Talk:Canonical normal form

This article is just wrong: there are no canonical CNF or DNF! Only ANF is canonical.

A terrible description of canonical form. Do some research and figure out what canonical form really is please.

sum of products
If both "sum of products" and "product of sums" redirects here, this page should have some discussion at *least* about the terms. Fresheneesz 07:19, 6 February 2006 (UTC)


 * Read the article again, closer. Dysprosia 07:20, 6 February 2006 (UTC)


 * Ok, I read closer. I saw each term mentioned once. No explanation about what either of them mean. Fresheneesz 08:54, 7 February 2006 (UTC)


 * "sum of products" (minterms OR'd in series). 
 * "product of sums" (maxterms AND'd in series). 
 * I would think that would be a sufficient explanation of a synonym used. There is a lot of explanation of the concepts elsewhere in the article. I don't know what you're expecting to be present in the article. Dysprosia 09:05, 7 February 2006 (UTC)


 * It'd probably help to put them in the head. SoP and PoS seem to be pretty commonly used. - mako 09:11, 7 February 2006 (UTC)


 * Ok, its fine now. I just expected that you wouldn't have to scour the article to find something about a term that links to the page. Fresheneesz 22:27, 7 February 2006 (UTC)


 * It would have helped greatly if you would have said words to that effect. Dysprosia 22:51, 7 February 2006 (UTC)

specific definition of minterm number
I've been taught that theres a standard way to number minterms, and I was wondering if everyone numbers minterms the same way - and if so, then how exactly is it determined. I know one format we use for four variables, but it may not be the only way. Does anyone know about this? Fresheneesz 04:45, 6 March 2006 (UTC)


 * For computer logic design, in my experience, numbering goes like the "indexing minterms" section says. It's a logical definition IMO. - mako 21:06, 6 March 2006 (UTC)

sop/pos
i'v replaced ...a Boolean function that is composed of standard logical operators... with ...any boolean function... since any boolean function can be expressed as pos/sop.

i'v also added a section about non cannonical sop.pos forms. since they both refer here i feel it is important to have a section about them.

Gregie156 16:16, 13 June 2007 (UTC)

an arbitrary Boolean algebra?
The heading said "in a Boolean algebra", so I disambiguated to Boolean algebra (structure) because of the indefinite article a. But it seems unlikely to me that such a result holds for arbitrary functions from Bn to B, where B is an arbitrary Boolean algebra. Would someone like to clarify what is intended here? --Trovatore 22:02, 23 July 2007 (UTC)
 * The fact that every Boolean expression can be written in both forms holds in an arbitrary Boolean algebra, because it follows from Boolean algebra (uncountable). I will remove the definite article, change the link, and edit the article so it also mentions the terms that mathematicians use: disjunctive normal form and conjunctive normal form. --Hans Adler (talk) 16:06, 29 January 2008 (UTC)

Major expansion of this article
I've tried to respond to the editors' desire for expansion and clarification, plus all the issues raised in readers' posts. My viewpoint, as one of the designers of the Apollo Guidance Computer, is to pursue two goals. The first is of course the academic definition of canonical form, minterms, and maxterms. The second is to show how these academic concepts rub up against the real world. Hughbs (talk) 23:22, 5 January 2009 (UTC)

Doesn't read like an encyclopedic article
This article doesn't read like an encyclopedic article at all. Jwh335 (talk) 22:16, 25 January 2009 (UTC)

Addressing concerns of Jwh335 and SmackBot
First, thanks to Jwh335 for his careful and systematic editing, including standardization of table formats. I put in an expanded section title where he expressed uncertainty. As to whether it reads like an encyclopedic article, I think I preserved the original style up to my major addition of the Application example. That addition, admittedly, reads more like an engineering text, departing from the dry academic tone of the first part. I think it's a useful thing to do here even if it is a change of tone, but I did tone down the most colorful image (lemon/lemonade). I'm definitely a beginner at Wiki-ing, so I hope it's not ill-mannered to have removed the front notes about tone and citations (having addressed both issues to some extent). Hughbs (talk) 04:08, 2 February 2009 (UTC)
 * The main problem with the overall tone is that it reads as if one is being instructed through a how to article. I will see what I can do to revise this. Jwh335 (talk) 20:51, 13 February 2009 (UTC)

Relation to DNF and CNF
As far as I can see, "sum of products" is the same as Disjunctive Normal Form, and "product of sums" is the same as Conjunctive Normal Form. The article implies (under the 'Functional equivalence' headings that they are "a special form of" DNF and CNF respectively, but there doesn't seem to be any difference at all. It's not that unusual to have two completely redundant sets of terminology, but it seems odd for such a fundamental aspect of boolean algebra. What, if anything, am I missing? --David-Sarah Hopwood ⚥ (talk) 14:40, 24 December 2009 (UTC)


 * I don't know for sure, but maybe because classical Boolean algebra is performed as conventional arithmetic on variables assigned a restricted set of values { 0, 1 }, the terms "conjunctive" and "disjunctive" from set theory/logic don't apply. As I go through this, I observe that the sign " + " is a major source of confusion and needs to be further specified i.e. 1 +Boolean 1 = 1 versus 1 +arith 1 = 2
 * p' being defined as 1-p, the sign " - " being conventional from arithmetic
 * p & q being defined as p*q, the sign " * " being conventional from arithmetic
 * p +B q being defined as 1-(1-p)*(1-q) = 1-(1-p-q+p*q)= p +a q - p*q
 * Example: x'y' +B yz' is actually (1-x)*(1-y) +B y*(1-z) = (1-x)*(1-y) +a y*(1-z) - ((1-x)*(1-y))*(y*(1-z))
 * Thus the sum of products canonical form in Boolean algebra looks like DNF but isn't really quite the same thing technically. This needs more research. I have pdf cc's of some old stuff downloaded from googlebooks.com (Boole, Venn, etc). Maybe I can find something of historical import. Bill Wvbailey (talk) 16:14, 24 December 2009 (UTC)

There are more than two canonical forms
This article is inaccurate, as there are more canonical forms than conjunctive and disjunctive normal forms. For example, there is algebraic normal form. &mdash; Olathe (talk) 20:45, 3 July 2013 (UTC)

Article title
This article covers the canonical disjunctive and conjunctive normal forms in Boolean algebra, which are very similar in a deep sense (they are dual). The article title was recently changed to "canonical normal form", which is too vague: there are lots of canonical normal forms: in Unicode, in game theory, in computer algebra, etc. Perhaps the article should be entitled "canonical normal form (Boolean algebra)". But in that case, it should cover all the canonical forms in Boolean algebra. --Macrakis (talk) 00:02, 27 September 2013 (UTC)
 * I don't care much what the new title would be. Fact is that while CDNF and CCNF are similar, they are not the same. A redirect should go to an article that is a synonym, or a wider article that contains information about the subject that was redirected from. CDNF is not more abstract/wider than CCNF or the other way around and they are not the same thing, and redirecting one to the other suggested otherwise. I think it could even be redirected to "Canonical disjunctive and conjunctive normal form" or something like that. Sumurai8 (talk) 16:29, 28 September 2013 (UTC)

Etymology
What is the origin of the terms called maxterm and minterm, i.e. why "min" and "max"? — Preceding unsigned comment added by 91.125.85.104 (talk) 00:11, 31 January 2020 (UTC)