Talk:Karnaugh map

message: "This image actually shows two Karnaugh maps..." Oh, does it? Well I wish it didn't! It's quite unreadable. How is the person who has come here expected to learn if you throw them in at the deep end? How about having three images, with this being the third that shows how you have combined the first two?   — Preceding unsigned comment added by 203.241.147.20 (talk) 05:56, 8 December 2023 (UTC)
thread_title: Image in top right is utter garbage

message: Is really the same? Need a little topic here. See the redirectioning.  — Preceding unsigned comment added by 201.68.255.23 (talk) 08:17, 11 June 2012 (UTC)
thread_title: Marquand x Karnaugh

message: The current example illustrations of K maps on this page are atrociously har to read due to the coloration system used.  Such simple examples are made so awfully difficult to make out.  I propose replacing these with normal, standard K map illustrations that use colored outlines and no shading.
152.3.68.83 (talk) 19:26, 5 March 2013 (UTC)
thread_title: Current K map coloration impossible to read

message: Although there is now a reference to the Veitch diagram, this is a little misleading. The Karnaugh Map is a special case of a Veitch Diagram. Although the orig;linal form of the Veitch diagram doesn't enjoy any sort of uses now.
This also conflicts with the idea that the Karnaugh map was 'invented' in 1950 - it is more properly an extension of existing work. Anyone have any thoughts on how to resolve this? NVeitch
Additionally, The link to Veitch_chart is circular because it redirects back to this section. I'm not familiar with the preferred way to resolve. spartlow  —Preceding undated comment added 20:24, 7 January 2019 (UTC)
thread_title: Veitch Diagram

message: Perhaps we should mention that the rows and columns are ordered according to a gray code, or otherwise explain the importance of having precisely one input value flip between adjacent boxes. Bovlb 00:37, 2004 Mar 11 (UTC)
:Done. Fresheneesz
I do understand that if you don't use Gray code, Karnaugh maps no longer work the way they do. What's the significance, reason and advantage behind using Gray code in Karnaugh maps? 
ICE77 (talk) 22:22, 28 December 2010 (UTC)
replies: text: Yeah the 'why' would be nice, though, the K-maps still work no matter which order you choose. But, you will get more min/max-terms if you don't go with the gray code which then can be reduced. If you use the K-map with the gray code scheme you probably don't have to reduce your terms at all. The final result, however, will still be the same.
Note: Might say it in general. Just tried it on a few examples. 178.9.117.214 (talk) 14:34, 30 January 2012 (UTC)
thread_title:  Gray code 

message: Should there be mentionted that a K-diagram is wrapped around?
So the top left and top right connect and the same goes for bottom left and bottom right.
Kind regards
:: I second this. Fresheneesz 08:50, 8 March 2006 (UTC)
thread_title:  wrap around 

message: Should there be a mention that the cells need to be cirlced in a rectangular shape?
:Done (not by me tho) Fresheneesz 08:52, 8 March 2006 (UTC)
replies: text: Not wishing to be pedantic, but is this strictly true? When doing them by hand any rough shape that groups the right things will do - mine usually come out ellipsoid. The shape of the "circling" is not relevant to the use of the K-map, it's the grouping that matters.Graham 11:32, 8 March 2006 (UTC)
replies: text: Well, not only would that be confusing, but what we mean when we say that is that the circled numbers must trace a rectangular shape. Fresheneesz 19:39, 23 March 2006 (UTC)
thread_title:  rectangular circling 

message: What is the correct pronunciation of Karnaugh's name? Stern 00:00, 1 Dec 2004 (UTC)
replies: text: Same as Carnot, or CAR-NO. Graham 00:08, 1 Dec 2004 (UTC)
thread_title:  Pronunciation 

