Designing synchronous nonbinary counters The process for creating a synchronous counter that counts in a nonbinary sequence (custom MOD) is primarily based on:
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Aexternal logic circuits that decode the various states of the counter to apply the correct logic levels to the J-K inputs
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Bmodifying BCD counters to change states on every second input clock pulse
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Cmodifying asynchronous counters to change states on every second input clock pulse
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Delimination of the counter stages and the addition of combinational logic circuits to produce the desired counts
Answer
Correct Answer: external logic circuits that decode the various states of the counter to apply the correct logic levels to the J-K inputs
Explanation
Introduction / Context:Synchronous counters change state on a common clock edge, enabling precise custom sequences that are not simple powers of two. Building a nonbinary (arbitrary MOD) synchronous counter relies on steering the flip-flop inputs so that only the desired state transitions occur, while undesired states are skipped or reset predictably.
Given Data / Assumptions:
- Target is a nonbinary state sequence (e.g., MOD-10, MOD-12, Gray order, or custom codes).
- Flip-flops are clocked synchronously.
- Design freedom includes using combinational logic to drive J, K, T, or D inputs as functions of present state.
Concept / Approach:
The canonical method is to derive next-state equations from a state table or Karnaugh maps. External combinational logic decodes the present state (and possibly inputs) to generate the required control levels for the flip-flop inputs (e.g., J and K). This logic ensures that on each clock the counter advances to exactly the next desired state, creating the specified sequence and modulus.
Step-by-Step Solution:
Define desired sequence and assign binary codes to states.Write next-state equations Q_next = f(Q_present, inputs).Map equations onto flip-flop excitation tables to get J, K (or D/T) expressions.Implement the expressions with gates that decode the current state and drive the flip-flops.Verification / Alternative check:
Simulate the counter or step through states manually to verify that every present state transitions to the correct next state and that unintended states self-correct to the sequence (if needed via reset gating).
Why Other Options Are Wrong:
Modifying BCD or asynchronous counters to “every second pulse” does not generalize to arbitrary sequences and misses the synchronous design principle.
Eliminating counter stages is impossible; the flip-flops are what store state. Combinational logic alone cannot “count.”
Common Pitfalls:
Forgetting to analyze unused states (self-start or self-correcting behavior), neglecting hazards in the decode logic, or not meeting setup/hold timing on the synchronous inputs.
Final Answer:
external logic circuits that decode the various states of the counter to apply the correct logic levels to the J-K inputs