Terminal count of a MOD-11 binary counter — identify the binary value For a modulus-11 (MOD-11) binary counter that counts 0 through 10 before resetting, what is the terminal count value in binary?

Introduction / Context:
The terminal count of a truncated counter is the last valid state before the counter returns to its initial state. For MOD-N counters that begin at 0, the terminal count is N − 1. Converting this decimal value into binary yields the specific Q output pattern observed just prior to reset.

Given Data / Assumptions:

• Counter starts at 0 and advances in natural binary.
• MOD-11 ⇒ states 0 to 10 (inclusive).
• Reset occurs immediately after the terminal count.

Concept / Approach:
Compute N − 1 and convert to binary. For N = 11, N − 1 = 10. Express 10 in 4-bit binary to match the minimal number of bits required to represent the state in a typical circuit using four flip-flops (truncated from the natural MOD-16).

Step-by-Step Solution:

Verification / Alternative check:
Enumerate the sequence briefly: … 1000₂ (8), 1001₂ (9), 1010₂ (10), then reset to 0000₂. This matches the definition of terminal count for MOD-11 starting at 0.

Why Other Options Are Wrong:

• 1000 (8) and 1001 (9): intermediate states, not terminal.
• 1100 (12) and 1011 (11): beyond the allowed range; a proper MOD-11 never reaches 11 before reset.

Common Pitfalls:

• Confusing terminal count with modulus (10 vs 11), or assuming BCD behavior (MOD-10).

Final Answer:
1010