GATE CS 1987 Q1-vii — Number Representations (Fixed and Floating Point)

In floating-point representation, the exponent is stored using biased representation (also known as excess-$N$ code), where a bias $N$ is added to the actual exponent $E$ to get the stored exponent $E' = E + N$.

This encoding serves two main purposes:

1. Simplifies Comparison: It shifts the range of exponents from both negative and positive values to strictly non-negative values. This allows standard integer comparators to compare floating-point numbers directly without needing signed comparison logic.
2. Representation of Smallest Numbers: The most negative exponent (which represents the smallest non-zero magnitude) maps to a stored exponent of $0$. Consequently, the smallest numbers (including zero itself) are represented with all zeros in the exponent field.

Analysis of Options:

• Option A (Incorrect): The dynamic range is determined by the number of bits allocated to the exponent, not the encoding scheme.
• Option B (Incorrect): The precision is determined by the number of bits allocated to the mantissa (significand).
• Option C (Correct): The smallest exponent value corresponds to a stored value of $0$, represented as all zeros.
• Option D (Incorrect): Overflow is a consequence of exceeding the maximum representable limit and cannot be avoided merely by changing the encoding scheme.