GATE 2019 CS – Question 60
What is the minimum number of 2-input NOR gates required to implement a 4-variable function expressed in sum-of-minterms form as $f=\Sigma(0,2,5,7,8,10,13,15)$? Assume that all the inputs and their complements are available.
Answer: ________.
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Correct answer: 3
Explanation
The minterms group into $f=\bar B\bar D+BD$ (minterms 0, 2, 8, 10 and 5, 7, 13, 15), i.e. the XNOR of $B$ and $D$. Since complements are available, $f=\overline{\overline{(\bar B+D)}+\overline{(B+\bar D)}}$ needs three NOR gates: $\text{NOR}(\bar B,D)$, $\text{NOR}(B,\bar D)$ and a NOR of the two results.