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Lecture 11

Lecture 11. Timing diagrams Hazards. Timing diagrams (waveforms). Shows time-response of circuits Like a sideways truth table Example: F = A + BC. A. B. C. D. F. time. Timing diagrams. Real gates have real delays Example: A' • A = 0? Delays cause transient F=1.

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Lecture 11

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  1. Lecture 11 • Timing diagrams • Hazards

  2. Timing diagrams (waveforms) • Shows time-response of circuits • Like a sideways truth table • Example: F = A + BC

  3. A B C D F time Timing diagrams • Real gates have real delays • Example: A' • A = 0? • Delays cause transient F=1 width of 3 gate delays

  4. F = A + BC in 2-level logic C canonical sum-of-products B F1 A minimized sum-of-products F2 canonical product-of-sums F3 minimized product-of-sums F4

  5. Timing diagram for F = A + BC • Time waveforms for F1 – F4 are identical except for glitches

  6. Hazards and glitches • glitch: unwanted output • A circuit with the potential for a glitch has a hazard. • Glitches occur when different pathways have different delays • Causes circuit noise • Dangerous if logic makes a decision while output is unstable

  7. Hazards and glitches • Solutions • Design hazard-free circuits • Difficult when logic is multilevel • Wait until signals are stable

  8. 1 1 0 1 0 0 1 1 0 0 1 1 0 0 Types of hazards • Static 1-hazard • Output should stay logic 1 • Gate delays cause brief glitch to logic 0 • Static 0-hazard • Output should stay logic 0 • Gate delays cause brief glitch to logic 1 • Dynamic hazards • Output should toggle cleanly • Gate delays cause multiple transitions

  9. Static hazards • Often occurs when a literal and its complement momentarily assume the same value • Through different paths with different delays • Causes an (ideally) static output to glitch

  10. A B S S' F static-0 hazard Static hazards A multiplexer A S F B S'

  11. Timing diagram for F = A + BC

  12. F = A + BC in 2-level logic 0 1 C 0 B 0 A canonical product-of-sums F3

  13. Timing diagram for F = A + BC

  14. F = A + BC in 2-level logic 1 0 C 1 0 canonical sum-of-products B F1 1 0 A

  15. Dynamic hazards • Often occurs when a literal assumes multiple values • Through different paths with different delays • Causes an output to toggle multiple times Dynamic hazards

  16. A C B1 B2 B3 F Dynamic hazard Dynamic hazards 3 A F 2 B 1 C

  17. A AB 00 01 11 10 CD 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 00 01 D 11 C 10 B Eliminating static hazards • Key idea: Glitches happen when a changing input spans separate K-map encirclements • Example: 1101 to 0101 change can cause a static-1 glitch

  18. A AB 00 01 11 10 CD 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 00 01 D 11 C 10 B Eliminating static hazards • ABCD: 1101  0101 F = AC' + A'D 0 1 0 0 1 1 1 0 1 0 1 1 1 0 1 A C' 0 F 1 1 A' D 0 0 1

  19. Eliminating static hazards • Solution: Add redundant K-map encirclements • Ensure that all single-bit changes are covered by same block • First eliminate static-1 hazards: Use SOP form • If need to eliminate static-0 hazards, use POS form • Technique only works for 2-level logic

  20. Eliminating static hazards A AB F = AC' + A'D + C'D 00 01 11 10 CD 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 00 A C' 01 D A' 11 F D C C' 10 D B

  21. Summary of hazards • We can eliminate static hazards in 2-level logic for single-bit changes • Eliminating static hazards also eliminates dynamic hazards • Hazards are a difficult problem • Multiple-bit changes in 2-level logic are hard • Static hazards in multilevel logic are harder • Dynamic hazards in multilevel logic are harder yet

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