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## When two 8-bit numbers A7 ... A0 and B7 ... B0 in 2s complement representation (with A0 and B0 as the least significant bits) are added using ripple-carry adder. the sum bits obtained are S7 ... S0 and the carry bits are C7 ... C0. An overflow is said to have occured if : -gate computer science 2017

A) the carry bit C7 is 1

B) all the carry bits (C7, ... , C0 ) are 1

C) (A7 . B7 . S7 + A7 . B7 . S7) is 1

D) (A0 . B0 . S0 + A0 . B0 . S0) is 1

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## Answers

**C) (A7 . B7 . S7' + A7' . B7' . S7) is 1**

Explanation:

Overflow indicates that the result was too large or too small to fit in the original data type.

Overflow flag indicates an overflow condition for a signed operation. Signed numbers are represented in two's complement representation.

The overflow occurs only when two positive number are added and the result is negative or two negative number are added and the result is positive. Otherwise, the sum has not overflowed.

Therefore, a XOR operation can quickly determine if an overflow condition exists. i.e.,

(A7 . B7 )⊕(S7) = (A7 . B7 . S7‘ + A7‘ . B7‘ . S7 = 1

This explanation is contributed by

__Deepak Raj.__deepuckraj

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