1. Introduction to Sequential Logic Design
Finite State-Machine Analysis

2. Prev…
Flip Flops
D FFs
T FFs
J-K FFs

3. Clocked Synchronous State-Machine
State machine: generic name for sequential circuits; (Finite State Machine: FSM)
Clocked: the storage elements (FFs) use a clock input;
Synchronous: all of the FFs in a circuit use the same clock signal.
Such a FSM changes states only when a triggering edge (rising or falling) on the clock signal.

4. State Machine Structure
State memory: n FFs to store current states. All FFs are connected to a common clock signal.
Next-state logic: determine the next state when state changes occur;
Output logic: determines the output as a function of current state and input
Mealy machine vs. Moore machine

5. Mealy Machine Next state= F (current state, input)
Output= G (current state, input)

6. Moore Machine Next state= F (current state, input)
Output= G (current state)

7. Characteristic Equations
A Characteristic equation specifies the FF’s (or latch’s) next state as a function of its current state and inputs.

8. Analysis of FSM with D FFs
Next state= F (current state, input)
Output= G (current state, input)
Step 1: Determine the next-state and output functions F, G
Step 2: Use F, G to construct a state/output tables that completely specifies the next state and output of the circuit for every possible combination of current state and input.
Step 3: Draw a state diagram which is a graphical form of the state/output table.

9. Example: clocked synchronous FSM using positive-edge triggered D FFs

10. Transition, state, state/output tables
D0=Q0.En’+Q0’.EN, D1=Q1.EN’+Q1’.Q0.EN+Q1.Q0’.EN…These come from circuit analysis
Q0*=D0=Q0.EN’+Q0’.EN, Q1*=D1=Q1.EN’+Q1’.Q0.EN+Q1.Q0’.EN….Note: S*=Q1*Q08, This makes table a)
We use A=00, B=01, C=10, D=11. This makes table (b)
MAX=Q1.Q0.EN, this completes table (c)
Excitation equations
Transition Equations (next-state equations)
Output equations

11. State Diagram

12. Try Logisim

13. Timing Diagram? CLK EN Q0 Q1 MAX
ASSUME Q0, Q1 ARE AT 00 AT INITIAL CONDITION. See page 550, but no MAXS Q1
MAX

14. Again-Detailed: how to analyze a clocked synchronous state machine?
Determine the excitation equations for the FF control inputs;
Substitute the excitation equations into the FF characteristic equations to obtain transition equations;
Use the transition equations to construct a transition table;
Determine the output equations;
Add output values to the transition table for each state (Moore) or state/input combination (Mealy) to create a transition/output table;
Name the states and substitute state names for state-variable combinations in the transition/output table to obtain state/output table;
Draw a state diagram corresponding to the state/output table.

15. Another Example Excitation Eq Tran. Eq Tran.Table Output Eq
Tran/out Table
State/out Table
State Dagram