message: :Image:Karnaugh_map_showing_minterms.png
I made the above picture to specify how to find minterms from a karnaugh map. I didn't put this on the main page, because I'm not sure if this is univerasal. Comments please. Fresheneesz 04:57, 6 March 2006 (UTC)
replies: text: I have made an SVG image :Image:K-map minterms.svg. Cburnett 06:06, 22 December 2006 (UTC)
thread_title: Minterms

message: This article should mention the possibility and how-to of finding xor terms when minimizing. Fresheneesz 01:56, 19 October 2006 (UTC)
replies: text: A karnaugh map doesn't attempt to get the minimum form, it attempts to get the minimum form for a two stage implementation using a particular gate in each stage. Yes there may be tricks that allow one to occasionally spot that there is another way that might save a bit when working in discrete logic but they aren't the main purpose of the maps. Plugwash 16:04, 20 October 2006 (UTC)
thread_title:  circling xor or xnor terms 

message: I created a few SVG images for this article and, in the process, discovered the listed minterms were not reflected correctly in the images.
Please, give the example a thorough review if you have a chance.
I did confirm what I could with . Cburnett 08:08, 22 December 2006 (UTC)
replies: text: Under Race hazards, first bullet point - shouldn't that read when C is 1, D is 0 and not "when C and D are both 0"?  I could be wrong - it's only been 30 years since I have looked at these. Great graphic by the way.--Larry In Cincinnati 03:31, 7 January 2007 (UTC)
replies: text: Correct and I've fixed it.  Thanks for the complements on the graphics. :) Cburnett 04:01, 7 January 2007 (UTC)

text: I feel it appropriate to raise the concern here that illustrations created "de novo" run the risk of being factually incorrect, and fail the encyclopedic requirement of a sound reference source. You can avoid this by using a trusted reference as the source of the illustration's details, even if you create a new rendering to meet copyright requirements. Does anyone else have the same concern? Cburnett seems to have edited the illustration several times to correct errors. This could be avoided by use of an authoritative source material/example. JoGusto (talk) 14:15, 10 August 2013 (UTC)
thread_title:  Image changes 

message: What is a Karnaugh map? Neither in your article, nor in the general literature on the subject, will you find a definition (with one exception). Given a function f:\{0,1\}^n \mapsto \{0,1\}, we call its 2^n 'arguments' (x_1,\dots,x_n) — each an element of \{0,1\}^n — an input combination or input event. We can now define:
A Karnaugh map for n input variables x_1,\dots,x_n is a Venn diagram whose universe consists of all 2^n input events (x_1,\dots,x_n). The sets defined and pictured on the universe are n non-disjoint sets \mathcal{X}_1,\dots,\mathcal{X}_n,
any such set \mathcal{X}_i containing all input events whose i-th input variable 
x_i is 1, i.e., (x_1,\dots,x_i,\dots,x_n)\in \mathcal{X}_i\Leftrightarrow x_i=1.
Karnaugh maps and their usage are covered quite extensively in chapters 6, 7 and 21 (Reduced K-maps) of
Shimon P. Vingron:'Switching Theory. Insight through Predicate Logic' Springer-Verlag, 2004, . 
I have not put this, and other aspects touched on in the above reference, in the main article so as not to intrude on your work: I leave it to you whether you want to make use of the above comment.
S.P.Vingron, 81.217.16.172 14:16, 28 August 2007 (UTC)
thread_title:  Definition of Karnaugh Map 

message: Why must the blue inverse term be restricted by \overline{A}? If we really don't care about the m15 case, it can be treated as 1 for the non-inverse case and 0 for the inverse case; while this makes the non-inverse and inverse cases non-equivalent for all inputs, they are still equivalent for all inputs that we care about.
However, it doesn't really matter, since treating the don't-care as 1 allows the inverse function to be simplified to F = \left(A + B\right)\left(A + C\right)\left(A + \overline{D}\right). I can't take credit for this second bit though, an applet gave it to me when I was checking the first paragraph. Anomie 17:07, 14 October 2007 (UTC)
thread_title: Don't cares

