Is Karnaugh Map possible for Maxterms?

Problem Detail: 

I read about Minterms i.e. sums of products, simplification using Karnaugh Graph. Can this graph be used for Maxterms, i.e. products of sums, as well? If yes, then how?

If not, then is there some other similar way to use, for simplification of Maxterms? I know, one can always convert Maxterms to Minterms and then use K-Map. I mam looking for some direct way.

Asked By : SimpleGuy

Answered By : Fizz

Yes you can do it directly on the K-map. In order to get a minimal product of maxterms (aka product-of-sum [POS], aka conjunctive-normal-form [CNF]), you simply circle/unify the zeros that appear in the K-map instead of the ones. (It doesn't matter how you got the K-map, it can be from any representaiton of the function, it's just a table of the function's output after all). You can also build the K-map from a (not necessarily minimal) POS by adding a zero the K-map for every maxterm (with the remaining squares being ones.) This should be said to varying extents in most textbooks, e.g.

• Digital Fundamentals by Thomas L. Floyd, 9th edition, pp. 221-224 has a very detailed example. (I'm guessing the latest, 11th edition has it too, but I haven't checked.)
• The Electronics Handbook, Second Edition edited by Jerry C. Whitake, pp. 55-57 has an example too, but this isn't as detailed.
• Introduction to Digital Electronics by Reid and Dueck, p. 114 also has an example.
• Digital Logic Techniques, 3rd Edition by John Stonham, p. 43.

That this approach is correct comes from De Morgan's laws and double negation. It's the same as if you flipped all zeros and ones in the K-map and SOP-minimized the negated function and then finally applied De Morgan to the result double-negating the function. This is explained on an example in

• Principles of Modern Digital Design by P.K. Lala, p. 70.

and probably other textbooks as well.

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Question Source : http://cs.stackexchange.com/questions/35897