GATE CS 2017 Set 1 — Question 21
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Digital Logic → Boolean Algebra & Logic Gates → K-Map Minimization
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Question
Consider the Karnaugh map given below, where X represents "don't care" and blank represents 0.
Assume for all inputs , the respective complements are also available. The above logic is implemented using 2-input NOR gates only. The minimum number of gates required is ________ .
Correct answer
1 to 1
Solution
From the K-map:
Using De Morgan's laws, .
Thus, .Since the complements are available, we can directly feed and into a single NOR gate.
Total gates required = 1.
- Columns represent (00, 01, 11, 10).
- Rows represent (00, 01, 11, 10).
- Row 01 (), Col 00 ()
- Row 11 (), Col 00 ()
- Row 11 (), Col 10 ()
- Row 01 (), Col 10 ()
- Rows 01 and 11 correspond to .
- Columns 00 and 10 correspond to .
Using De Morgan's laws, .
Thus, .Since the complements are available, we can directly feed and into a single NOR gate.
Total gates required = 1.
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