Geek asks and answers

Can I NOT use OR and AND?

I know that I can invert X using NOT. NOT x = x '

But is it possible to invert X only with OR and AND?

Example

Given this function, F = W'.YZ '+ V.W'.Z'

Is it possible to create a schema only with OR and AND?

thank

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3 answers

Cannot make NOT from AND and OR. The first obvious reason is that NOT takes only one argument, while AND and OR take two. Even if you enter the same variable twice into the AND / OR gate, they will not invert its value

OTOH, you can define AND in terms of OR + NOT, and you can define OR in terms of AND + NOT

x AND y = NOT((NOT x) OR (NOT y))
x OR y = NOT((NOT x) AND (NOT y))
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, NOT AND ORs.

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You cannot get NOT from OR and AND. Evidence:

When you enter 0, OR and AND will be equal to 0. The system will not have a single 1. With one input, OR and AND will be equal to 1. There will not be 0.

That's why NAND and NOR chips are popular for small / hobby electronics, as they can do any other logical combination.

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