Truncated modulus — identify the non-truncated case Which of the following is <em>not</em> an example of a truncated modulus in a binary counter design?

Introduction / Context:
A “truncated modulus” results when a binary counter, which naturally cycles through 2^n states, is forced to recycle earlier using decode/reset logic to achieve a non-power-of-two modulus (e.g., 9, 11). Identifying which modulus is not truncated reinforces the relationship between natural binary capacity and custom count lengths.

Given Data / Assumptions:

• Binary counters natively implement moduli of 2^n.
• Any other modulus requires decoding and resetting.
• We compare 8, 9, 11, and 15.

Concept / Approach:

Check if each choice equals 2^n for an integer n. If yes, it is a natural modulus and therefore not truncated. If not, it must be truncated from a higher power-of-two sequence by early reset.

Step-by-Step Solution:

Verification / Alternative check:

Design examples: MOD-9 or MOD-11 counters are made by decoding a specific state and resetting; MOD-8 requires simply three flip-flops with no extra decode.

Why Other Options Are Wrong:

9, 11, and 15 require truncation from 16 (2^4) using reset logic.

Common Pitfalls:

Confusing “MOD-15” with “4-bit maximum” (which is 16). MOD-15 is indeed truncated; the natural 4-bit modulus is 16.

Final Answer:

8