Question

The modulo \(2^N\) counter consist of the following number of states and flip-flops respectively

• A. \(2N-1\) and \(N-1\)
• B. \(2^{2N}\) and \(N-1\)
• C. \(2^{N-1}\) and \(N-1\)
• D. \(2^N\) and \(N\)

Hint:

Number of states generated by a binary counter: \[ M=2^N \] where \(N\) is the number of flip-flops.

Answer 1

The Correct Option is D

Concept: An \(N\)-flip-flop binary counter can generate \[ 2^N \] distinct states.

Step 1: Determine states.
For \(N\) flip-flops, \[ \text{States}=2^N. \]

Step 2: Determine flip-flops required.
A modulo-\(2^N\) counter requires exactly \[ N \] flip-flops.

Step 3: Final answer.
\[ \boxed{2^N\text{ states and }N\text{ flip-flops}} \]