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The minimum number of 2-input NAND gates required to implement a 2-input XOR gate is
- a)4
- b)5
- c)6
- d)7
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
The minimum number of 2-input NAND gates required to implement a 2-inp...
The number of 2-input NAND gates required to implement a 2-input XOR gate is 4.
Similarly, the number of 2-input NOR gates required to implement a 2-input XNOR gate is 4.
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The minimum number of 2-input NAND gates required to implement a 2-inp...
Explanation:
To implement a 2-input XOR gate using 2-input NAND gates, we can use the following logic:
1. Connect the two inputs A and B to two separate NAND gates (N1 and N2).
2. Connect the output of N1 to one input of another NAND gate (N3).
3. Connect the output of N2 to the other input of N3.
4. Connect the output of N3 to the input of another NAND gate (N4).
5. Connect the output of N1 to one input of another NAND gate (N5).
6. Connect the output of N2 to the other input of N5.
7. Connect the output of N4 and N5 to two separate inputs of another NAND gate (N6).
8. The output of N6 is the output of the XOR gate.
Calculation:
We can see that we need a total of 6 NAND gates (N1 to N6) to implement a 2-input XOR gate using 2-input NAND gates. Therefore, the correct answer is option A (4 is not enough and options B and C are too many).
Conclusion:
Thus, the minimum number of 2-input NAND gates required to implement a 2-input XOR gate is 6.
To implement a 2-input XOR gate using 2-input NAND gates, we can use the following logic:
1. Connect the two inputs A and B to two separate NAND gates (N1 and N2).
2. Connect the output of N1 to one input of another NAND gate (N3).
3. Connect the output of N2 to the other input of N3.
4. Connect the output of N3 to the input of another NAND gate (N4).
5. Connect the output of N1 to one input of another NAND gate (N5).
6. Connect the output of N2 to the other input of N5.
7. Connect the output of N4 and N5 to two separate inputs of another NAND gate (N6).
8. The output of N6 is the output of the XOR gate.
Calculation:
We can see that we need a total of 6 NAND gates (N1 to N6) to implement a 2-input XOR gate using 2-input NAND gates. Therefore, the correct answer is option A (4 is not enough and options B and C are too many).
Conclusion:
Thus, the minimum number of 2-input NAND gates required to implement a 2-input XOR gate is 6.
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