GATE CS 2019 Set 1 — Question 60
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Digital Logic → Boolean Algebra & Logic Gates → K-Map Minimization
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Question
What is the minimum number of 2-input NOR gates required to implement a 4-variable function expressed in sum-of-minterms form as ? Assume that all the inputs and their complements are available. Answer: ________.
Correct answer
3 to 3
Solution
The function can be simplified using a K-map:
Groups:
| CD\AB | 00 | 01 | 11 | 10 |
|---|---|---|---|---|
| 00 | 1 | 0 | 0 | 1 |
| 01 | 0 | 1 | 1 | 0 |
| 11 | 0 | 1 | 1 | 0 |
| 10 | 1 | 0 | 0 | 1 |
1.Corners ():
2.Middle block ():
Simplified expression: (XNOR function).Given that all inputs and their complements () are available, we can implement the XNOR function using 2-input NOR gates as follows:1.
2.
3.
Thus, the minimum number of 2-input NOR gates required is 3.Continue learning with Success Tracker
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