Overflow in Two's Complement: The Carry-In vs Carry-Out Rule
Hardware ALUs rely on a single XOR gate connected to the most significant bit to detect signed arithmetic overflow.
The system performs 8-bit two's complement addition on operands A and B to produce sum S. The carry into the most significant bit (bit 7) is C_in and the carry out of bit 7 is C_out. Four specific addition cases are presented for analysis:
Case 1: A = 01010101, B = 00111000 Case 2: A = 10000000, B = 10000000 Case 3: A = 01111111, B = 11111111 Case 4: A = 10101010, B = 01010101
Evaluate the carry bits for each case and determine the state of the overflow flag V.
Constraints
- Operands
AandBare 8-bit two's complement integers. - Bit 7 is the sign bit.
C_inrefers specifically to the carry entering bit 7.C_outrefers specifically to the carry leaving bit 7.
Topics
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