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Which of the following logic expression is incorrect?

  1. $1\oplus0=1$
  2. $1\oplus1\oplus0=1$
  3. $1\oplus1\oplus1=1$
  4. $1\oplus1=0$
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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.
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10 Answers

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Option B

1 xor 1 xor 0 -> (1xor1 = 0) xor 0 -> 0 xor 0 = 0 so it is false
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Ans B as it's EX-OR gate and having even number of input as '1'. So the output should be '0'.
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Option B is the correct answer because 1 EXOR 1 EXOR 0 should be 0
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EX OR operation can be seen as sum mod 2, that is divide the sum by 2 and see the remainder.

for example 1⊕1=2 mod 2=0,

1⊕0=1 mod 2=1,

0⊕0=0 mod 2=0,

0⊕1=1 mod 2=1

you can also check 1⊕1⊕1⊕1⊕1⊕1=6 mod 2=0

Given option (a) 1⊕0 will be 1 mod 2=1 true

option (b) 1⊕1⊕0 will be 2 mod 2=0 but in option it is given as 1 hence it is incorrect.

option (c) 1⊕1⊕1 will be 3 mod 2=1 true

option (d) 1⊕1=0 true 

Hence Option (B) Is Incorrect.

Answer:

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