NIELIT 2016 MAR Scientist B - Section C: 1

Question

Which of the following logic expression is incorrect?

• A. $1\oplus0=1$
• B. $1\oplus1\oplus0=1$
• C. $1\oplus1\oplus1=1$
• D. $1\oplus1=0$

Comments

ExOR operator is left associative and whenever there is odd nos of 1 ,the result is 1 ( true).

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Yes option b is the incorrect  as exor gate gives output on getting odd number of 1's else output will be 0,

A) contains odd number of 1's so output is 1

B)contains even number of 1's so output should be 0..but it is given 1.

C) contains odd number of 1's so output should be 1 yes it is 1.

D)even number of 1's so output should be 0..yes it is zero.

Answer 1

option (b) is correct

Answer 2

EXOR gate is an odd number of $1’s$ detector. It gives $0$ as output for the same input and for different input it gives $1$ as output, also the EXOR logic gate is left-associative.

1. $1\oplus 0=1:$ This is true, different input,so output is $1.$
2. $1\oplus 1\oplus 0=1:$ It can be written as: $((1\oplus 1)\oplus 0)\implies(0\oplus 0)=0\neq1$,so this options is false.
3. $1\oplus 1\oplus 1=1$: $((1\oplus 1)\oplus 1)\implies (0\oplus 1)=1$,so this is true.
4. $1\oplus 1=0$: This is true, for the same input value EXOR gate gives $0$ as output.

So Option $(B)$ is incorrect.