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"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)
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)
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)
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)
Hm the C,D-row is upside-down. It should go as (0,0)-(0,1)-(1,1)-(1,0). -- BL
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)
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)
Note: Might say it in general. Just tried it on a few examples. 178.9.117.214 ( talk) 14:34, 30 January 2012 (UTC)
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
There is a line that reads "just as m0, m8, m2, and m10 can be combined into a four-by-four group."(accessed 21/jun/2010). I think that this should read 'a two-by-two group' because there are only two squares on each side making a total of four squares in the group when wrapping the four corners together. Note, I could be really wrong, because I don't understand any of this and there is likely to be more to it than I get. ElTimbalino ( talk) 12:16, 21 June 2010 (UTC)
Should there be a mention that the cells need to be cirlced in a rectangular shape?
What is the correct pronunciation of Karnaugh's name? Stern 00:00, 1 Dec 2004 (UTC)
What's the purpose of the second diagram? I don't understand it, it appears to duplicate the first with a less clear labelling, and the text doesn't refer to it. I think it should go. Graham 00:29, 21 Dec 2004 (UTC)
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)
This article should mention the possibility and how-to of finding xor terms when minimizing. Fresheneesz 01:56, 19 October 2006 (UTC)
Are you talking about Reed-Muller logic ? -- 68.0.120.35 14:58, 7 December 2006 (UTC)
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 [2]. Cburnett 08:08, 22 December 2006 (UTC)
Should these be mentioned?
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 , we call its 'arguments' — each an element of — an input combination or input event. We can now define:
A Karnaugh map for n input variables is a Venn diagram whose universe consists of all input events . The sets defined and pictured on the universe are n non-disjoint sets , any such set containing all input events whose i-th input variable is 1, i.e., .
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, ISBN 3-540-40343-4.
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)
Why must the blue inverse term be restricted by ? 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 . 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)
Shouldn't the 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)
The section title "Elimination" seems unhelpful and obtuse for a section which deals with race hazards and how to eliminate them. The origin of a race hazard as the result of the reduction, how to fix the race hazard, when is the race hazard important (purely combinatoric logic) and when might it be ignored (registered, clocked "sequential" circuits). JoGusto ( talk) 14:28, 10 August 2013 (UTC)
For the green encircling, besides A and B, C also maintains the same state of 1. So, shouldn't the second term be and not ?
Sepia tone 04:40, 25 October 2007 (UTC)
You are right. My bad. Sepia tone ( talk) 02:53, 30 November 2007 (UTC)
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)
If you think that the above suggestion is about 32 entries or an additional dimension, then you have miss-read it. It is describing how to add an extra variable without increasing the number of dimensions. We learnt this at university circa 1992-1995. It may have another name. Look at the example it has 5 variable, but only 2 dimensions. From what I remember it allows 6 variable with 2 dimensions. Ctrl-alt-delor ( talk) 12:21, 01 October 2019 (UTC)
You can use 4×4×2 cuboid for 5 variables. 220.228.194.112 ( talk) 03:34, 11 December 2020 (UTC)
Shouldn't entries such as K-Map link to this page? Thanks
129.7.108.128 ( talk) 18:28, 6 February 2008 (UTC)
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)
What the heck is the "axion law"? This term is used at least twice in this article, and links to the boolean logic page, in which the word "axion" never appears. linas ( talk) 21:34, 4 June 2008 (UTC)
"...Two Boolean laws having no numeric counterpart are the laws characterizing logical negation, namely x∧¬x = 0..."