message: Shouldn't the \left(A + \overline{D}\right) term be added to the inverse case to remove a hazard when moving from m7 to either m3 or m5? Anomie 17:07, 14 October 2007 (UTC)
thread_title: Race hazards

message: For the green encircling, besides A and B, C also maintains the same state of 1. So, shouldn't the second term be A\overline{B}C and not A\overline{B}?
Sepia tone 04:40, 25 October 2007 (UTC)
replies: text: I don't know which image you're looking at, but I can't find one where a green encircling has C remaining unchanged. In :Image:K-map 6,8,9,10,11,12,13,14.svg, for example, the green circles all four minterms in the rightmost (A\overline{B}) column, overlapping with the right half of the red group. Anomie 11:20, 25 October 2007 (UTC)
thread_title:  map 

message: Can we have examples for 5 and 6 variables?
For 5 variables A,B,C,D,E: We can make a 4 variable frame A,B,C,D, then fill in each entry  with 1,0,x(don't care),E,e(Ebar). Then put in the circles, noting that E is not 0 and is not 1.
Truth table
 ABCDE Out
 00000 0
 00001 1
 00010 0
 00011 1
 00100 0
 00101 1
 00110 0
 00111 1
 01000 0
 01001 1
 01010 0
 01011 1
 01100 0
 01101 1
 01110 0
 01111 1
 10000 0
 10001 0
 10010 0
 10011 0
 10100 1
 10101 1
 10110 1
 10111 1
 11000 1
 11001 1
 11010 0
 11011 0
 11100 0
 11101 0
 11110 1
 11111 1
Map
   |0110|C
   |0011|D
 --|----|
 00|EEEE|
 10|0110|
 11|1010|
 01|EEEE|
 --|----|
 AB|
Out=aE+AbC+ACD+ABcd
(lower case is not)
:No, usually you would use Boolean Algebra when simplifying five, six, or more variable circuits.  It's certainly possible, but do you really want to have thirty-two squares to fill out? ChyranandChloe (talk) 02:29, 14 June 2008 (UTC)
replies: text: It is possible to work with 5 variables any beyond. For an odd number like 5 you would create two 2x2 maps. One for E = 0 and one for E = 1. However, like ChyranandChloe said it isn't wise to work with a huge K-map unless you have to but even then I'd rather look for a software solution. 178.9.117.214 (talk) 14:44, 30 January 2012 (UTC)

text: I agree... but you would probably use an automated tool based on the Quine-McCluskey minimization algorithm. Perhaps it should be mentioned. JoGusto (talk) 14:31, 10 August 2013 (UTC)
thread_title:  More than 4 variables 

message: Shouldn't entries such as K-Map link to this page?  Thanks
129.7.108.128 (talk) 18:28, 6 February 2008 (UTC)
replies: text: K-map does, K-Map doesn't because "map" isn't capitalized.  But if you put "K-Map" in the search box then you hit this article just fine.  Cburnett (talk) 19:03, 6 February 2008 (UTC)
thread_title:  Link-to's 

message: I think it would helpful if we could include a unsimplified digital electronic circuit design and a simplified circuit design in addition to the boolean algebra - it makes it difficult to apply if you don't have the circuit to refer to. ChyranandChloe (talk) 00:01, 30 May 2008 (UTC)
replies: text: Good point!  Can you do it?  yoyo (talk) 05:40, 9 June 2010 (UTC)
thread_title:  Circuit Design Image 

