1. Finite State Machines Mealy machine inputs Outputs next state function
current state
next state function
output function
Outputs
inputs
clock
next state function: Fnext state ( I, S(i) )  S(i+1)
output function: Foutput ( I, S(i) )  O(i)
S(i) - Current state

2. Example -- Traffic Lights Controller
The controller operates the traffic lights at one intersection.
Detectors in both directions provide input signals to controllers: car approaching NS / car approaching EW.
Outputs control the traffic light: set to green / set to red.
When cars approach in both directions, toggle the light.
The controller needs two states, green/red.
state(i) carNS carEW state(i+1)
NSgo no no NSgo
NSgo no yes EWgo
NSgo yes no NSgo
NSgo yes yes EWgo
EWgo no no EWgo
EWgo no yes EWgo
EWgo yes no NSgo
EWgo yes yes NSgo
A state/output table is used to construct the controller

3. State Diagram NSgo EWgo
carEW or both directions
NSgo
EWgo
carNS or both directions
carNS or nothing
carEW or nothing
Calculate next state transitions using the table and Boolean identities
This example is a Moore machine  the outputs are a function only of the state.
In this case the output function is trivial: In state NSgo we want a signal for a NS green light. In state EWgo we want a signal for an EW green light.

4. Moore and Mealy Machines
Both these machine types follow the basic characteristics of state machines, but differ in the way that outputs (not next state) are produced.
Moore Machine:
Outputs are independent of the inputs, i. e. outputs are effectively produced from within only the state of the state machine.
Mealy Machine:
Outputs can be determined by the present state alone, or by the present state and the present inputs, i. e. outputs are produced as the machine makes a transition from one state to another.

5. Machine Models Moore Machine Mealy Machine Inputs Combinatorial
Logic to
Determine State
Present State
Register Bank
Determine
Output Based on:
Output
Moore Machine
Inputs
Combinatorial
Logic to
Determine State
Present State
Register Bank
Determine
Output Based on:
Present Inputs
Output
Mealy Machine

6. Advantages of Mealy FSM
Moore and Mealy FSMs Can Be Functionally Equivalent.
Mealy FSM Has a Richer Description and Usually Requires Smaller Number of States
Smaller circuit area.
Mealy FSM Computes Outputs as soon as Inputs Change
Mealy FSM responds one clock cycle sooner than equivalent Moore FSM.

7. Advantages of Moore FSM
Moore FSM Has No Combinational Path Between Inputs and Outputs.
output changes only when clock ends  short inputs that temporarily generated during the clock cycles will be ignored.

8. Moore FSM that Recognizes Sequence 101
reset
S0: No
elements
of the
sequence
observed
S1: “1”
observed
S1: “10”
observed
Meaning
of states:

9. Mealy FSM that Recognizes Sequence 10
0 / 0
1 / 0
1 / 0 S0 S1
reset
0 / 1
S0: No
elements
of the
sequence
observed
S1: “1”
observed
Meaning
of states:

10. Moore & Mealy Time Line clock input 0 1 0 0 0 Moore S0 S1 S2 S0 S0
Moore
S S S S S0
Mealy
S S S S S0

11. Finite State Machine Any circuit with memory is a Finite State Machine
Even computers can be viewed as huge FSMs
Design of FSMs Involves
Defining states
Defining transitions between states
Optimization / minimization

12. Implementation Finite state machine with a state variable Outputs
Combinational Logic
State Register
inputs

13. General Digital System
Control
control
lines
Combinational Logic
Architecture
State Register
CLOCK
Opcode

14. Finite State Machine: Conclusion
State Diagram
Illustrates the form and function of a state machine. Usually drawn as a bubble-and-arrow diagram.
State
A uniquely identifiable set of values measured at various points in a digital system.
Next State
The state to which the state machine makes the next transition, determined by the inputs present when the device is clocked.
Mealy Machine
A state machine that determines its outputs from the present state and from the inputs.
Moore Machine
A state machine that determines its outputs from the present state only.