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EE365

EE365. Sequential-circuit analysis. 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

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EE365

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  1. EE365 Sequential-circuit analysis

  2. 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)

  3. output depends onstate and input typically edge-triggered D flip-flops State-machine structure (Mealy)

  4. output dependson state only typically edge-triggered D flip-flops State-machine structure (Moore)

  5. 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”).

  6. 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

  7. 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-f’s). 2b. Construct output table • For each state/input combination, determine the output value. (Can be combined with state table.) 3. (Optional) Draw state diagram

  8. Example state machine

  9. Excitation equations

  10. Transition equations • Excitation equations • Characteristic equations • Substitute excitation equations into characteristic equations

  11. (output equation) state/outputtable state table transitiontable Transition and state tables (transitionequations)

  12. State diagram • Circles for states • Arrows for transitions (note output info)

  13. Modified state machine • Moore machine MAXS MAXS = Q0  Q1

  14. Updated state/output table, state diagram

  15. Timing diagram for state machine • Not a complete description of machine behavior

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