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SEQUENTIAL LOGIC DESIGN PRINCIPLES

SEQUENTIAL LOGIC DESIGN PRINCIPLES. BISTABLE ELEMENTS. BISTABLE ELEMENTS. BISTABLE ELEMENTS. LATCHES, FLIP-FLOPS. LATCH: OUTPUT CHANGES AT ANY TIME BASED ON INPUT FLIP-FLOP: OUTPUT CHANGES CONTROLLED BY SAMPLED INPUTS AND CLOCK. S-R LATCH. S-R LATCH SYMBOL. S-R LATCH TIMING.

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SEQUENTIAL LOGIC DESIGN PRINCIPLES

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  1. SEQUENTIAL LOGIC DESIGN PRINCIPLES

  2. BISTABLE ELEMENTS

  3. BISTABLE ELEMENTS

  4. BISTABLE ELEMENTS

  5. LATCHES, FLIP-FLOPS • LATCH: OUTPUT CHANGES AT ANY TIME BASED ON INPUT • FLIP-FLOP: OUTPUT CHANGES CONTROLLED BY SAMPLED INPUTS AND CLOCK

  6. S-R LATCH

  7. S-R LATCH SYMBOL

  8. S-R LATCH TIMING

  9. S-R LATCH TIMING PARAMETERS

  10. S\-R\ LATCH

  11. S-R LATCH WITH ENABLE

  12. D LATCH • NO PROBLEM WITH R=S=1

  13. D LATCH • TRANSPARENT LATCH:

  14. EDGE-TRIGGEREDD FLIP-FLOP • MASTER, SLAVE

  15. EDGE-TRIGGEREDD FLIP-FLOP • DYNAMIC INPUT INDICATOR

  16. EDGE-TRIGGEREDD FLIP-FLOP WITH ENABLE

  17. SCAN FLIP-FLOP

  18. MASTER/SLAVE S-R FLIP-FLOP • PULSE-TRIGGERED FLIP-FLOP

  19. MASTER/SLAVE J-K FLIP-FLOP • SOLVE PROBLEM OF S=R=1 • 1s CATCHING, 0s CATCHING

  20. EDGE-TRIGGERED J-K FLIP-FLOP • SOLVES 1s AND 0s CATCHING PROBLEM

  21. T FLIP-FLOP • CHANGES STATE EVERY CLOCK TICK

  22. T FLIP-FLOP WITH ENABLE

  23. CLOCKED SYNCHRONOUS STATE MACHINES • STATE: COLLECTION OF STATE VARIABLES CONTAINING ALL INFORMATION FROM PAST NEEDED TO PREDICT FUTURE BEHAVIOR • STATE VARIABLES BINARY VALUES • CIRCUIT WITH n VARIABLES HAS 2n STATES

  24. CLOCKED SYNCHRONOUS STATE MACHINES • STATE MACHINE - GENERIC NAME • CLOCKED - FLIP-FLOPS HAVE CLOCK INPUT • SYNCHRONOUS - SAME CLOCK • STATE CHANGES BASED ON CLOCK ACTIVITY

  25. STATE-MACHINE STRUCTURE • MEALY MACHINE • MOORE MACHINE

  26. CHARACTERISTIC EQUATION • DESCRIBES FUNCTIONAL BEHAVIOR OF LATCH OR FLIP-FLOP • EXAMPLES: • S-R LATCH Q* = S + R’  Q • EDGE TRIG’D D FLIP-FLOP Q* = D

  27. STATE MACHINE next state = F(current state, input) output = G(current state, input) • ANALYSIS GOAL: DETERMINE F, G

  28. STATE MACHINE ANALYSIS • DETERMINE F AND G • USE F AND G TO CONSTRUCT STATE/OUTPUT TABLE • DRAW STATE DIAGRAM (OPTIONAL)

  29. STATE MACHINE DESIGN • CONSTRUCT STATE/OUTPUT TABLE • MINIMIZE NUMBER OF STATES (OPTIONAL) • ASSIGN STATE VARIABLES • CHOOSE FLIP-FLOP TYPE (D OR J-K) • CONSTRUCT EXCITATION TABLE • DERIVE EXCITATION EQUATIONS • DERIVE OUTPUT EQUATIONS • DRAW LOGIC DIAGRAM

  30. DESIGN EXAMPLE • DESIGN A CLOCKED SYNCHRONOUS STATE MACHINE WITH TWO INPUTS, A AND B AND A SINGLE OUTPUT Z THAT IS 1 IF: • A HAD THE SAME VALUE AT EACH OF THE TWO PREVIOUS CLOCK TICKS, OR • B HAS BEEN 1 SINCE THE LAST TIME THE FIRST CONDITION WAS TRUE • OTHERWISE THE OUTPUT SHOULD BE 0.

  31. STATE ASSIGNMENT • CODED STATE: BINARY COMBINATION ASSIGNED TO STATE • NUMBER OF FLIP-FLOPS NEEDED IS log2(TOTAL NUMBER OF STATES) • MAY HAVE UNUSED STATES

  32. STATE ASSIGNMENT • CHOOSE INITIAL STATE CODE WHICH IS EASY TO FORCE • MINIMIZE CHANGES AT TRANSITIONS • EXPLORE UNUSED STATES • CONSIDER USING MORE THAN THE MINIMUM NUMBER OF STATE VARIABLES • ETC.

