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...