Consider the IEEE single-precision floating-point format.

Further, consider the case:

Exponent bit field = all 1's
Fraction bit field not all 0's

Then the 'number' represented is NaN (Not a Number) .

Question

Consider the IEEE single-precision floating-point format.

Further, consider the case:

Exponent bit field = all 1's
Fraction bit field not all 0's

Then the 'number' represented is NaN (Not a Number) .

BlackTom AI · Accepted Answer

The question describes a specific pattern in the IEEE 754 single-precision floating-point format and asks what number is represented under those conditions.
First, recall how binary32 is structured: 1 sign bit, 8 exponent bits, and 23 fraction (mantissa) bits. The special cases are determined by the combination of exponent and fraction fields.
Next, consider the case where the exponent field is all 1s. This signals either Infinity or NaN depending on the fraction field.
If the fraction field were all zeros while the exponent is all ones, the value would encode as ±Infinity, because the significand is outright zero and the exponent is at its maximum (this is a well-known representation of infinity in IEEE 754).
In contrast, if the exponent is all ones and the fraction field is not all zeros, the value is designated as NaN (Not a Number). The nonzero fraction provides a payload that distinguishes NaN from infinity and allows signaling of invalid or indeterminate results in computations.
Now apply this to the given scenario: exponent = all ones and fraction = not all zeros. This combination matches the NaN pattern rather than Infinity, so the represented value is NaN.
Why this distinction matters: NaN propagates through arithmetic operations and can carry diagnostic information in the fraction (often called the payload), whereas Infinity has a defined sign and propagates differently under arithmetic (e.g., 1/0 yields Infinity, and many operations with Infinity follow defined extended rules).
If the question were to consider a case where the fraction were exactly zero with exponent all ones, then Infinity would be the result instead, indicating the importance of the precise fraction bits in determining the outcome.
In summary, given exponent all ones and fraction not all zeros, the representation is NaN, because the nonzero fraction signals an undefined or unrepresentable value in IEEE 754 semantics.

ELEC 220 001 Exam 01

Consider the IEEE single-precision floating-point format. Further, consider the case: Exponent bit field = all 1's Fraction bit field not all 0's Then the 'number' represented is NaN (Not a Number) .

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