NAND#
NAND is AND followed by inversion: the output is low only when all inputs are high, and high otherwise. That small change — putting a bubble on the AND — turns out to be one of the most important facts in digital logic, because NAND can build everything else.
| A | B | A NAND B |
|---|---|---|
| 0 | 0 | 1 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 0 |
Why NAND Is Universal#
NAND is functionally complete: any Boolean function whatsoever can be built from NAND gates alone. An inverter is a NAND with its inputs tied together; an AND is a NAND followed by that inverter; an OR is a NAND with both inputs inverted — which, by De Morgan’s theorems, a NAND already is when its inputs are read as inverted. From those, every other gate and every larger function follows. A designer given nothing but NAND gates is not missing anything.
Why It Became the Workhorse#
Universality would be a curiosity if NAND were expensive, but the opposite is true. In CMOS the inverting gates are the native ones: a two-input NAND is four transistors, while a true AND needs six (the NAND plus an inverter). NAND is therefore both the cheapest useful gate and a complete logic set — so standard-cell libraries and hand-built logic alike lean on it heavily. It is no accident that the archetypal first TTL part, the 7400, is a quad two-input NAND, or that so much fixed logic is designed in NAND with bubbles pushed around by De Morgan.
Beyond Combinational#
Cross-couple two NAND gates — each feeding the other — and the pair becomes bistable: an SR latch with active-low set and reset inputs. The same universality that lets NAND build any combinational function also lets it build memory, which is why a bin of NAND gates is, in principle, a complete logic kit.