Consider the Karnaugh map given below, where \(X\) represents "don't care" and…
2017
Consider the Karnaugh map given below, where \(X\) represents "don't care" and blank represents 0.
Assume for all inputs \(\left ( a,b,c,d \right )\), the respective complements \(\left ( \bar{a}, \bar{b}, \bar{c}, \bar{d} \right )\) are also available. The above logic is implemented using 2-input NOR gates only. The minimum number of gates required is ____________ .
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Correct answer: 1
Final answer: 1 two-input NOR gate.
Reasoning and simplification:
Locate the 1s and don't-cares in the K-map and use don't-cares to form the largest group possible. The four-cell block formed by rows where c = 1 and columns where a = 0 contains the three required 1s plus a don't-care, so it is valid.
That 2×2 block corresponds to the product term a' c (a = 0 and c = 1).
Implementing a' c with only 2-input NOR gates is simple because complements of inputs are available. Use the identity: a' c = NOT(a OR c'). So a single 2-input NOR gate with inputs a and c' produces a' c directly.
Therefore the minimum number of 2-input NOR gates required is 1.
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