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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.
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
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Competency focused Practice Questions ISC Class XII Computer ScienceTopic
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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.
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.
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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