what is the largest $n$ for which one can solve within one second a problem using an algorithm that requires $\log_{2}(n)$ operations? Each bit needs $10^{-9}$ seconds. I did it basically as follows:
$$1 (bit) \to 10^{-9}$$
$$\log_{2}(n) \to t$$
so, we have $t = 10^{-9} \times \log_{2}(n)$, so since algorithm has to run within 1 second, so we have $t=1$, so we have $10^{9} = \log_{2}(n)$??