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Expressing Karnaugh maps 
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#1
Jun1611, 11:59 PM

P: 14

My silly lecturer doesn't explain things properly so I can't find any decent information in our lecture notes to revise for my exam next week.
My questions are: 1. What is canonical maxterm form? 2. What is canonical minterm form? 3. How do you express these using 'big M' notation? I've searched the internet for answers but I think if somebody explains it to me and shows a simple example it would be the best and quickest way. Thanks 


#2
Jun1711, 06:27 AM

Sci Advisor
P: 2,751

Since maxterms are used in products (that is, ANDed together) it follows that each maxterm (when = 0) represents a unique cell in the KMap which is zero. Since minterms are used in sums (that is, ORed together) it follows that each minterm (when = 1) represents a unique cell in the KMap.which is one. Example in three variables (a b c). Minterm : a' b c = m3 Maxterm : (a + b' + c) = M2 Notice how the maxterms are indexed in what at first might seem a counterintuitive way. Here the complemented variables are assign "one" in the binary code. It's done this way so that each maxterm index corresponds in a very direct way to a specific cell in the KMap that is zero. For example, given M2 as above, the KMap will have a zero in the position where a,b,c = 0 1 0. 


#3
Jun1711, 06:32 AM

Sci Advisor
P: 2,751

Products of maxterms are usually denoted with a product symbol (Pi) followed by an "M" list, for example.
[tex](a + b' + c) (a' + b + c) = \prod M(2,4)[/tex] Sums of minterms are usually denoted as a sum symbol (Sigma) followed by an "m" list, for example. [tex]a' b c + a b' c = \sum m(3,5)[/tex] 


#4
Jun2011, 08:27 PM

P: 14

Expressing Karnaugh maps
Ok thanks. So what does 'big M' notation mean?
The question is written thus: Write f in canonical maxterm form. (Use 'big M' notation). I'm guessing it means just write it in maxterms again. 


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