C data types and ranges: evaluate the claim “Range of float is from -2.25e+308 to +2.25e+308.” Assume a typical C implementation targeting IEEE-754 formats unless explicitly stated otherwise.
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ACorrect
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BIncorrect
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CDepends only on the compiler optimizations
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DTrue on 16-bit compilers but not on 32-bit
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EApplies only to long double
Answer
Correct Answer: Incorrect
Explanation
Introduction / Context:In the C language, floating-point ranges depend on the underlying representation, which on most modern systems follows IEEE-754. Knowing the typical limits for float (single precision), double (double precision), and long double helps you choose the right type without overflow or underflow surprises. This question tests whether a quoted range matches the usual capacity of a float.
Given Data / Assumptions:
- Typical C implementation using IEEE-754 formats.
- float is usually 32-bit single precision; double is usually 64-bit double precision.
- We evaluate the statement “float range is about ±2.25e+308”.
Concept / Approach:IEEE-754 single precision (float) has approximately 7 decimal digits of precision and a maximum finite magnitude near 3.4e+38. IEEE-754 double precision (double) has roughly 15–16 digits and a maximum finite magnitude near 1.7e+308. Therefore, a bound as high as 2.25e+308 cannot describe float; it is closer to, but still not exactly, the double limit.
Step-by-Step Solution:
Identify target type in the claim: float.Recall typical float max magnitude: about 3.4e+38.Compare with claimed 2.25e+308: vastly larger, off by ~270 orders of magnitude.Conclude the statement does not match float; it resembles double's order of magnitude (about 1.7e+308), but even then the number 2.25e+308 is not the standard double limit.Verification / Alternative check:On a standard system, printing FLT_MAX and DBL_MAX from
Why Other Options Are Wrong:
Correct: wrong because float cannot reach e+308.Depends only on the compiler optimizations: optimization has nothing to do with fundamental representation limits.True on 16-bit vs 32-bit: historical memory models do not turn float into e+308.Applies only to long double: some long double formats exceed double, but the claim explicitly names float.Common Pitfalls:Confusing float with double, or assuming all platforms use identical sizes while ignoring standard macros like FLT_MAX and DBL_MAX.
Final Answer:Incorrect.