What is the worst-case number of arithmetic operations performed by recursive binary search on a sorted array of size $n$?

In a recursive binary search on a sorted array of size $n$, each recursive step performs a constant number of arithmetic operations (such as finding the midpoint $\lfloor (\text{low} + \text{high})/2 \rfloor$ and index increments/decrements).

The recurrence relation for the number of operations $T(n)$ in the worst case is:

Applying the Master Theorem (or unrolling the recurrence):

Thus, the worst-case number of arithmetic operations is $\Theta(\log_2(n))$, which corresponds to option (B).