When two 8-bit numbers A7…A0 and B7…B0 in 2’s complement representation (with A0 and B0 as the least significant bits) are added using a ripple-carry adder, the sum bits obtained are S7….S0 and the carry bits are C7…..C0. An overflow is said to have occurred ifa)the carry bit C7 is 1b)all the carry bits C7…..C0 are 1c)d)Correct answer is option 'C'. Can you explain this answer?

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When two 8-bit numbers A₇…A₀ and B₇…B₀ in 2’s complement representation (with A₀ and B₀ as the least significant bits) are added using a ripple-carry adder, the sum bits obtained are S₇….S₀ and the carry bits are C₇…..C₀. An overflow is said to have occurred if

a)
the carry bit C₇ is 1
b)
all the carry bits C₇…..C₀ are 1
c)
d)

Correct answer is option 'C'. Can you explain this answer?

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When two 8-bit numbers A7…A0 and B7…B0 in 2’s complement representati...

Explanation

Overflow flag indicates an overflow condition for a signed operation. Some points to remember in a signed operation:

* MSB is always reserved to indicate sign of the number.

* Negative numbers are represented in 2’s – complement.

* An overflow results in invalid operation.

2's complement overflow rules:

* If the sum of two positive numbers yields a negative result, the sum has- overflowed.

* If the sum of two negative number yields a positive result, the sum has overflowed.

* Otherwise, the sum has not overflowed.

Overflow for signed numbers occurs when the carry-in into the MSB (most significant bit) is not equal to carry-out. Conveniently, an XOR-operation on these two bits can quickly determine if an overflow condition exists.

Therefore,

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When two 8-bit numbers A7…A0 and B7…B0 in 2’s complement representation (with A0 and B0 as the least significant bits) are added using a ripple-carry adder, the sum bits obtained are S7….S0 and the carry bits are C7…..C0. An overflow is said to have occurred ifa)the carry bit C7 is 1b)all the carry bits C7…..C0 are 1c)d)Correct answer is option 'C'. Can you explain this answer?

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