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[Boolean Algebra]

Assertion (A): The truth table for the XOR gate shows that the output is HIGH only when an odd number of inputs are HIGH.

Reason (R): The XOR gate performs addition modulo 2, thus producing a HIGH output when the number of HIGH inputs is odd.

ID: #24956 Competency focused Practice Questions ISC Class XII Computer Science 3 views
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Competency focused Practice Questions ISC Class XII Computer ScienceTopic

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  • A Both A and R are true, and R is the correct explanation of A.
  • B Both A and R are true, but R is not the correct explanation of A.
  • C A is true, but R is false.
  • D A is false, but R is true.
Correct Answer: Option A

Explanation

[Boolean Algebra]

Assertion (A): The truth table for the XOR gate shows that the output is HIGH only when an odd number of inputs are HIGH.

Reason (R): The XOR gate performs addition modulo 2, thus producing a HIGH output when the number of HIGH inputs is odd.
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is not the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.
Correct Answer: (a)

Step 1: Understanding the Assertion (A)

XOR gate output becomes HIGH only when an odd number of inputs are HIGH.

This statement is true.

XOR (Exclusive OR) gate gives output:

  • 1 (HIGH) → when the number of HIGH inputs is odd
  • 0 (LOW) → when the number of HIGH inputs is even

2-Input XOR Truth Table:

A B A XOR B
0 0 0
0 1 1
1 0 1
1 1 0

Output becomes HIGH only when odd number of inputs are HIGH.

0 XOR 1 = 1 1 XOR 0 = 1 1 XOR 1 = 0

Step 2: Understanding the Reason (R)

XOR gate performs addition modulo 2.

This statement is also true.

XOR operation behaves exactly like:

Binary Addition Modulo 2

Modulo 2 Addition Rules:

Expression Result
0 + 0 0
0 + 1 1
1 + 0 1
1 + 1 0

This exactly matches XOR gate behavior.

Why R Correctly Explains A?

The reason explains why XOR output becomes HIGH for odd number of HIGH inputs:

  • XOR works as modulo 2 addition
  • Odd number of 1s gives remainder 1
  • Even number of 1s gives remainder 0

Therefore, Reason (R) correctly explains Assertion (A).

Important Concept:

XOR → Odd Parity Detector

XOR gate is commonly used in:

  • Error detection
  • Parity generation
  • Digital circuits

Final Conclusion:

  • Assertion (A) → True ✅
  • Reason (R) → True ✅
  • R correctly explains A ✅
Correct Answer: (a)

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