How can a school modify its student ID representation to ensure unique IDs for all students as its enrollment doubles?

The most effective way to ensure that a school can accommodate unique IDs for all students as enrollment doubles is to double the number of bits in the student ID representation. This is because each additional bit exponentially increases the number of available IDs.

When you simply add a bit to studentID, you don't effectively double the available IDs. Instead, the correct approach is to double the number of bits, which would allow for a more significant expansion of unique IDs. For example, if a student ID is currently represented using 8 bits, it can represent (2^8 = 256) unique IDs. By doubling the number of bits to 16, it could represent (2^{16} = 65,536) unique IDs, thus easily accommodating an increased enrollment.

It's important to understand that using fewer bits or reserving bits for classification could lead to a limitation in the number of unique IDs available, which contradicts the requirement for unique identifiers as student numbers increase. Therefore, the strategy of doubling the number of bits is the most robust method to ensure unique identification for all students.