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

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Discussion Overview

The discussion revolves around understanding canonical maxterm and minterm forms, as well as the use of 'big M' notation in the context of Karnaugh maps. Participants seek clarification on definitions and examples related to these concepts, particularly in preparation for an exam.

Discussion Character

  • Exploratory
  • Technical explanation
  • Homework-related

Main Points Raised

  • One participant asks for definitions of canonical maxterm and minterm forms, expressing difficulty in finding information in lecture notes.
  • Another participant explains that a maxterm is a sum term involving all input variables, while a minterm is a product term involving all input variables, and both are considered canonical forms.
  • It is noted that maxterms are used in products (ANDed together) and represent unique cells in a Karnaugh map when equal to zero.
  • A specific example is provided for three variables, illustrating the relationship between minterms, maxterms, and their corresponding indices in a Karnaugh map.
  • Another participant describes the notation for products of maxterms and sums of minterms, using symbols (Pi for products and Sigma for sums) followed by lists of indices.
  • A participant seeks clarification on the meaning of 'big M' notation, suggesting it may simply refer to writing in maxterms again.

Areas of Agreement / Disagreement

Participants express varying levels of understanding regarding the definitions and applications of canonical forms and 'big M' notation. There is no consensus on the interpretation of 'big M' notation, as one participant questions its meaning while another provides an explanation.

Contextual Notes

Some participants may have assumptions about the prior knowledge expected in the discussion, and there may be limitations in the clarity of definitions provided. The discussion does not resolve the ambiguity surrounding 'big M' notation.

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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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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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:
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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