Experiment 18  Conversion of the NAND Operation
The special feature of the NAND operation is that you
can create the NOT, AND and OR operation using only this operation.
Thereby, the idempotence,
double negation law and De Morgan law is used...
The NOT Operation
With the Idempotence you get the
NOT operation...
$$\neg (A \wedge A) = \neg A$$
Logic diagram NOT operation with a NAND operation.

Logic circuit NOT operation with a NAND operation.
(Enlarge)

The AND Operation
With the double negation law you get the
AMD operation...
$$\neg ( \neg (A \wedge B)) = (A \wedge B)$$
Logic diagram AND operation with a NAND operation.

Logic circuit AND operation with a NAND operation.
(Enlarge)

The OR Operation
With the De Morgan law you can turn the
NAND operation into an
OR operation...
$$\neg ( \neg A \wedge \neg B) = (A \vee B)$$
Logic diagram OR operation with a NAND operation.

Logic circuit OR operation with a NAND operation.
(Enlarge)

This has consequences for the completeness...