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 table that completely specifies the next state and output of the circuit for every possible combination of current state and input. Step 3: (optional) 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 Excitation equations Transition Equations (next-state equations) Output equations

11 State Diagram

12 Summary: how to analyze a clocked synchronous state machine? 1)Determine the excitation equations for the FF control inputs; 2)Substitute the excitation equations into the FF characteristic equations to obtain transition equations; 3)Use the transition equations to construct a transition table; 4)Determine the output equations; 5)Add output values to the transition table for each state (Moore) or state/input combination (Mealy) to create a transition/output table; 6)Name the states and substitute state names for state-variable combinations in the transition/output table to obtain state/output table; 7)Draw a sate diagram corresponding to the state/output table.

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

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