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Laws of Boolean Algebra??
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n3rdwannab3

Posted: Sun Jan 26, 2014 9:03 pm   Post subject: Laws of Boolean Algebra??

Convert the following product of sums into a sum of products using the laws of Boolean Algebra

(x' + y) * (y' + z) * (z' + x)

where x' is NOT x
+ is OR
* is AND

I have no clues how to start... is this like mathematics?

Insectoid

Posted: Sun Jan 26, 2014 9:20 pm   Post subject: RE:Laws of Boolean Algebra??

Look at De Morgan's laws.

NOT(A OR B) = (NOT A) AND (NOT B)

Also,

NOT(A AND B) = (NOT A) OR (NOT B)

This also means that NOT((NOT A) AND (NOT B)) = A OR B. Or you can do NOT((NOT A) AND B) = A OR (NOT B).

Look for these identities in your product of sums, and swap them out for their equivalent pair. For example, (x' + y) can be re-written as (x * y')'.

It's been a while since I've done this, so I might have a mistake or two in there.
Tony

Posted: Sun Jan 26, 2014 9:21 pm   Post subject: Re: Laws of Boolean Algebra??

n3rdwannab3 @ Sun Jan 26, 2014 9:03 pm wrote:
is this like mathematics?

Yes. https://en.wikipedia.org/wiki/Boolean_algebra
Tony's programming blog. DWITE - a programming contest.
Raknarg

Posted: Mon Jan 27, 2014 8:37 am   Post subject: RE:Laws of Boolean Algebra??

@Insectoid everything looks good there
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