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MACHINE ARCHITECTURE AND THEIR HISTORICAL CONTEXT

10. Example: Design of a 3-bit Binary Counter

Example: Design of a 3-bit Binary Counter

  • Specification: The counter should count from 000 to 111 and then reset to 000.
  • State Diagram: Represent the sequence of states from 000 to 111.
  • State Encoding: Use binary encoding (000, 001, 010, ..., 111).
  • Flip-Flop Selection: Use D flip-flops.
  • Excitation Equations: Derive the D input equations for each flip-flop.
  • Combinational Logic: Implement the logic gates to generate the D inputs.
  • Verification: Simulate the counter to ensure it counts correctly.

Timing Considerations

Clock Skew:

  • The difference in arrival times of the clock signal at different flip-flops.
  • Can cause incorrect operation if not managed properly.

Setup and Hold Time:

  • Setup Time: The time before the clock edge during which the input must be stable.
  • Hold Time: The time after the clock edge during which the input must remain stable.
  • Violating these times can lead to metastability and incorrect state transitions.

Propagation Delay:

  • The time it takes for a change in the input to propagate through the combinational logic and affect the output.
  • Must be considered to ensure proper timing in sequential circuits.