Truncated modulus — select the example that is not a power-of-two count Which of the following moduli is an example of a truncated counter (i.e., not equal to 2^n for any integer n)?

Introduction / Context:
Binary counters naturally produce moduli that are powers of two because each new flip-flop doubles the number of states. When a design requires a modulus that is not a power of two, truncation via reset/load logic is used. Recognizing which moduli require truncation is important for choosing between a simple binary counter and additional decode/clear logic.

Given Data / Assumptions:

• Binary counters without extra logic yield 2^n states (n = number of flip-flops).
• A truncated modulus requires additional gating.

Concept / Approach:
Identify whether the candidate modulus equals 2^n. Values like 8, 16, 32, and 64 are 2^3, 2^4, 2^5, 2^6 respectively. Any other integer (e.g., 13) is not a power of two and therefore must be implemented by truncation from the next higher power-of-two counter modulus (here 16) using decode/reset logic.

Step-by-Step Reasoning:

Verification / Alternative check:
Design sketch: use a 4-bit counter and decode decimal 13 (1101₂) to clear back to 0000; the counter then cycles through 0–12 (MOD-13).

Why Other Options Are Wrong:

• 8, 16, 32, 64 are all natural binary moduli; no truncation required.

Common Pitfalls:

• Assuming decimal-friendly moduli (10, 12) are natural; they are truncated unless implemented with decade counters.

Final Answer:
13