Understanding Canonical Maxterm Form and 'Big M' Notation for Karnaugh Maps

  • Thread starter Idyllic
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In summary, 'big M' notation is used to represent canonical maxterm form, which involves using maxterms to express a function. It is commonly used in Boolean algebra and can be written using a product symbol (Pi) followed by an "M" list.
  • #1
Idyllic
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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
 
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  • #2
Idyllic said:
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

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.
 
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  • #3
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]
 
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  • #4
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.
 

1. How do Karnaugh maps help in simplifying boolean expressions?

Karnaugh maps are graphical tools that help in simplifying boolean expressions by visually organizing the truth table and identifying patterns. This allows for easier identification of groups and simplification of terms.

2. What are the steps for expressing a Karnaugh map?

The steps for expressing a Karnaugh map are as follows:
1. Create the truth table for the given boolean expression.
2. Group together adjacent 1s in the truth table to form rectangles in the Karnaugh map.
3. Simplify each rectangle to the smallest possible term.
4. Combine the simplified terms to form the simplified boolean expression.

3. Can Karnaugh maps be used for expressions with more than 4 variables?

Yes, Karnaugh maps can be used for expressions with more than 4 variables by creating a larger map with more cells. However, the process can become more complex as the number of variables increases.

4. How do I know if my simplified expression is correct?

To ensure the correctness of the simplified expression, you can compare it to the original expression and check if they produce the same output for all possible combinations of inputs. Additionally, you can use boolean algebra laws to verify the simplification steps.

5. Are there any limitations to using Karnaugh maps?

While Karnaugh maps are a useful tool for simplifying boolean expressions, they can only be used for expressions with up to 6 variables. Additionally, the process can become more complex for expressions with more variables, and it may be more efficient to use other methods of simplification for larger expressions.

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