@kapil If we consider that one compare operation gives us all the information (wether the element being searched is to be searched on the left part or right or already found), then logN does represent the number of compare operations in the worst case for an array of $2^N$ elements.
1, 2, 3, 4, 5, 6, 7, 8
suppose we are searching for 0. first comparison with 4. now we know we have to search on left portion. so compare with 2, then with 1. total 3 comparisons. $2^3$ = $8$