ISRO-DEC2017-72

Question

We consider the addition of two ${2}'s$ compliment numbers $b_{n-1}b_{n-2}\ldots b_{0}$ and
$a_{n-1}a_{n-2}\ldots a_{0}$. A binary adder for adding two unsigned binary numbers is used
to add two binary numbers.The sum is denoted by $c_{n-1}c_{n-2}\ldots c_{0}$.The carry out
is denoted by $c_{out}$.The overflow condition is identified by

• A. $c_{out}(\overline{a_{n-1}\oplus b_{n-1}})$
   
• B. $\overline{a_{n-1}}b_{n-1} \overline{c_{n-1}}+\overline{a_{n-1}b_{n-1}}c_{n-1}$
   
• C. $c_{out}\oplus c_{n-1}$
   
• D. $a_{n-1}\oplus b_{n-1}\oplus c_{n-1}$

Comments

I think this question should not be closed as duplicate of GATE2006-39. If we observe carefully the option B in question paper, they've made a slight difference.😀 Even though they've copied the question but they made it different. so clearly OPTION C is correct.  

this will clear all things regarding 2's complement------>

https://www.youtube.com/watch?v=DKj8p2nfdA8

{skip to 08:23}

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I also thought the same thing that C is the answer but if you look closely, the correct expression is:

(Cin of last stage) XOR (Cout of last stage)

But in option C, C(n-1) refers to the sum output for the last stage and not the carry in.

So, all options are incorrect.

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https://gateoverflow.in/1815/gate-cse-2006-question-39

Answer 1

i think no one is correct option.

it should be optoin B if an-1 bn-1 (cn-1)' + (an-1 bn-1)' cn-1