Which of the following logic expressions is incorrect ?
2016
Which of the following logic expressions is incorrect ?
- A.
1 ⊕ 0 = 1
- B.
1 ⊕ 1 ⊕ 1 = 1
- C.
1 ⊕ 1 ⊕ 0 = 1
- D.
1 ⊕ 1 = 0
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Show answer & explanation
Correct answer: C
Key idea: XOR (⊕) outputs 1 when an odd number of inputs are 1, and outputs 0 when an even number of inputs are 1.
Evaluate 1 ⊕ 0 = 1: there is one '1' (odd), so result = 1. The statement is true.
Evaluate 1 ⊕ 1 ⊕ 1 = 1: there are three '1's (odd), so result = 1. The statement is true.
Evaluate 1 ⊕ 1 ⊕ 0 = 1: there are two '1's (even), so actual result = 0. The statement claiming the result is 1 is incorrect.
Evaluate 1 ⊕ 1 = 0: there are two '1's (even), so result = 0. The statement is true.
Conclusion: The expression 1 ⊕ 1 ⊕ 0 = 1 is incorrect because the XOR of those inputs is 0.