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Consider addition in two's complement arithmetic. A carry from the most significant bit does not always correspond to an overflow. Explain what is the condition for overflow in two's complement arithmetic.
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XOR of $C_{\text{in}}$ with $C_{\text{out}}$ of the MSB position.
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(a) In 2's complement addition Overflow happens only when :

  • Sign bit of two input numbers is 0, and the result has sign bit 1.
  • Sign bit of two input numbers is 1, and the result has sign bit 0.
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FOR overflow to happen during addition of two number in 2's complement form they must have same sign and result is of opposite sign

(+A) + (+B)= -C

(-A) + (-B)= +C

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