# Expressing Karnaugh maps

1. Jun 16, 2011

### Idyllic

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. Jun 17, 2011

### uart

A maxterm is a sum term that involved each of the input variables while a minterm is a product term that involves each of the the input variables. Products of maxterms (and sums of minterms) are considered canonical forms.

Since maxterms are used in products (that is, ANDed together) it follows that each maxterm (when = 0) represents a unique cell in the K-Map 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 K-Map.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 counter-intuitive 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 K-Map that is zero. For example, given M2 as above, the K-Map will have a zero in the position where a,b,c = 0 1 0.

Last edited: Jun 17, 2011
3. Jun 17, 2011

### uart

Products of maxterms are usually denoted with a product symbol (Pi) followed by an "M" list, for example.

$$(a + b' + c) (a' + b + c) = \prod M(2,4)$$

Sums of minterms are usually denoted as a sum symbol (Sigma) followed by an "m" list, for example.

$$a' b c + a b' c = \sum m(3,5)$$

Last edited: Jun 17, 2011
4. Jun 20, 2011

### Idyllic

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.