Consider a simple algorithm to find the maximum element of an array containing integers. We just loop through the array, storing the maximum found so far and updating it whenever an element larger than the existing maximum is encountered.
This algorithm is often considered to have $O(N)$ complexity. But doesn't accessing the array take $O(\log N)$ time in each iteration of the for loop? After all, an array of size $N$ requires $\log N$ address bits, so accessing each element should take $\log N$ time steeps? So the total time complexity should be $O(N \log N)$, unless I'm missing something here?