message: I just discovered that geneticists describe Mendelian inheritance using a diagram called a Punnett square which strikes me as being both structurally and functionally very similar to a Karnaugh map.  Is it worth mentioning this correspondence anywhere? (Perhaps just a See Also link?)  —Steve Summit (talk) 03:33, 30 June 2009 (UTC)
replies: text: I can see the "structurally similar" here (inputs along the borders) but not the "functionally similar" --- the analogy actually seems quite superficial, as any Cartesian product of mappings can be represented as somewhat along these lines. So some further explanation about how the Punnett square is functionally similar is required. The P square is not used (afaik) to find minimal representations or prime implicants, whatever the analogs in genetics might be. (I am both a geneticist and a logician, so I think I would have spotted any such analogy, but then I do not wish to claim outright that it isn't there just because I failed to observe it.) 2A01:CB0C:CD:D800:9C38:3BDB:AF80:1542 (talk) 15:56, 11 May 2021 (UTC)
thread_title:  compare with [[Punnett square]]? 

message: A Karnaugh map is not the same thing as a Veitch diagram. Veitch's diagram is used by virtually no one. I have the originals of both papers. The 2nd drawing on the right is a virtual reproduction of drawings from both papers. Notice that the Veitch diagram does not use the "Gray (en)coding" or the encoding from the "vertices of a hypercube". 
I'll have change this paragraph eventually unless someone persuades me to do otherwise. Bill Wvbailey (talk) 18:20, 22 December 2009 (UTC)
thread_title:  Lead sentence is wrong 

message: I reverted the recent edits made in good faith by 108.41.142.178; here is why:
* According to the Karnaugh map methodology, the "green group" in the picture in section "Karnaugh map#Solution" should be as large as possible in order to obtain the simplest possible expression realizing the function f. Since the whole rightmost column contains 1s, the green group should be at least that large (it can't be larger, on the other hand). That is, it should be AB' rather than AB'C only ("'" denoting complement here).
* The inner caption of the picture says "F=AC'+AB'+BCD'" rather than "F=AC'+AB'C+BCD'". The text should be consistent with that.
* Looking very closely at the square ABCD=1001, some green can be seen at its bottom, probably intended to indicate that the green area is not restricted to the two fields below it.
In order to avoid repetitions of 108.41.142.178's misunderstanding of the picture, the extensions of the red, green, and blue field should be made more clear in an improved version of the picture. There could be more emphasis on the borders and less on the areas; and the border lines of the red and green field should not coincide exactly, such that both are visible. If the partitioning of the 0 area is not discussed in the article (I didn't check that), it should be removed from the picture. - Jochen Burghardt (talk) 16:39, 30 September 2013 (UTC)
thread_title:  Picture in section "Solution" difficult to read / justification of revert 

message: From the article: "For the red grouping: [...] C does not change. It is always 0, so its complement, NOT-C, should be included. Thus, \overline{C} should be included."
This is true in the bottom picture, but not the top picture (:File:Karnaugh.svg). That picture shows "CD" as "10" or "11" in the red group, in which case C is always 1. Can anyone fix either the image or description? 108.202.199.178 (talk) 15:38, 18 February 2015 (UTC)
thread_title:  Solution Section Picture Error 

message: Just before the sub-section labeled "Karnaugh map", it may be helpful to actually write out the complete (16-term/16-factor) function for both sum-of-products and product-of-sums. I figured this out on my own after carefully reading the math and the definition of minterm/maxterm (from the linked Canonical_normal_form), but the SoP/PoS notion is a lot simpler than either article makes it appear.
I think having the complete function would also really help to illustrate how the solution below (of 3 terms) is vastly simpler than the trivial (canonical?) version. However, if showing the entire function is thought out of scope, is there perhaps a better/more-straightforward description that could be linked at this point in the article?--preferably one that clearly explains how one might construct the full form, but not as overly complicated as the Canonical_normal_form article. 108.202.199.178 (talk) 16:14, 18 February 2015 (UTC)
thread_title:  Include Original Function for Example 

message: Are Karnaugh Map solutions to truth tables an example of a heuristic ? They will usually produce a good solution, even if they don't always find the best solution?
Paul Murray (talk) 03:56, 18 June 2015 (UTC)
thread_title:  Is this an example of a heuristic?