A programming language stores integers in a 16-bit two’s-complement representation. Which of the following arithmetic expressions would potentially cause an overflow problem? (You can assume that the operations are completed from left to right.)Question 2Select one:-16,384 + 16,384-32,000 + 32,768 + 32,000-32,000 + 32,000 - 32,76825,000 – (-7,767)
Question
A programming language stores integers in a 16-bit two’s-complement representation. Which of the following arithmetic expressions would potentially cause an overflow problem? (You can assume that the operations are completed from left to right.)Question 2Select one:-16,384 + 16,384-32,000 + 32,768 + 32,000-32,000 + 32,000 - 32,76825,000 – (-7,767)
Solution
The arithmetic expression that would potentially cause an overflow problem in a 16-bit two's-complement representation is "-32,000 + 32,768 + 32,000".
Here's why:
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"-16,384 + 16,384": The result of this operation is 0, which is within the range of a 16-bit two's-complement representation (-32,768 to 32,767).
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"-32,000 + 32,768 + 32,000": The operation is completed from left to right. So, first, "-32,000 + 32,768" is calculated, which gives 768. Then, 768 is added to 32,000, which gives 32,768. This is outside the range of a 16-bit two's-complement representation, hence it would cause an overflow.
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"-32,000 + 32,000 - 32,768": The operation is completed from left to right. So, first, "-32,000 + 32,000" is calculated, which gives 0. Then, 0 is subtracted from 32,768, which gives -32,768. This is within the range of a 16-bit two's-complement representation.
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"25,000 – (-7,767)": The result of this operation is 32,767, which is within the range of a 16-bit two's-complement representation.
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