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This document presents a detailed analysis of various cases of numerical overflow in data processing. It includes cases categorized as Positive Overflow (Case 4), Normal (Case 3), and Negative Overflow (Case 1). Each case is examined based on its specific conditions, with focus on scenarios involving two distinct widths and their implications on processing efficiency and data integrity. The analysis aims to aid developers and engineers in understanding overflow behaviors and implementing effective solutions to handle such scenarios.
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x + y +2w Positive overflow Case 4 x +ty +2w –1 +2w –1 Case 3 0 Normal 0 Case 2 –2w –1 –2w –1 Case 1 Negative overflow –2w