Suppose there is an array containing unsorted data and I need to choose either linear search or binary search for searching. Then which option should I choose? The time complexity for linear search is O(n) and for binary search is O(log n). But, the fastest sorting algorithm gives the time complexity of O(n \* log n). Now, I don't know how to "add" complexities of two algorithms (if that's the right word) and hence, I am asking this question. 

So my question is if sorting then binary searching is better than simply linear searching or is it the other way? 

Plus, how do I prove whatever the case maybe using big O notation ( I mean "adding" and "comparing" the time complexities) ?

Thank you so much for reading!!! It means a lot.