GATE Overflow Test Series | Digital Logic | Test 1 | Question: 8

Question

If $A\odot B=C$, ($\odot$ is XNOR operator) then which of the following is/are TRUE? (Mark all the appropriate choices)

• A. $A\odot C=B$
• B. $B\odot C=A$
• C. $A\odot B\odot C=1$
• D. $A\odot B\odot C=0$

Answer 1

We can make a truth table and observe that, which one is true.
$${\begin{array}{|c|c|c|}\hline
A& B& C&A\odot B &B\odot C&A\odot C &A\odot B \odot C\\\hline
0& 0& 0&1&1&1&0  \\\hline   
{\color{Green} {0}}& {\color{Blue} {0}}&{\color{Red} {1}}&{\color{Red} {1}}&{\color{Green} {0}}&{\color{Blue} {0}}&{\color{Magenta} {1}}  \\\hline {\color{Green} {0}}&{\color{Blue} {1}}&{\color{Red} {0}}&{\color{Red} {0}}&{\color{Green} {0}}&{\color{Blue} {1}}&{\color{Magenta} {1}}   \\\hline
0&1&1&0&1&0 &0    \\\hline
{\color{Green} {1}}&{\color{Blue} {0}}&{\color{Red} {0}}&{\color{Red} {0}}&{\color{Green} {1}}&{\color{Blue} {0}}&{\color{Magenta} {1}}     \\\hline
1&0&1&0&0&1&0      \\\hline
1&1&0&1&0&0&0     \\\hline
{\color{Green} {1}}&{\color{Blue} {1}}&{\color{Red} {1}}&{\color{Red} {1}}&{\color{Green} {1}}&{\color{Blue} {1}}&{\color{Magenta} {1}}      \\\hline
\end{array}}$$
From the above truth table, if $A\odot B = C, $ then $A\odot C= B,\;B\odot C= A,\;A\odot B \odot C = 1.$

So, the correct answer is A;B;C

Answer 2

$A \odot B = C$

So, C option gives $C \odot C = 1.$

So, option C is True.

Correct Answer: A;B;C

Comments

ex-nor gate is not associative. So the order of A$A\bigodot B\bigodot C if taken in this way A\bigodot (B\bigodot C)=A\bigodot B$. Hence, it is not clear here. The answer is 1 only if we take the associativity as $(A\bigodot B)\bigodot (C)=C\bigodot C$

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@Rajat Maheshwari Sorry, bad miss.

@Sourav Ganguly $B \odot C = A$ right?

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Yes I guess I made a blunder

Answer 3

given

$A⊙B=C$

checking each option

Option (A)

$A⊙C = A⊙A⊙B = 0⊙B=B$  (as EX-NOR is true if even number of zeros appear in input) 

is true

Option (B)

B⊙C=B⊙A⊙B=B⊙B⊙A=1⊙A=A   (EX-NOR is associative)

true

Option (C)

A⊙B⊙C = A⊙B⊙A⊙B=A⊙A⊙B⊙B=1⊙1=1

So, answer: A;B;C

Answer 4

Expand C in all options

 

for odd number of operands xnor is equal to XOR gate so A and B are true

for even number xnor gives 1 for even parity thus C is true.
 

 

therefore answer is A;B;C