Fundamental property of ring counters For an n-stage ring counter implemented with flip-flops and a circulating single 1, the ________ equals the number of flip-flops in the register.

Introduction / Context:
Ring counters are simple sequential circuits formed by connecting a shift register in a loop with a single circulating 1 (or 0). They are used for sequencing and time-slot generation. Understanding their modulus is key to predicting cycle length.

Given Data / Assumptions:

• There are n flip-flops connected in a ring.
• A single 1 circulates; at any time, exactly one flip-flop is HIGH.
• No fault states (e.g., multiple ones) are present after initialization.

Concept / Approach:
Each clock shifts the 1 to the next position. After n shifts, the 1 returns to its original position, so the number of unique states visited equals n. Therefore, the modulus (the number of states before repetition) equals the number of flip-flops.

Step-by-Step Solution:

Verification / Alternative check:
Simulate a 4-bit ring (states: 1000, 0100, 0010, 0001 → repeat). Four states confirm modulus 4.

Why Other Options Are Wrong:
“number of invalid states” depends on initialization, not fixed at n. “number of CASE statements” is a coding artifact. “other states are” is not a proper property statement.

Common Pitfalls:
Confusing ring counters with Johnson counters (twisted ring) whose modulus is 2n; assuming a ring naturally recovers from illegal states without additional logic.

Final Answer:
modulus is