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Timing and Hazards

Timing and Hazards. Logical levels. Negative Logic. Positive Logic. 0v = 1. 5v = 1. 5v = 0. 0v = 0. Noise – basic concepts. 1. Ideal World. 0. Noise – basic concepts. Positive Logic. 1=5v. Ideal World. Voltage. 0=0v. 1. Real World. Voltage. 0. Noise – basic concepts.

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Timing and Hazards

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  1. Timing and Hazards

  2. Logical levels Negative Logic Positive Logic 0v = 1 5v = 1 5v = 0 0v = 0

  3. Noise – basic concepts 1 Ideal World 0

  4. Noise – basic concepts Positive Logic 1=5v Ideal World Voltage 0=0v 1 Real World Voltage 0

  5. Noise – basic concepts Positive Logic 1 Real World 0

  6. Noise – basic concepts High Value 5v Output Range Input Range 4v 3.5v Low Value 1.5v 1v Input Range Output Range 0v

  7. Timing – basic concepts 1 Ideal World 0 “zero” time to change

  8. Timing 1 Ideal World 0 “zero” time to change 1 Real World 0 measurable time to change

  9. Timing Ideal World Input Output 1 1 0 0

  10. Timing Ideal World Input Output 1 1 0 0 Real World 1 1 0 0

  11. Timing – Delay Time 5V 50% 50% Input 0 tLH Time tHL Output 50% 50% Propagation delay = tPD = max(tHL,tLH)

  12. Timing – Contamination time 5V 50% Input 0 Time tCD Output The minimum time in which the input changed (50%) and the output didn’t change.

  13. Timing Rise and Fall time(measured on the output) Output 1 90% 90% 10% 10% 0 tr tf Rise Time Fall Time

  14. The tpd of a circuit The function : X1*X2 + X3’ X1 A X2 C Y B X3

  15. The tpd of a circuita single assignment The function : X1*X2 + X3’ X1=1 A X2=01 C Y B X3=1

  16. The tpd of a circuita single assignment The function : X1*X2 + X3’ X1=1 01 A X2=01 C B X3=1

  17. The tpd of a circuita single assignment The function : X1*X2 + X3’ X1=1 01 A X2=01 C Y 01 B X3=1

  18. The tpd of a circuita single assignment X2=01 tLH(A) Output of A tLH(B) Output of C

  19. The tpd of a circuit a single assignment X2=01 tLH(A) Output of A tLH(B) Output of C tLH(A) + tLH(B)

  20. The tpd of a circuit The tpd of a circuit is the maximal value Over all the possible single assignments

  21. The tcd of a circuita single assignment X2=01 Output of A Output of C Real tCD(Circuit)

  22. The tcd of a circuita single assignment X2=01 tCD(A) Output of A R tCD(B) Output of C

  23. The tcd of a circuita single assignment X2=01 tCD(A) Output of A R tCD(B) Output of C Real tCD(Circuit) = tCD(A) + tCD(B) + R

  24. The tcd of a circuita single assignment • Since tCD is the minimum tCD(Circuit) = tCD(A) + tCD(B) < tCD(A) + tCD(B) +R = Real tCD(circuit)

  25. The tCD of a circuit The tCD of a circuit is the minimal value Over all the possible single assignments

  26. Timing The minimum time for the output to change What is the minimal time that the output will change over a single assignment?

  27. The minimum time for the output to change a single assignment X2=01 tLH(A) Output of A tLH(B) Output of C tLH(A) + tLH(B)

  28. The minimum time for the output to change a single assignment X2=01 tLH(A) Output of A tLH(B) Output of C tLH(A) + tLH(B)

  29. The minimum time for the output to change a single assignment Real Minimum Time = tLH(A) + tHL(A) + Tr(X2) + Tr(C) 2

  30. The minimum time for the output to change a single assignment Real Minimum Time = tLH(A) + tHL(A) + Tr(X2) + Tr(C) 2 < Max(Tr(X2), Tr(C))

  31. The minimum time for the output to change a single assignment Estimated Minimum Time = tLH(A) + tHL(A) +Max(Tr(X2),Tr(C)) > Real Minimum time

  32. A Problems in timing Y = X2*X3 + X1*X2’ Assume tHL=tLH > 0 And equal for all gates X1 B X2 D Y C X3

  33. A Problems in timing Y = X2*X3 + X1*X2’ X1=1 B X2=1 D Y=1 C X3=1

  34. A Problems in timing Y = X2*X3 + X1*X2’ 0 X1=1 B 0 X2=1 D Y=1 C 1 X3=1

  35. A Change in input – final state Y = X2*X3 + X1*X2’ We changed the input But the result remained the same 1 X1=1 B 1 X2=10 D Y=1 C 0 X3=1

  36. A Change in input – Time slice 1 Y = X2*X3 + X1*X2’ X1=1 B X2=10 D Y=1 C X3=1

  37. A Change in input – Time slice 2 Y = X2*X3 + X1*X2’ 0 X1=1 B 01 X2=10 1 D Y=1 C 10 X3=1

  38. A Change in input – Time slice 3 Y = X2*X3 + X1*X2’ 01 X1=1 B 1 X2=10 10 D Y=0 C 0 X3=1

  39. A Change in input – Time slice 4 Y = X2*X3 + X1*X2’ 1 X1=1 B 1 X2=10 01 D Y=1 C 0 X3=1

  40. Input Change Time 0 1 X2 0 1 A 0 1 B 0 1 C 0 1 Y 0

  41. Input Change Time 1 1 X2 0 1 A 0 1 B 0 1 C 0 1 Y 0

  42. Input Change Time 2 1 X2 0 1 A 0 1 B 0 1 C 0 1 Y 0

  43. Input Change Time 3 1 X2 0 1 A 0 1 B 0 1 C 0 1 Y 0

  44. Input Change Time 4 1 X2 0 1 A 0 1 B 0 1 C 0 1 Y 0

  45. Static Hazard 1 X2 0 1 A 0 1 B Static Hazard – A change in a single input That should not change the output Leads to a momentary change. 0 1 C 0 1 Y 0

  46. Static hazard – another point of view X2X3 X1

  47. Static hazard – another point of view X2X3 X1

  48. Static hazard – another point of view X2X3 X1

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