Problem

To determine the behavior of a state machine using present state and next state tables along with characteristic excitation equations.

Prelab

Analyze the above synchronous sequential D-flip-flop circuit by:

1. Using the present state variables of Y1 and Y2 for the top and bottom flip-flops, write the excitation equations:
   • Excitation equations are the functions that describe the effect of the circuit inputs.
   • Inputs: X, Y1, Y2 where Y1 and Y2 are the present states of Y1+ and Y2+
     • D-flip-flop inputs are: D0, D1. where: D0 = F1(X, Y1, Y2) and D1=F2(X, Y1, Y2).
2. Write the next state equations.
   • The characteristic equation of D-flip-flop is Q+ = D.
3. Write the output equation for Z.
   • Z = F(Y1, Y2), where F is the function of the AND gate with one input inverter.
4. Create the present-state/next-state (PS/NS) table.
5. Create the state diagram.

Procedure

1. Enter the schematic from Figure 1 in Logisim. The flip-flop is a D-flip-flop found under the Memory tab.
2. Using the state diagram you created in Section 5 of the Pre-lab, confirm the state machine operation.
   • To view the state machine in operation, continuously Poke the CLK input and make note of the Y1, Y2 and Z outputs.
3. Create a timing diagram demonstrating the operation of the state machine.

Conclusions

1. Comment on the circuit simulation.
2. Explain the timing diagram created in Section 3 of the Lab.