Discussion
Which of these is a universal gate?
Answer: A
Correct answer: NAND
NAND is a universal gate, meaning that any logic function whatever can be built using NAND gates alone. NOR is the other universal gate. The proof is constructive. An inverter is a NAND with both inputs tied together. An AND is a NAND followed by that inverter. An OR is a NAND fed by two inverters, which is De Morgan’s theorem realised in hardware: \( \overline{\bar{A} \cdot \bar{B}} = A + B \). Since AND, OR and NOT together are sufficient for every Boolean function, and all three can be made from NAND, NAND alone is sufficient. The property matters commercially. A manufacturer can fabricate a whole logic family from one repeated cell, which simplifies design, testing and inventory, and the regularity suits automated layout. AND, OR and XOR are not universal, because none of them can produce an inversion: with only non-inverting gates, an input of all 1s can never yield a 0.
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