Which of the following is true of how computers represent numbers?

Question

A. Using a fixed but large number of bits can eliminate the possibility of round off error when representing numbers in binary
B. With a fixed number of bits some numbers are too large to represent in a computer which will lead to overflow errors.
C. Using a fixed but large number of bits, for example 128, eliminates the possibility of overflow errors.
D. With a large but fixed number of bits it is possible to eliminate either round-off errors or overflow errors, but not both.

Answer 1

The correct statement regarding how computers represent numbers is:

B. With a fixed number of bits, some numbers are too large to represent in a computer which will lead to overflow errors.

Let's analyze the other options:

• A. Using a fixed but large number of bits can eliminate the possibility of round-off error when representing numbers in binary: This is not true. Increasing the number of bits can reduce round-off errors but cannot completely eliminate them, as certain numbers (like irrational numbers) cannot be represented exactly in binary.

• C. Using a fixed but large number of bits, for example 128, eliminates the possibility of overflow errors: This statement is false because no matter how many bits you allocate, there will always be some numbers that exceed that range, leading to overflow errors.

• D. With a large but fixed number of bits, it is possible to eliminate either round-off errors or overflow errors, but not both: This statement is misleading. You cannot eliminate overflow errors regardless of bits, and while increasing the number of bits may help reduce round-off errors, it does not eliminate either type of error.

Therefore, option B is the only true statement.