A floating point number is said to be normalized, if the left most digit of…
2025
A floating point number is said to be normalized, if the left most digit of the mantissa is
- A.
Zero
- B.
Fraction
- C.
Exponent
- D.
Nonzero
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Correct answer: D
A floating-point number is considered normalized when its mantissa (or significand) is adjusted so that the leftmost digit is non-zero. This convention ensures maximum precision by utilizing all available bits in the mantissa to represent significant information, rather than wasting space on leading zeros. For example, in base-10 representation, a number like 0.0023 would be normalized to 2.3 × 10⁻³, where the leading digit '2' is non-zero. Option D correctly identifies this requirement as "Nonzero." Options A and B are incorrect because a leading zero would imply an unnormalized form, reducing precision, while "Fraction" is not the defining characteristic of normalization. Option C refers to the exponent, which controls the scale but does not define whether the mantissa itself is normalized. Therefore, adhering to the non-zero leading digit rule is essential for standard floating-point representation.