GATE Overflow | Digital Logic | Test 1 | Question: 15

Question

The addition of 4 bits two complement binary numbers $1101$ and $0100$ results in

• A. 0001 and an overflow
• B. 1001 and no overflow
• C. 0001 and no overflow
• D. 1001 and an overflow

Answer 1

Overflow cannot occur when number under addition are of opposite sign

Here one number is +ve and another is -ve

Now we perform 2's compliment arithmetic

 1101 + 0100 == 10001 discard carry as in 2's compliment rule

Final answer 0001 no overflow

Comments

how do you know whether it is 1’s compliment addition or 1’s compliment addition

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adding 2’s complement number means 2’s complement addition

adding 1’s complement number means 1’s complement addition

In 1’s complement addition, carry is added back to result.

In 2’s complement addition, carry is discarded.

Adding +ve and -ve number there is no overflow.

Adding two +ve number or two -ve number may or may not overflow

1101     //In 2’s complement as given in Question

0100    //In 2’s complement

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0001   and carry =1 which will be discarded

https://gateoverflow.in/3546/gate-it-2006-question-7-isro2009-41

(same Question)