Which of the following statements about overflow and underflow in numerical calculations is correct? (Multiple choice)

Question

Options

• AUnderflow occurs when the number close to zero Is rounded to zero
• BOverflow occurs when the number close to zero 1s rounded to zero
• COverflow occurs when a large number of levels are approximated as 1P or - 1P
• DUnderflow occurs when a large number of levels are approximated as 1P or - 1P

• A
  74% (42)
• B
  18% (10)
• D
  9% (5)

Explanation

A and C are correct because they accurately match the definitions of each error type. Underflow (A) happens when a number is so close to zero that the floating-point system lacks the precision to represent it, so it gets flushed to zero - a loss of very small magnitudes. Overflow (C) happens in the opposite direction: when a number is so large it exceeds the maximum representable value, it gets approximated as ±infinity (written here as ±IP).

B is wrong because it swaps the definition - rounding near-zero values to zero is underflow, not overflow. D is wrong for the same swap in the other direction: approximating very large values as ±infinity is overflow, not underflow.

Memory tip: Think of a bowl of water. Underflow = the bowl runs under empty (too little → rounds to zero). Overflow = the bowl spills over the top (too much → goes to infinity). The direction of the problem matches the prefix.

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