Question
Which of the following is true of how computers represent numbers?
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.
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.
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GPT-4o mini
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.
**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.
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