COMP541 State Machines

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COMP541State Machines

• Montek Singh
• Feb 6, 2007

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Topics

• How to design machines that go through a sequence
  of events
• Basically, close this loop

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Representation of Sequential Circuits

• Earlier we learned how to specify combinational
  circuits
• Truth tables, Boolean equations,
• Now extend to synchronous sequential circuits
• Include time
• Use state tables and state diagrams

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Input Equations

• Can describe inputs to FF with logic equations

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Time is Implied

• Note that last circuit used the
• Previous state to determine next state
• State and inputs to determine outputs
• Synchronous circuit
• So timing is discrete
• When are transitions?

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State Table

• Just truth table with state added

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Another Table

• Same info, different layout style

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Sequential Circuit Types

• Moore model outputs depend on states

• Mealy model outputs also depend on inputs

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State Diagram

• Alternative representation for state table
• Moore

Inputs
State/Output
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Mealy Model

• Output depends on input and state

Input/Output
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State Table vs. Diagram

• Same information
• Table is perhaps easier to fill in from
  description
• Diagram is perhaps easier to understand
• You can label states with English description

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Design Procedure

• Take problem description and refine it into a
  state table or diagram
• Assign codes to the states
• Derive Boolean equations and implement
• Or, write Verilog and compile
• See example next class
• Designing with gates and FFs more involved
  because you have to derive input and output
  functions

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Example Sequence Recognizer

• Circuit has input, X, and output, Z
• Recognizes sequence 1101 on X
• Specifically, if X has been 110 and next bit is
  1, make Z high

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How to Design States

• States remember past history
• Clearly must remember weve seen 110 when next 1
  comes along
• Tell me one necessary state

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Beginning State

• Start state lets call it A
• If 1 appears, move to next state B

Input / Output
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Second 1

• New state, C
• To reach C, must have seen 11

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Next a 0

• If 110 has been received, go to D
• Next 1 will generate a 1 on output Z

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What else?

• What happens to arrow on right?
• Must go to some state.
• Where?

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What Sequence?

• Here we have to interpret problem
• Weve just seen 01
• Is this beginning of new 1101?
• Or do we need to start over w/ another 1?
• Textbook decides that its beginning (01)

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Cover every possibility

• Well, must have every possibility out of every
  state
• In this case, just two X 0 or 1
• You fill in other cases

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Fill in
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Answer From Book
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State Minimization

• When we make state diagram, do we need all those
  states?
• Some may be redundant
• State minimization procedures can be used
• We wont cover now

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Reading

• 7-1 and 7-11

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Today

• Simple state machines
• How to code them in Verilog
• Next Class
• More on state machine styles
• Registers
• Counters