Signed Overflow Detection in Two's Complement Addition
Hardware arithmetic logic units must distinguish between valid results and numbers that exceed the representable bit width.
The scenarios presented cover four distinct N-bit addition operations: positive plus positive, negative plus negative, positive plus negative, and negative plus positive. The operands are A and B, the result is S, and the carry into the most significant bit (MSB) is Cin while the carry out of the MSB is Cout.
Determine which operand sign combinations can trigger signed overflow and identify the precise Boolean logic used to detect it at the hardware level.
Constraints
- Operands
AandBare represented in standard two's complement format. - The MSB of an N-bit value represents its sign bit: 0 for positive, 1 for negative.
Topics
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