State capacity of a 3-bit asynchronous counter How many distinct count states does a 3-bit (three-flip-flop) asynchronous binary counter provide?

Introduction / Context:
Each flip-flop holds one binary digit. Regardless of ripple or synchronous style, n flip-flops can encode up to 2^n distinct states. This question checks basic recall of binary capacity for a 3-bit counter, a recurring building block in larger designs and in divide-by-N frequency generation.

Given Data / Assumptions:

• Three flip-flops (n = 3).
• Binary counting (no truncation/reset early).
• Idealized behavior without illegal states.

Concept / Approach:

The number of representable states equals the number of distinct combinations of 3 bits: 2 * 2 * 2 = 8. In free-running counters, these states cycle naturally from 000 to 111 and back to 000.

Step-by-Step Solution:

Verification / Alternative check:

Enumerate explicitly: 000, 001, 010, 011, 100, 101, 110, 111 → 8 states.

Why Other Options Are Wrong:

2 and 4 correspond to 1-bit and 2-bit capacities.

16 corresponds to 4 bits (2^4).

Common Pitfalls:

Confusing modulus with number of flip-flops; forgetting that truncation (e.g., MOD-6) requires extra decode beyond the natural 2^n states.

Final Answer:

8