Suppose an algorithm processes n data elements using exactly log2n operations, where n = 4. If we quadruple the number data elements, how many additional operations will the algorithm perform?

Sure, let's break it down:

1. First, we need to find out how many operations the algorithm performs when n = 4. According to the problem, the algorithm uses log2n operations. So, when n = 4, the algorithm performs log2(4) = 2 operations.

2. Next, we need to find out how many operations the algorithm performs when we quadruple the number of data elements. Quadrupling n means n = 4 * 4 = 16. So, when n = 16, the algorithm performs log2(16) = 4 operations.

3. Finally, to find out how many additional operations the algorithm will perform, we subtract the number of operations performed when n = 4 from the number of operations performed when n = 16. So, 4 - 2 = 2 additional operations.

Therefore, when we quadruple the number of data elements, the algorithm will perform 2 additional operations.