In the example diagram it is not obvious that the brown section is the overlapping of the red and green sections. This got me confused for quite a while! I suggest that using eg striped red and green for the overlapping section, or make the outlines easier to see.-- Czar Kirk ( talk) 04:30, 13 June 2008 (UTC)
The yellow square and teal square are both redundant groupings. The actual minimal POS and SOP equations should only have 3 terms each, not 4. 75.151.246.133 ( talk) 22:11, 2 May 2010 (UTC)
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)
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)
I just went ahead and changed the lead paragraph. If anyone doubts the truth of the above I'll just photograph or pdf the relevant drawings from both papers to make the point. BTW: I was able to get the Karnaugh paper off the web, but I had to buy the damn Veitch paper; someone with access to an academic library can probably get it from the ACM. It is not a particularly satisfactory paper when compared to the Karnaugh paper. Bill Wvbailey ( talk) 18:38, 22 December 2009 (UTC)
I am by no means a subject matter expert, but the second function in the example does not look right to me. Can someone confirm that it is indeed correct? Specifically, I am referring to this:
It doesn't seem to correspond with the previous example or what comes after.
I searched through the edit history and found a prior revision of that example that makes a lot more sense to me. Here is the revision where it changed from something I understand to something I don't.
207.182.200.34 ( talk) 15:18, 24 August 2011 (UTC)
If you look closely at the binary versions you'll see that as you go left to right or right to left, or up or down one square at a time (but not diagonally), only one "1" or "0" changes at a time. This includes the left-right edge wraparound and the top-bottom edge wrap-around. Other number-schemes are allowed but the "only-one-variable change" cannot be violated. That's the key to the Karnaugh map.
See the proper box-numbering scheme above (circa 2004 -- but this is a different example, but the numbering scheme is correct), and the 8-square version directly above.
Hope this helps. Bill Wvbailey ( talk) 20:58, 24 August 2011 (UTC)
I went back to my sources to see their cell-numbering schemes. To a man/woman they numbered them in a different way than what I showed above. This includes M. Karnaugh himself in his very-most original paper. Here is how they all do it:
In words: the "classical" numbering scheme shown above is "my" numbering scheme mirror-imaged and rotated counter-clockwise. This is just to set the record straight. Bill Wvbailey ( talk) 00:48, 28 August 2011 (UTC)
I reverted the recent edits made in good faith by 108.41.142.178; here is why:
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)
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)
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)
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)
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"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)
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)
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)
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)
Hm the C,D-row is upside-down. It should go as (0,0)-(0,1)-(1,1)-(1,0). -- BL
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)
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)
Note: Might say it in general. Just tried it on a few examples. 178.9.117.214 ( talk) 14:34, 30 January 2012 (UTC)
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
There is a line that reads "just as m0, m8, m2, and m10 can be combined into a four-by-four group."(accessed 21/jun/2010). I think that this should read 'a two-by-two group' because there are only two squares on each side making a total of four squares in the group when wrapping the four corners together. Note, I could be really wrong, because I don't understand any of this and there is likely to be more to it than I get. ElTimbalino ( talk) 12:16, 21 June 2010 (UTC)
Should there be a mention that the cells need to be cirlced in a rectangular shape?
What is the correct pronunciation of Karnaugh's name? Stern 00:00, 1 Dec 2004 (UTC)
What's the purpose of the second diagram? I don't understand it, it appears to duplicate the first with a less clear labelling, and the text doesn't refer to it. I think it should go. Graham 00:29, 21 Dec 2004 (UTC)
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)
This article should mention the possibility and how-to of finding xor terms when minimizing. Fresheneesz 01:56, 19 October 2006 (UTC)
Are you talking about Reed-Muller logic ? -- 68.0.120.35 14:58, 7 December 2006 (UTC)
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 [2]. Cburnett 08:08, 22 December 2006 (UTC)
Should these be mentioned?
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 , we call its 'arguments' — each an element of — an input combination or input event. We can now define:
A Karnaugh map for n input variables is a Venn diagram whose universe consists of all input events . The sets defined and pictured on the universe are n non-disjoint sets , any such set containing all input events whose i-th input variable is 1, i.e., .
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, ISBN 3-540-40343-4.
