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== References == {{reflist|refs= <ref name="Gardner_1972">{{cite magazine |title=The curious properties of the Gray code and how it can be used to solve puzzles |author-first=Martin |author-last=Gardner |author-link=Martin Gardner |date=August 1972 |series=[[Mathematical Games column|Mathematical Games]] |magazine=[[Scientific American]] |volume=227 |number=2 |page=106}} (1 page)</ref> <ref name="Lucas_1883">{{cite book |title=La tour d'Hanoï: Véritable casse tête annamite - Jeu rapporté du Tonkin par le Professeur N. Claus (de Siam) Mandarin du Collège Li Sou Stian! |language=fr |author-first=Édouard |author-last=Lucas |author-link=Édouard Lucas |date=November 1883 |publisher=Imprimerie Paul Bousrez, Tours.}} (NB. N. Claus de Siam is an anagram of Lucas d'Amiens, pseudonym of the author [[Édouard Lucas]].)</ref> <ref name="Parville_1883">{{cite journal |title=La tour d'Hanoï, véritable casse-tête annamite, jeu rapporté du Tonkin par le professeur N. Claus (de Siam), mandarin du collège Li-Sou-Stian. Un vrai casse-tête, en effet, mais intéressant. Nous ne saurions mieux remercier le mandarin de son aimable intention à l'égard d'un profane qu'en signalant la Tour d'Hanoï aux personnes patientes possédées par le démon du jeu. |language=fr |editor-first=Henri |editor-last=de Parville |editor-link=:fr:Henri de Parville |date=1883-12-27 |journal=[[Journal des Débats Politiques et Littéraires]] |series=Revue des science |type=Review |edition=Matin |publication-place=Paris, France |id=ark:/12148/bpt6k462461g |pages=1–2 [2] |url=https://gallica.bnf.fr/ark:/12148/bpt6k462461g/f2.item |access-date=2020-12-18 |url-status=live |archive-url=https://web.archive.org/web/20201218125345/https://gallica.bnf.fr/ark:/12148/bpt6k462461g/f2.item |archive-date=2020-12-18}} (1 page)</ref> <ref name="Allardice-Fraser_1883">{{cite journal |title=La Tour d'Hanoï |language=en, fr |editor-first1=Robert Edgar |editor-last1=Allardice |editor-link1=Robert Edgar Allardice |editor-first2=Alexander Yule |editor-last2=Fraser |editor-link2=Alexander Yule Fraser |journal=[[:nl:Proceedings of the Edinburgh Mathematical Society|Proceedings of the Edinburgh Mathematical Society]]<!-- :d:Q15492536 --> |volume=2 |number=5 |date=February 1883 |pages=50–53 |doi=10.1017/S0013091500037147 |issn=0013-0915 |eissn=1464-3839 |publisher=[[Edinburgh Mathematical Society]] |last1=Allardice |first1=R. E. |last2=Fraser |first2=A. Y. |doi-broken-date=1 November 2024 |s2cid=122159381 |doi-access=free }} [https://web.archive.org/web/20201218112132/https://www.cambridge.org/core/services/aop-cambridge-core/content/view/082EFE016BF3313A7BAA9335A9C0BCC1/S0013091500037147a.pdf/la-tour-d-hanoi.pdf] (4 pages)</ref> <ref name="Lucas_1892">{{cite book |author-first=Édouard |author-last=Lucas |author-link=Édouard Lucas |title=Récréations mathématiques |language=fr |volume=3 |orig-date=1892 |edition=Librairie Albert Blanchard reissue |date=1979 |page=58}} (The first edition of this book was published post-humously.)</ref> <ref name="Gros_1872">{{cite book |title=Théorie du baguenodier par un clerc de notaire lyonnais |language=fr |author-first=Luc-Agathon-Louis |author-last=Gros |date=1872 |publisher=[[Aimé Vingtrinier]] |edition=1 |publication-place=Lyon, France |url=https://books.google.com/books?id=EcoBJRekd-sC&pg=PP1 |access-date=2020-12-17 |url-status=live |archive-url=http://archive.wikiwix.com/cache/20170403080613/https://books.google.fr/books?id=EcoBJRekd-sC&pg=PP1 |archive-date=2017-04-03}} [https://web.archive.org/web/20201217202507/https://books.googleusercontent.com/books/content?req=AKW5Qacg5gq7SW9L1sUUqK7LQ0yJLqaCu90GFZZYzcH7dsoifr-n9hxiB30SJ1mXq3FhDejHQ7fXY2ZdzlhFywe8pQGNTgMHjX0ANYxRohedbG1FmoPTuKibswKOO7qS2X4MUwQP0dBn-vt3dfTIBFRvTBOVoZZA1ROBXTGTMybnA4gGndl8v0qIAeKsRNUuEddqabMqMngisr8fp-iNt7NMFfwq_tPk0we0yXNJWj74AFsFr1JGOlAmdQ6B_OJVTOj33IhoYybhf8LMzfpaHusXsY2BWT2ZwVQulW0mgBaem9xvRZ58TSw](2+16+4 pages and 4 pages foldout) (NB. This booklet was published anonymously, but is known to have been authored by Louis Gros.)</ref> <ref name="Rothen_1884">{{cite journal |title=Le télégraphe imprimeur Baudot |language=fr |author-first=Timotheus |author-last=Rothen |date=1884-12-25 |journal=Journal Télégraphique |publisher=Le Bureau International des Administrations Télégraphiques |publication-place=Berne, Switzerland |volume=VIII / #16<!-- A16 / 16e année --> |number=12 |id=ark:/12148/bpt6k5725454q |issn=2223-1420 |eissn=2725-738X |pages=241–253 [249] |url=https://gallica.bnf.fr/ark:/12148/bpt6k5725454q/f9.item |access-date=2020-12-20 |archive-date=2020-12-21 |archive-url=https://web.archive.org/web/20201221162054/https://gallica.bnf.fr/ark:/12148/bpt6k5725454q/f9.item.zoom |url-status=live }}</ref> <ref name="Pendry_1920">{{cite book |title=The Baudôt Printing Telegraph System |author-first=Henry Walter |author-last=Pendry |edition=2 |location=London, UK |publisher=[[Sir Isaac Pitman and Sons, Ltd.]] |publication-place=London, Bath, Melbourne, New York |date=1920 |orig-date=October 1919 |pages=43–44 |lccn=21005277 |oclc=778309351 |ol=OL6633244M |url=https://books.google.com/books?id=CfQKAQAAIAAJ |access-date=2020-12-20}} (vii+184 pages) (NB. A first edition was published in 1913.)