2’s-complement addition behavior: An overflow condition can occur when adding two signed numbers if both operands have the same sign; it is typically indicated by an incorrect sign bit (overflow flag). Complete the statement correctly.
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Aerror, both numbers, magnitude, negative sign
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Boverflow, both numbers, sign, incorrect sign bit
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Coverflow, signs, magnitude, incorrect sum
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Derror, the signs, polarity, incorrect polarity
Answer
Correct Answer: overflow, both numbers, sign, incorrect sign bit
Explanation
Introduction / Context:Overflow in signed 2’s-complement arithmetic occurs when the mathematical result lies outside the representable range. Recognizing the operand sign pattern that produces overflow is key for reliable ALU and software behavior.
Given Data / Assumptions:
- Operands are signed 2’s-complement numbers with the same width.
- We examine addition, not subtraction.
- Overflow flag reflects signed-range violation, distinct from carry-out.
Concept / Approach:If two positives yield a negative, or two negatives yield a positive, overflow has occurred. Equivalently, overflow = (carry into MSB) XOR (carry out of MSB). This differs from unsigned arithmetic, where carry-out indicates out-of-range without sign semantics.
Step-by-Step Solution:
Check operand signs: both positive or both negative.Add and inspect result sign.If the result sign differs from the operands’ sign, set overflow flag.Report using status flags or exceptions as required.Verification / Alternative check:Truth tables over MSB combinations and the carry-in/carry-out relation confirm the same-sign rule and the XOR overflow test.
Why Other Options Are Wrong:
- Option A/D: Use vague “error/polarity” language and do not identify overflow precisely.
- Option C: Mixes terms incorrectly and does not specify the same-sign requirement.
Common Pitfalls:Confusing overflow with carry-out; assuming different-sign addition can overflow (it cannot in 2’s complement).
Final Answer:overflow, both numbers, sign, incorrect sign bit