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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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$Remark:$
if the sign bit of both the signed numbers is not same as the sign bit of the product, then there is an overflow.
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XOR of $C_{\text{in}}$ with $C_{\text{out}}$ of the MSB position.
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$C_{out} \bigoplus C_{in} = 1 (Overflow) $

$C_{out} \bigoplus C_{in} = 0 ( No Overflow)$
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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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In 4 bits representation, 

$-3$ 1101 (2's complement of $-3$) $+$

$-2$ 1110 (2's complement of $-2$)


$-5$ 1011 (2's complement of $-5$)

This is an example where there is carry from MSB  but still there is no overflow. Is this right?

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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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