In the addition of two signed numbers represented in 2's complement form, an arithmetic overflow condition occurs if:
In the addition of two signed numbers represented in 2's complement form, an arithmetic overflow condition occurs if:
Multiple Choice Options
- A
A · B = 0
- B
A = 0
- C✓ Correct Option
A · B = 1
- D
A + B = 1
Detailed Technical Solution & Explanation
In 2's complement arithmetic, overflow occurs if and only if two numbers of the same sign are added together and the result has the opposite sign (e.g., adding two positive numbers yields a negative result, or adding two negative numbers yields a positive result). Adding two operands of opposite signs can never cause an overflow.
If boolean conditions and represent the sign conditions of the operands aligning with an overflow scenario (i.e., both operands are positive producing a negative result, or both operands are negative producing a positive result), overflow requires the condition (both required overflow conditions are simultaneously satisfied). Equivalently, in terms of carries, overflow .