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The truth table for the XOR gate shows that the output is HIGH only when an odd number of inputs…
Assertion: The truth table for the XOR gate shows that the output is HIGH only when an odd number of inputs are HIGH.
Reason: The XOR gate performs addition modulo 2, thus producing a HIGH output when the number of HIGH inputs is odd.
- aBoth A and R are true, and R is the correct explanation of A.
- bBoth A and R are true, but R is not the correct explanation of A.
- cA is true, but R is false.
- dA is false, but R is true.
Answer
Answer
AICorrect option: a
Answer: (a) Both A and R are true, and R is the correct explanation of A.
For a 2-input XOR gate the output is HIGH exactly when the inputs differ, i.e. exactly one input (an odd count) is HIGH, matching the assertion. This is because XOR performs addition modulo 2, which is HIGH precisely when the number of HIGH inputs is odd - exactly what the reason states, so R correctly explains A.
From ISC Computer Science - Competency Focused Practice Questions (CISCE, August 2024), question 23.
Check your working with the Boolean algebra solver: the steps law by law, the K-map and the logic circuit for any expression.