Johnson counter MOD number: evaluate the claim “In a Johnson (twisted-ring) counter, the MOD number will always be equal to one-half the number of flip-flops in the counter.” Decide whether this statement is accurate, adding justification from counter operation theory.

Introduction / Context:
A Johnson counter (also called a twisted-ring counter) is a common sequence generator used in digital electronics. Understanding how many unique states it produces for a given number of flip-flops is essential when selecting a counter for timing, sequencing, and divide-by-N applications. This item asks whether its MOD number equals one-half the number of flip-flops, which tests fundamental knowledge of counter state capacity.

Given Data / Assumptions:

• We are dealing with an n-stage Johnson counter built from n edge-triggered flip-flops.
• The feedback is the inverted output from the last stage fed to the first stage (twisted-ring topology).
• All flip-flops are clocked synchronously by the same clock.

Concept / Approach:
For a conventional ring counter with n flip-flops and a single circulating 1, the MOD is n. A Johnson counter differs: it circulates a pattern of consecutive 1s followed by consecutive 0s created by feeding back the inverted last output. This structure produces 2n distinct states, not n, and certainly not n/2. Therefore, the MOD (the number of unique states before repetition) equals 2 * number_of_flipflops.

Step-by-Step Solution:
Let n = number of flip-flops.Johnson sequencing yields 2n valid codes (a run-length of 1s grows from 0 to n and then shrinks back to 0).Hence, MOD = 2 * n.The claim “MOD equals one-half the number of flip-flops” implies MOD = n/2, which contradicts the known result.

Verification / Alternative check:
Example: With n = 4, the Johnson counter generates 8 distinct states (0000 → 1000 → 1100 → 1110 → 1111 → 0111 → 0011 → 0001 → back to 0000), confirming MOD = 8 = 2n.

Why Other Options Are Wrong:
“Depends on propagation delay only” is irrelevant to the count of unique states. “Cannot be determined without the clock frequency” is incorrect because MOD depends on topology and n, not frequency. “Correct” contradicts the 2n property.

Common Pitfalls:
Confusing Johnson counters with ring counters; assuming MOD equals n; overlooking the role of the inverted feedback in doubling the count.

Final Answer:
Incorrect