Advanced Placement (AP) Computer Science

What does an overflow error result from?

1. Data being incorrectly formatted.

2. Insufficient bits to hold the number.

3. Exceeding the maximum iteration count.

4. Improper selection conditions in algorithms.

The correct answer is: Insufficient bits to hold the number.

An overflow error occurs when a computation produces a result that is outside the range that can be represented within a given number of bits. For instance, in binary systems, if you attempt to store a number larger than what the designated data type can accommodate, the excess "overflows" beyond its maximum limit. For example, in an 8-bit signed integer, the maximum positive value is 127. If a calculation results in 128 or higher, the storage capacity is exceeded, leading to an overflow error. This concept is fundamental in programming and computer science as it directly affects data integrity and calculations, particularly when dealing with operations that can rapidly increase values, such as loops or accumulative sums. The other options relate to different types of issues like formatting errors or algorithm inefficiencies, but they do not specifically address the limitations of numerical representation in memory, which is the essence of what causes overflow errors.