{0}^{+}=Q_{2}^{\prime} & Q_{0}^{+}=Q_{2}^{\prime} \\ Z=Q_{2} Q_{1} & Z=Q_{1} Q_{0}^{\prime} \end{array}\)