How many states does a binary counter with n flip-flops have?a.nb.2nc.2^nd.n + 1

Break Down the Problem

1. Identify the Key Concept: We need to determine how many states a binary counter can represent based on the number of flip-flops $n$.
2. Understanding Flip-Flops: Each flip-flop can be in one of two states (0 or 1).

Relevant Concepts

1. Formula for States: The number of states in a binary counter with $n$ flip-flops is given by $2^n$. This is because each flip-flop adds a binary digit, doubling the number of possible combinations with each additional flip-flop.

Analysis and Detail

1. Calculation for Different Values of n: For instance, when $n = 1$, the count is $2^1 = 2$ states (0 and 1); for $n = 2$, it is $2^2 = 4$ states (00, 01, 10, 11); and this pattern continues for higher $n$.

Verify and Summarize

1. General Verification: The formula $2^n$ applies consistently across the binary system, confirming our approach is correct.
2. Summarization: In conclusion, a binary counter with $n$ flip-flops will have $2^n$ possible states.

Final Answer

Therefore, the answer is $2^n$.