How Computers Work Lecture 8 Asynchronous State Machines and Metastability



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How Computers Work Lecture 8 Asynchronous State Machines and Metastability




Maximum Frequency



Skew



What we will cover today: The Trouble with Asynchronous Inputs



A Synchronizer as Arbiter



What Happens Now?



Buridan’s Ass



The Game Show Arbiter



A Simpler Arbiter



With Both Inputs High



Static Metastability



Static Metastability: Inverted Pendulum Analogy



What does Heisenberg Say ?



What if we relax accuracy?



The Remarkable Fact



Dynamic Metastability (More Stupid Classroom Tricks)



Lecture Demonstration Circuit



Is It Possible to Build This?



Practical Metastability



A Simple Model of Static Metstability



Evolution of Vout



How Small must Vin(0) be to make time to saturation take longer than time t?



If Vin(0) is uniformly distributed:



How much time do we need to achieve a certain pmetastable?



Example: How Long for 1 failure / year?



How often will failures occur if we wait 100 ns?



Is this a Good Excuse For Cruising a Light?



What did we Learn Today?

  • If we violate setup or hold times, a flip-flop can give a random digital output.

  • If we violate setup or hold times, we can’t bound the propagation delay of a flip-flop.

  • Metastability usually causes strange outputs, but flip-flops are sold that have valid, stable, outputs while internal nodes are metastable. They can still change their minds when coming out of metastability.

  • In practice, we can choose a propagation time that will have a forever stable output “most” of the time.

  • If we wait long enough (typ. 10-100 ns) “most of the time” is almost all of the time.

  • We can easily detect when settling happens, but we can’t say how long it will take.



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