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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.
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Introduction to Sequential Logic Design
Finite State-Machine Analysis
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Prev…
Flip FlopsD FFsT FFsJ-K FFs
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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.
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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
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Mealy Machine
Next state= F (current state, input)Output= G (current state, input)
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Moore Machine
Next state= F (current state, input)Output= G (current state)
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Characteristic Equations
A Characteristic equation specifies the FF’s (or latch’s) next state as a function of its current state and inputs.
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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.
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Example: clocked synchronous FSM using positive-edge triggered D FFs
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Transition, state, state/output tables
Excitation equationsTransition Equations (next-state equations)Output equations
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State Diagram
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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.
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Excitation EqTran. EqTran.TableOutput EqTran/out TableState/out TableState Dagram
Another Example
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