I read everywhere that $N$ qubits correspond to $2^N$ bits. Let's start with 1 qubit, which is commonly represented by $\alpha |0\rangle + \beta |1\rangle$ where alpha and beta are complex numbers. This looks to me like infinite bits. How do they choose alpha and beta so that it becomes 2 bits?
Edit: Why is it commonly said that $N$ qubits correspond to $2^N$ bits?