  33. STATE ASSIGNMENT

  34. UNUSED STATES • MINIMAL RISK APPROACH • MINIMAL COST APPROACH

  35. SYNTHESIS... • TRANSITION TABLE: NEXT CODED STATE FOR EACH STATE AND INPUT • EXCITATION TABLE: FLIP-FLOP EXCITATION INPUT VALUES NEEDED TO GO TO NEXT STATE • D FLIP-FLOPS: TRANSITION/EXCITATION TABLE

  36. SYNTHESIS WITH J-K FLIP-FLOPS • CHARACTERISTIC EQUATION: Q* = J  Q’ + K’  Q • NO INDEPENDENT EQUATIONS FOR J, K • J-K APPLICATION TABLE

  37. FEEDBACK SEQUENTIAL CIRCUITS • FUNDAMENTAL MODE CIRCUITS - INPUTS NOT ALLOWED TO CHANGE SIMULTANEOUSLY • ANALYZE: BREAK FEEDBACK LOOPS • INSERT BUFFER

  38. FEEDBACK SEQUENTIAL CIRCUITS • TOTAL STATE: INTERNAL AND INPUT STATE • STABLE TOTAL STATE • UNSTABLE TOTAL STATE

  39. MULTIPLE FEEDBACK LOOPS • BREAK ALL LOOPS • CUT SETS • ANY MINIMAL CUT SET IS OK • NON-MINIMAL CUT SET GIVE SAME RESULT, MORE STATES

  40. RACES • ONE INPUT CHANGES  MULTIPLE INTERNAL VARIABLES CHANGE STATE • NON-CRITICAL RACE • CRITICAL RACE

  41. STATE AND FLOW TABLES • TRANSITION TABLE  STATE TABLE • STATE TABLE  FLOW TABLE • FLOW TABLES ELIMINATE: • UNUSED STATES • NEXT-STATE ENTRIES THAT CANNOT BE REACHED FROM A STABLE STATE WITH A SINGLE INPUT CHANGE

  42. FEEDBACK SEQUENTIAL CIRCUIT DESIGN • Q* = (forcing term) + (holding term)Q

  43. FEEDBACK SEQUENTIAL CIRCUIT DESIGN • HAZARD-FREE EXCITATION LOGIC • KARNAUGH MAPS - CONSENSUS TERM(S)

  44. DESIGN EXAMPLE • PULSE-CATCHING CIRCUIT: DESIGN A FEEDBACK CIRCUIT WITH TWO INPUTS, P (PULSE) AND R (RESET), AND A SINGLE OUTPUT Z THAT IS NORMALLY 0. Z IS 1 WHENEVER A 0-TO-1 TRANSITION OCCURS ON P, AND SHOULD BE RESET TO 0 WHENEVER R IS 1.

  45. FEEDBACK SEQUENTIAL CIRCUIT DESIGN • WORD DESCRIPTION  PRIMITIVE FLOW TABLE • MINIMIZE NUMBER OF FLOW TABLE STATES • RACE-FREE ASSIGNMENT OF STATES • CREATE TRANSITION TABLE • GET EXCITATION MAP, HAZARD-FREE EXCITATION EQUATIONS • ELIMINATE ESSENTIAL HAZARDS • DRAW LOGIC DIAGRAM

  46. RACE-FREE ASSIGNMENT OF STATES • ADJACENCY DIAGRAM • n-CUBE: 2n VERTICES LABELED WITH n-BIT STRING; EACH VERTEX ADJACENT TO n OTHERS WHOSE LABELS DIFFER IN ONE BIT • RACE-FREE ASSIGNMENT: MAP NODES AND ARCS OF ADJACENCY DIAGRAM ONTO NODES AND ARCS OF n-CUBE

  47. FUNDAMENTAL-MODE CIRCUIT REQUIREMENTS • ONLY ONE INPUT CHANGES AT A TIME • MAX. PROPAGATION DELAY LESS THAN TIME BETWEEN INPUT CHANGES • STATES ASSIGNED WITHOUT CRITICAL RACES • EXCITATION LOGIC HAZARD FREE • NO ESSENTIAL HAZARDS

  48. ESSENTIAL HAZARDS • POSSIBILITY OF ERRONEOUS NEXT STATE • INPUT CHANGE NOT SEEN BY ALL EXCITATION CIRCUITS BEFORE SOME STATE VARIABLE TRANSITIONS PROPAGATE BACK TO THEIR INPUTS

  49. ESSENTIAL HAZARDS • TIMING SKEW = DIFFERENCE IN INPUT ARRIVAL TIMES • TIMING SKEW HAS TO BE LESS THAN PROPAGATION DELAY OF EXCITATION CIRCUITS AND FEEDBACK LOOPS • ELECTRICAL CIRCUIT LEVEL PROBLEM

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