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)
Why must the blue inverse term be restricted by ? 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 . 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)
Shouldn't the 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)
The section title "Elimination" seems unhelpful and obtuse for a section which deals with race hazards and how to eliminate them. The origin of a race hazard as the result of the reduction, how to fix the race hazard, when is the race hazard important (purely combinatoric logic) and when might it be ignored (registered, clocked "sequential" circuits). JoGusto ( talk) 14:28, 10 August 2013 (UTC)
For the green encircling, besides A and B, C also maintains the same state of 1. So, shouldn't the second term be and not ?
Sepia tone 04:40, 25 October 2007 (UTC)
You are right. My bad. Sepia tone ( talk) 02:53, 30 November 2007 (UTC)
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)
If you think that the above suggestion is about 32 entries or an additional dimension, then you have miss-read it. It is describing how to add an extra variable without increasing the number of dimensions. We learnt this at university circa 1992-1995. It may have another name. Look at the example it has 5 variable, but only 2 dimensions. From what I remember it allows 6 variable with 2 dimensions. Ctrl-alt-delor ( talk) 12:21, 01 October 2019 (UTC)
You can use 4×4×2 cuboid for 5 variables. 220.228.194.112 ( talk) 03:34, 11 December 2020 (UTC)
Shouldn't entries such as K-Map link to this page? Thanks
129.7.108.128 ( talk) 18:28, 6 February 2008 (UTC)
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)
What the heck is the "axion law"? This term is used at least twice in this article, and links to the boolean logic page, in which the word "axion" never appears. linas ( talk) 21:34, 4 June 2008 (UTC)
"...Two Boolean laws having no numeric counterpart are the laws characterizing logical negation, namely x∧¬x = 0..."
In the example diagram it is not obvious that the brown section is the overlapping of the red and green sections. This got me confused for quite a while! I suggest that using eg striped red and green for the overlapping section, or make the outlines easier to see.-- Czar Kirk ( talk) 04:30, 13 June 2008 (UTC)
The yellow square and teal square are both redundant groupings. The actual minimal POS and SOP equations should only have 3 terms each, not 4. 75.151.246.133 ( talk) 22:11, 2 May 2010 (UTC)
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)
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)
I just went ahead and changed the lead paragraph. If anyone doubts the truth of the above I'll just photograph or pdf the relevant drawings from both papers to make the point. BTW: I was able to get the Karnaugh paper off the web, but I had to buy the damn Veitch paper; someone with access to an academic library can probably get it from the ACM. It is not a particularly satisfactory paper when compared to the Karnaugh paper. Bill Wvbailey ( talk) 18:38, 22 December 2009 (UTC)
I am by no means a subject matter expert, but the second function in the example does not look right to me. Can someone confirm that it is indeed correct? Specifically, I am referring to this:
It doesn't seem to correspond with the previous example or what comes after.
I searched through the edit history and found a prior revision of that example that makes a lot more sense to me. Here is the revision where it changed from something I understand to something I don't.
207.182.200.34 ( talk) 15:18, 24 August 2011 (UTC)
If you look closely at the binary versions you'll see that as you go left to right or right to left, or up or down one square at a time (but not diagonally), only one "1" or "0" changes at a time. This includes the left-right edge wraparound and the top-bottom edge wrap-around. Other number-schemes are allowed but the "only-one-variable change" cannot be violated. That's the key to the Karnaugh map.
See the proper box-numbering scheme above (circa 2004 -- but this is a different example, but the numbering scheme is correct), and the 8-square version directly above.
Hope this helps. Bill Wvbailey ( talk) 20:58, 24 August 2011 (UTC)
I went back to my sources to see their cell-numbering schemes. To a man/woman they numbered them in a different way than what I showed above. This includes M. Karnaugh himself in his very-most original paper. Here is how they all do it:
In words: the "classical" numbering scheme shown above is "my" numbering scheme mirror-imaged and rotated counter-clockwise. This is just to set the record straight. Bill Wvbailey ( talk) 00:48, 28 August 2011 (UTC)
I reverted the recent edits made in good faith by 108.41.142.178; here is why:
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)
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)
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)
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)