The minimum number of NAND gates required to implement the Boolean function f…
2023
The minimum number of NAND gates required to implement the Boolean function f = x'y + xy' is:
- A.
3
- B.
4
- C.
6
- D.
More than one of the above
- E.
None of the above
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Correct answer: B
Recognize the function: f = x'y + xy' is the XOR function.
A minimum NAND-only implementation can be built as follows:
g1 = x NAND yg2 = x NAND g1g3 = y NAND g1f = g2 NAND g3
This gives x XOR y = x′y + xy′ using exactly 4 NAND gates.
A method that first separately creates x' and y' uses more gates, but it is not the minimum construction.
Answer: 4