What is the time complexity of binary search?

Binary search over a sorted array works as: Each time the target number is compared to the middle element. If it is bigger, the first part from the array is removed. (or vice versa)

For the worst case, we have to perform k operations, by which 2^k=n. (n is the lenght of the array)
Therefore, k=log2n, which implies complexity is log(n).