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Boolean Algebra
f-alpha.net » Mathematics » Algebra » Boolean Algebra » Let's go... » Experiment 18 - Conversion NAND

Experiment 18 - Conversion of the NAND Operation

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...

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