Which of the following statements is/are FALSE? (i) In floating-point…

Answer: Only statement (ii) is false — the claim that floating-point arithmetic can never produce exponent overflow or underflow is incorrect.

Why the claim that addition and subtraction are more complex is true:

• Exponent alignment: before adding or subtracting, the operand with the smaller exponent must have its mantissa shifted to align exponents, which is an extra step not needed for multiplication.

• Rounding and sticky bits: shifting may require tracking guard/round/sticky bits to round the result correctly, adding complexity.

• Normalization: after the operation the result may need normalization (adjusting mantissa and exponent) and possible re-rounding.

• By contrast, multiplication/division operate on mantissas and add/subtract exponents; they still may need normalization, but they do not require exponent alignment prior to the core mantissa operation.

Why the claim that exponent overflow/underflow can never occur is false:

• Overflow: occurs when a result's exponent exceeds the maximum representable exponent; IEEE 754 typically produces Infinity or signals an overflow and sets related status flags.

• Underflow: occurs when a result's magnitude is smaller than the smallest normalized value; implementations may produce subnormal (denormal) numbers or zero and raise an underflow flag.

• Both overflow and underflow are real behaviors in floating-point arithmetic and are handled according to the floating-point standard or the implementation's choices.

Conclusion: addition and subtraction are indeed more complex in many implementations due to exponent alignment and related steps, and floating-point arithmetic can produce exponent overflow and underflow; therefore only the statement denying overflow/underflow is false.