APCSP DAT-1.B Overflow and Limitations of Data

What is the main reason that integer values have a fixed range in many programming languages?

• Integer values are stored as text rather than numbers.

• The number of bits allocated to store integers is limited.

• Computers cannot process numbers larger than 100,000.

• Integer values change unpredictably in memory.

What can happen when an integer calculation exceeds the maximum value that can be stored in a fixed number of bits?

• The program will always crash.

• The result will wrap around to a very small or negative number (overflow error).

• The calculation will continue normally with no issue.

• The program will automatically increase the storage space for the number.

What is an overflow error?

• When a number is too small to be stored accurately.

• When an integer exceeds its maximum representable value and wraps around.

• When a floating-point number is converted to an integer.

• When a program runs out of memory.

What is the primary issue caused by using a fixed number of bits to store real numbers?

• Some real numbers cannot be represented exactly, leading to round-off errors.

• Real numbers cannot be stored in memory at all.

• Real numbers take up less memory than integers.

• The computer must always store real numbers as exact values.

What causes round-off errors in floating-point representation?

• The computer runs out of memory.

• Some real numbers cannot be perfectly represented in binary.

• The program attempts to divide by zero.

• Floating-point numbers use too many bits for storage.

Which of the following is an example of a round-off error?

• A calculation results in 3.333333333333 instead of exactly 1/3.

• A program crashes due to a missing semicolon.

• A negative number is stored when it should be positive.

• A file fails to open due to incorrect permissions.

Why do some real numbers need to be approximated in computer storage?

• Computers cannot store decimal numbers.

• Many real numbers have infinite decimal expansions that cannot fit in a fixed number of bits.

• Computers do not use floating-point arithmetic.

• Real numbers are always stored as whole numbers.

In which scenario is an overflow error most likely to occur?

• Storing an extremely large integer in a fixed-bit integer variable.

• Rounding a floating-point number to two decimal places.

• Adding two small numbers together.

• Converting a number from binary to decimal.

Why might a programmer need to be aware of round-off errors?

• They can accumulate over multiple calculations and affect accuracy.

• Round-off errors are always ignored by the computer.

• They only occur in text-based programs.

• Round-off errors do not impact real-world applications.

In a certain computer program, two positive integers are added together, resulting in an overflow error. Which of the following best explains why the error occurs?

• The program attempted to perform an operation that is considered an undecidable problem.

• The precision of the result is limited due to the constraints of using a floating-point representation.

• The program can only use a fixed number of bits to represent integers; the computed sum is greater than the maximum representable value.

• The program cannot represent integers; the integers are converted into decimal approximations, leading to rounding errors.