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What is the maximum possible range of bit-count specifically in n-bit binary counter consisting of ‘n’ number of flip-flops?

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Answer & Explanation

Correct AnswerC. 0 to 2n − 1

Quick Explanation

An n-bit binary counter has 2ⁿ distinct states. If it starts at 0, the highest count is therefore 2ⁿ − 1, giving the range 0 to 2ⁿ − 1.

Formula / Key Relation

Number of states = 2ⁿ

Count range = 0 to (2ⁿ − 1)

Detailed Explanation

Concept & Reasoning

Each flip-flop stores one binary bit, so n flip-flops form 2ⁿ unique bit patterns. A 4-bit counter, for example, runs from 0000₂ (0) to 1111₂ (15), i.e. 0 to 2⁴−1. This generalizes directly to n bits.

How to Solve It in the Exam

n bits → 2ⁿ states → maximum numeric count 2ⁿ−1.

Important Exam Point

Separate 'number of states' from 'largest count'.

Related Revision Path

This question sits in the revision path Digital Electronics → Sequential Logic → Counters .

n-bit Binary Counter Range explanatory diagram

Quick Trick

n bits → 2ⁿ states → maximum numeric count 2ⁿ−1.

Common Mistake

Using 2ⁿ as the maximum count instead of the number of states.

Exam Tip

Separate 'number of states' from 'largest count'.

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Study concept · n-bit Binary Counter Range →Practice concept Practice topic

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