Editing Logic gate (section)

== Universal logic gates ==
{{further|topic=the theoretical basis|Functional completeness}}
[[Charles Sanders Peirce]] (during 1880–1881) showed that [[NOR logic|NOR gates alone]] (or alternatively [[NAND logic|NAND gates alone]]) can be used to reproduce the functions of all the other logic gates, but his work on it was unpublished until 1933.<ref>Peirce, C. S. (manuscript winter of 1880–1881), "A Boolian Algebra with One Constant", published 1933 in ''[[Charles Sanders Peirce bibliography#CP|Collected Papers]]'' v. 4, paragraphs 12–20. Reprinted 1989 in ''[[Charles Sanders Peirce bibliography#W|Writings of Charles S. Peirce]]'' v. 4, pp. 218–221, Google [https://archive.org/details/writingsofcharle0004peir/page/218]. See {{cite book |author-last=Roberts |author-first=Don D. |title=The Existential Graphs of Charles S. Peirce |date=2009 |publisher=[[De Gruyter]] |isbn=978-3-11022622-5 |pages=131 |chapter=7.12 The Graphical Analysis of Propositions |chapter-url=https://books.google.com/books?id=Q4K30wCAf-gC&pg=PA113}}</ref> The first published proof was by [[Henry M. Sheffer]] in 1913, so the NAND logical operation is sometimes called ''[[Sheffer stroke]]''; the [[logical NOR]] is sometimes called ''[[Peirce's arrow]]''.<ref name="BüningLettmann1999">{{cite book |author-first1=Hans Kleine |author-last1=Büning |author-first2=Theodor |author-last2=Lettmann |title=Propositional logic: deduction and algorithms |url=https://books.google.com/books?id=3oJE9yczr3EC&pg=PA2 |date=1999 |publisher=[[Cambridge University Press]] |isbn=978-0-521-63017-7 |page=2}}</ref> Consequently, these gates are sometimes called ''universal logic gates''.<ref name="Bird2007">{{cite book |author-first=John |author-last=Bird |title=Engineering mathematics |url=https://books.google.com/books?id=1-fBmsEBNUoC&pg=PA532 |date=2007 |publisher=[[Newnes (publisher)|Newnes]] |isbn=978-0-7506-8555-9 |page=532}}</ref>

{| class="wikitable skin-invert-image"
|+	
!type
!NAND construction
!NOR construction
|-
|NOT
|[[File:NOT from NAND.svg]]
|[[File:NOT from NOR.svg]]
|-
|AND
|[[File:AND from NAND.svg]]
|[[File:AND from NOR.svg]]
|-
|NAND
|[[File:NAND ANSI Labelled.svg]]	
|[[File:NAND from NOR.svg]]	
|-
|OR
|[[File:OR from NAND.svg]]
|[[File:OR from NOR.svg]]
|-	
|NOR	
|[[File:NOR from NAND.svg]]	
|[[File:NOR ANSI Labelled.svg]]	
|-	
|XOR	
|[[File:XOR from NAND.svg]]	
|[[File:XOR from NOR.svg]]	
|-
|XNOR
|[[File:XNOR from NAND 2.svg]]
|[[File:XNOR from NOR.svg]]
|-
|IMPLY
|[[File:IMPLY from NAND.svg]]
|[[File:IMPLY from NOR.svg]]
|-
|NIMPLY
|[[File:NIMPLY from NAND.svg]]
|<!--File is missing.-->
|}