Question

Not with standing overflow, the addition and subtraction of K-bit signed binary numbers can be realized using one K-bit full adder and

• A. 2-Input AND Gates
• B. 2-Input OR Gates
• C. 2-Input NOR Gates
• D. 2-Input XOR Gates

Answer 1

The correct option is D 2-Input XOR Gates

Condition for overflow is checked when both the numbers are of same sign.
There is no overflow if result will be also of same sign.

If it is not the case, then this overflow condition will be checked by using 2-input XOR gate.


Where $C_{in}\to$ is carry to MSB.

$C_{out}\to$ Carry generated after addition is performed at MSB.

if both are same then no overflow i.e. Y=0

if both are different then overflow i.e. Y=1

We can understand it as suppose both are -ve numbers. Then MSB will be zero for both.

If carry is there at MSB then $C_{in}=1and{C}_{out}=0$ so Y=1 and MSB of result = 1 which is not zero so overflow.

If $C_{in}=0,thenY=0,$ overflow also clear that MSB of result = 0.