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  • Using a D register as the memory component

  • in our sequential logic system works great!

  • At each rising edge of the clock,

  • the register loads the new state,

  • which then appears at the register's output

  • as the current state for the rest of the clock period.

  • The combinational logic uses the current state and the value

  • of the inputs to calculate the next state and the values

  • for the outputs.

  • A sequence of rising clock edges and inputs

  • will produce a sequence of states, which

  • leads to a sequence of outputs.

  • In the next chapter we'll introduce a new abstraction,

  • finite state machines, that will make it easy to design

  • sequential logic systems.

  • Let's use the timing analysis techniques we've learned

  • on the sequential logic system shown here.

  • The timing specifications for the register and combinational

  • logic are as shown.

  • Here are the questions we need to answer.

  • The contamination delay of the combinational logic isn't

  • specified.

  • What does it have to be in order for the system

  • to work correctly?

  • Well, we know that the sum of register and logic

  • contamination delays has to be greater

  • than or equal to the hold time of the register.

  • Using the timing parameters we do know along

  • with a little arithmetic tells us

  • that the contamination delay of the logic

  • has to be at least 1ns.

  • What is the minimum value for the clock period tCLK?

  • The second timing inequality from the previous section

  • tells us that tCLK has be greater

  • than than the sum of the register and logic propagation

  • delays plus the setup time of the register.

  • Using the known values for these parameters

  • gives us a minimum clock period of 10ns.

  • What are the timing constraints for the Input signal

  • relative to the rising edge of the clock?

  • For this we'll need a diagram!

  • The Next State signal is the input to the register

  • so it has to meet the setup and hold times as shown here.

  • Next we show the Input signal and how

  • the timing of its transitions affect

  • to the timing of the Next State signal.

  • Now it's pretty easy to figure out when Input has to be stable

  • before the rising clock edge, i.e., the setup time for Input.

  • The setup time for Input is the sum

  • of propagation delay of the logic

  • plus the setup time for the register, which

  • we calculate as 7ns.

  • In other words, if the Input signal is stable at least 7ns

  • before the rising clock edge, then Next State will be stable

  • at least 2ns before the rising clock edge and hence meet

  • the register's specified setup time.

  • Similarly, the hold time of Input

  • has to be the hold time of the register

  • minus the contamination delay of the logic, which

  • we calculate as 1ns.

  • In other words, if Input is stable at least 1ns

  • after the rising clock edge, then Next State

  • will be stable for another 1ns, i.e., a total of 2ns

  • after the rising clock edge.

  • This meets the specified hold time of the register.

  • This completes our introduction to sequential logic.

  • Pretty much every digital system out

  • there is a sequential logic system

  • and hence is obeying the timing constraints imposed

  • by the dynamic discipline.

  • So next time you see an ad for a 1.7 GHz processor chip,

  • you'll know where the “1.7” came from!

Using a D register as the memory component


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B1 中級

5.2.6 タイミング例 (5.2.6 Timing Example)

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    林宜悉 に公開 2021 年 01 月 14 日