Asynchronous (Ripple) Counter — Number of States How many distinct states are available in a 2-bit asynchronous (ripple) binary counter?

Introduction / Context:The number of unique states in a counter determines its modulus and how often it repeats. Whether synchronous or asynchronous, an N-bit binary counter can represent 2^N distinct states. Recognizing this quickly is a core digital logic skill.

Given Data / Assumptions:

• Counter type: binary asynchronous (ripple) counter.
• Width: 2 bits (Q1 Q0).
• No truncation or preset modulus less than 2^N is specified.

Concept / Approach:A binary counter with N flip-flops cycles through all binary combinations from 0 to (2^N − 1) unless gating trims the count. For N = 2, the set is {00, 01, 10, 11}, which totals four distinct states and constitutes a MOD-4 counter.

Step-by-Step Solution:Compute 2^N with N = 2 → 2^2 = 4.Enumerate states: 00, 01, 10, 11.Confirm wrap: after 11, the next count wraps back to 00.Therefore, there are 4 distinct states.

Verification / Alternative check:Simulate a ripple counter with two T flip-flops toggling on the preceding Q. The observed sequence shows four unique patterns before repeating.

Why Other Options Are Wrong:

• 1, 2: Underestimate the state space; even a single flip-flop has 2 states.
• 8: Would require 3 bits (2^3).

Common Pitfalls:Confusing number of states with number of flip-flops; forgetting the 2^N relationship.

Final Answer:4