NIELIT 2017 July Scientist B (IT) - Section B: 51

Question

In digital logic, if $A\oplus B=C$, then which one of the following is true?

• A. $A\oplus C=B$
• B. $B\oplus C=A$
• C. $A\oplus B\oplus C=0$
• D. Both (A) and (B)

Comments

@Lakshman Patel RJIT question not visible.

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Same Question: https://gateoverflow.in/336357/nielit-2017-july-scientist-b-cs-section-b-18 

Answer 1

XOR is associative and commutative,given $C=A \oplus B$

Option A

$A \oplus C$ Put value of C

$A \oplus A \oplus B$

$0 \oplus B$

$B$  equal to RHS  so OPTION A is TRUE

 

Option B

$B \oplus C$  Put value of C

$B \oplus A \oplus B$

$B \oplus B \oplus A$

$0 \oplus A$

$A$ equal to RHS  so OPTION B is TRUE

 

Option C

$A \oplus B \oplus C$

$C \oplus C$

$0$ not equal toRHS so it is false

OPTION D IS ANSWER

Comments

Option C, is also correct.

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@Mohit Kumar 6 Why option C is not correct?

You will get 0 when you will evaluate A xor B xor C.

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yes c is also correct

Answer 2

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

So, the correct answer is $(D).$

Comments

Option C is also correct.

 

A⊕B⊕C=0.

Let’s take L.H.S. and put A⊕B=C ( Given in the question itself )

                                 => (A⊕B)⊕C

                                  => C ⊕ C

                                 => 0 = R.H.S.