Talk:NAND logic

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Probably not super important, but there are other input combinations that generate XOR (with the same number of gates) than shown here. The two gates that have a&b connected to them will achieve the same goal with a,a on one and b,b on the other. The BLIF output that describes this is below:

.input a b c
.output 0
.names 1 6 0
0- 1
-0 1
.names c 3 1
0- 1
-0 1
.names b b 3
0- 1
-0 1
.names b 8 6
0- 1
-0 1
.names a a 8
0- 1
-0 1

In simplifying the algebra by hand, this yields XOR sooner than the way presented in the page.

Do we Really need to show how to make a nand gate with a nand gate? —Preceding unsigned comment added by (talk) 21:56, 14 October 2007 (UTC)

the truth diagram for this 'NAND' gate is not correct!! Someone please modify it! —Preceding unsigned comment added by (talk) 14:55, 6 March 2008 (UTC)

Is it possible to add link to my NAND logic equivalent page at ? —Preceding unsigned comment added by (talk) 14:34, 5 March 2009 (UTC)

The use of 0 and 1 is very common, but (perhaps being picky) is not fundamental as it makes the assumption that True=1 and False=0. It is better to use T & F. (talk) 10:03, 11 April 2009 (UTC)

Hasse diagram[edit]

The following diagram shows all binary logical connectives expressed only by NAND operations, represented by the black circles. I propose to include it at the end of the article, to show, how the functions themselves are interlaced - not only the logic gates in some computer.

When I included this file in the Logical NAND article, the reactions have been quite bad, and in a discussion we came to the conclusion, that it doesn't match there. As the diagram reflects quite exactly the content of this article, I think it matches here. If you agree, feel free to include it. Lipedia (talk) 16:32, 29 July 2009 (UTC)

A B not (A) not (B) contradiction tautology XOR (A,B) XNOR (A,B) NOR (A,B) nonimplication (A,B) converse nonimplication (A,B) AND (A,B) NAND (A,B) converse implication (A,B) implication (A,B) OR (A,B)
All logical connectives expressed by interlaced NAND operations (represented by circles around the two arguments) (file) (zoom in)

The diagram looks nicely drawn, but I don't understand it. What information is it supposed to convey? Also, if it is a Hasse diagram, what's the relation between the nodes of the graph? Adrianwn (talk) 19:41, 1 August 2009 (UTC)

As the binary truth values indicate, the Hasse diagram is ordered by implication, exactly like this one, so the lower nodes imply the connected higher nodes.

Every node stands for a logical connective. This connective can be expressed by interlaced NAND operations, represented by interlaced circles. If you look in the bottom right corner, you see the AND connective: Expressed by the NAND operation its NAND(NAND(A,B),NAND(A,B)). If you know, that all operations are NAND you may write ((A,B),(A,B)) - thats what the black circles show.

By the way, its interesting, that this NAND diagram is exactly the vertically mirrored NOR diagram. Greetings, Lipedia (talk) 09:43, 4 August 2009 (UTC)

Although the information, how to construct the boolean operators exclusively from NAND gates, is interesting, it is already contained in the article (albeit in graphical form) for nearly all non-trivial operators. Apart from this, the relation between the operators conveyed in the Hasse diagram is irrelevant for the article's subject.
In my opinion the diagram is too complicated and too confusing, and requires a lot of explanation in order to be understandable. Furthermore, the only relevant information can be visualized in better ways, like "A -> B = A nand (B nand B)". Adrianwn (talk) 20:59, 7 August 2009 (UTC)

NOR and XNOR using NOTs without ANDs?[edit]

I realize that this is entirely too pedantic, but maybe that is appropriate for such an article. In the NOR and XNOR proofs, it looks like not everything is represented by NAND logic (I see cases where there is a NOT with no AND).

For example, in NOR, the proof is written as NOT{ NOT[ NOT( A AND A ) AND NOT( B AND B )]}

It occurs to me that the NOT with curly braces doesn't employ an AND, so maybe a more purely NANDish version would look like this: NOT{ NOT[ NOT( A AND A ) AND NOT( B AND B )] AND NOT[ NOT( A AND A ) AND NOT( B AND B )]}

I realize that we have already proven NOT in a previous section, but in the spirit of demonstrating NAND logic, shouldn't we write out the full statement instead of taking a shortcut? Or maybe I missed something else? I'll make the edits, but feel free to chastise me if I am wrong. capitocapito - Talk 23:30, 26 August 2014 (UTC)