EE365

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EE365

• Sequential-circuit analysis

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Clocked synchronous seq. circuits

• A.k.a. state machines
• Use edge-triggered flip-flops
• All flip-flops are triggered from the same master
  clock signal, and therefore all change state
  together
• Feedback sequential circuits
• No explicit flip-flops state stored in feedback
  loops
• Example edge-triggered D flip-flop itself (4
  states)
• Sections 7.9, 7.10 (advanced courses)

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State-machine structure (Mealy)
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State-machine structure (Moore)
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State-machine structure (pipelined)

• Often used in PLD-based state machines.
• Outputs taken directly from flip-flops, valid
  sooner after clock edge.
• But the output logic must determine output
  value one clock tick sooner (pipelined).

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Notation, characteristic equations

• Q? means the next value of Q.
• Excitation is the input applied to a device
  that determines the next state.
• Characteristic equation specifies the next
  state of a device as a function of its
  excitation.
• S-R latch Q? S R Q
• Edge-triggered D flip-flop Q? D

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State-machine analysis steps

• Assumption Starting point is a logic diagram.
• 1. Determine next-state function F and output
  function G.
• 2a. Construct state table
• For each state/input combination, determine the
  excitation value.
• Using the characteristic equation, determine the
  corresponding next-state values (trivial with D
  f-fs).
• 2b. Construct output table
• For each state/input combination, determine the
  output value. (Can be combined with state table.)
• 3. (Optional) Draw state diagram

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Example state machine
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Excitation equations
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Transition equations

• Excitation equations
• Characteristic equations
• Substitute excitation equations into
  characteristic equations

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Transition and state tables
(transitionequations)
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State diagram

• Circles for states
• Arrows for transitions (note output info)

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Modified state machine
MAXS
MAXS Q0 ? Q1

• Moore machine

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Updated state/output table, state diagram
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Timing diagram for state machine

• Not a complete description of machine behavior