Which of the following result overflow with 2's complement arithmetic ?

Question

1.  1 1 1 1 1 1 1 1 + 1 1 1 1 1 1 1 1
2.  0 1 1 1 1 1 1 1 + 1 1 1 1 1 1 1 1 
3.  0 1 0 0 0 0 0 0 + 0 1 1 0 0 0 0 0 
   
   Please justify your answer. I'm not getting a clue whether the given number is in 2's complement . Should I have to find 2's complenet of the given number or not

Answer 1

Overflow = (Carry out of MSB) Ex-OR (Carry on MSB)

3rd will give Overflow.

Ref.http://sandbox.mc.edu/~bennet/cs110/tc/add.html

Comments

Since in any number system Most Significant Bit represents the sign bit, hence signs of both the operands should be different in option 2.

So without delving into much arithmetic, I daresay addition operator will not end up with an overflow.

Right?

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@Anurag overflow and carry are different.

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Yes Arjun sir, but the resulting number will always be between 01111111 & 11111111 in option 2.So how overflow is possible?

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Yes, 2 option is adding a positive and negative number (if we take numbers as signed)- can not produce overflow but can produce carry.