</ref> <ref name="Zemanek_1976">{{cite conference |chapter=Computer prehistory and history in central Europe |author-first=Heinrich "Heinz" Josef |author-last=Zemanek |author-link=Heinrich Josef Zemanek |date=1976-06-07 |conference=AFIPS '76: Proceedings of the June 7–10, 1976, national computer conference and exposition June 1976 |title=International Workshop on Managing Requirements Knowledge |publisher=[[American Federation of Information Processing Societies]], [[Association for Computing Machinery]] |publication-place=New York, USA |location=Vienna, Austria |volume=1 |isbn=978-1-4503-7917-5 |doi=10.1145/1499799.1499803 |s2cid=14114959 |pages=15–20 |chapter-url=https://www.computer.org/csdl/pds/api/csdl/proceedings/download-article/12OmNzZEAtH/pdf |access-date=2020-12-17 |url-status=live |archive-url=https://web.archive.org/web/20201217230013/https://www.computer.org/csdl/pds/api/csdl/proceedings/download-article/12OmNzZEAtH/pdf |archive-date=2020-12-17 |quote-page=17 |quote=[…] In 1874, {{ill|Otto Schäffler{{!}}Schaeffler|de|Theodor Heinrich Otto Schäffler}}<!-- *1838-10-15 Unterheimbach bei Heilbronn, Germany; †1928-07-31 Vienna, Austria 1928 --> invented another [[printing telegraph]], a quadruple system like the [[Baudot telegraph|Baudot]], but mechanically more sophisticated. The [[Hughes telegraph]] had two synchronously rotating fingers, one in the sender and one in the receiver. By a piano-like keyboard the operator selected a letter and thereby made contact with the rotating finger in the corresponding direction. Since the receiving finger was in the same direction at this moment, the receiver could print the correct letter. The Baudot and the Schaeffler printing telegraphs use a five-bit binary code. ... Schaeffler's code is a reflected binary code! What [[Frank Gray (researcher)|F. Gray]] patented in 1953 for [[PCM]], Schaeffler had applied in his telegraph in 1874, and for a similar reason: reliability. He had contact fingers sensing on five cams consecutively all combinations; the right one triggers printing. If the fingers are to make a minimal number of movements, the solution is the reflected binary code. For Schaeffler, this idea was a minor one. More exactly, the code is described in a letter by the Austrian Post employee, J[ohann] N[epomuk] Teufelhart, {{citeref|Rothen|1878|inserted there|style=plain}} as a footnote and telling that Schaeffler found the code by combining wooden bars with the different combinations until he had the best solution. Another Post employee, Alexander Wilhelm Lambert of Linz, claims to have shown this code to Schaeffler as early as 1872, but this claim is not clear and cannot be checked. […]}} (6 pages)</ref> <ref name="Zemanek_1979">{{cite book |title=Otto Schäffler (1838-1928). Pionier des Telephons, der Telegraphie und der Lochkarte sowie Erbauer der ersten Wiener Telephonzentrale |language=de, en |author-first=Heinrich "Heinz" Josef |author-last=Zemanek |author-link=Heinrich Josef Zemanek |series=Blätter für Technikgeschichte |volume=41–43 (1979–1981) |issn=0067-9127 |edition=1 |pages=81–118 |publication-place=Vienna, Austria |publisher=[[Technisches Museum für Industrie und Gewerbe]], Forschungsinstitut für Technikgeschichte / [[Springer-Verlag]] |date=1983-12-01 |isbn=3-21181779-4 |oclc=952698275}}</ref> <ref name="Stibitz_1941">{{cite web |title=Binary counter |author-first=George Robert |author-last=Stibitz |author-link=George Robert Stibitz |id={{US patent|2307868}}. Serial No. 420537 |orig-date=1941-11-26<!-- fdate --> |date=1943-01-12<!-- gdate --> |publisher=[[Bell Telephone Laboratories, Incorporated]] |publication-place=New York, USA |url=https://patents.google.com/patent/US2307868?oq=US2307868 |access-date=2020-05-24 |quote-page=2, right column, rows 43–73 |quote=[…] A clearer idea of the position of the balls after each pulse will be obtained if the set of balls is represented by a number having a similar number of digits, each of which may have one of two arbitrary values, for example 0 and 1. If the upper position is called 0 and the lower position […] 1, then the setting of the counter […] may be read from left to right as 0,100,000. […] Following is a translation of the number of pulses received into this form of binary notation for the first sixteen pulses as received on the first five balls […] Pulse number […] Binary notation […]}} [https://web.archive.org/web/20201217181617/https://patentimages.storage.googleapis.com/51/a5/54/f2f6faf23da3fb/US2307868.pdf] (4 pages)</ref> <ref name="Gray_1947">{{cite book |author-first=Frank |author-last=Gray |author-link=Frank Gray (researcher) |title=Pulse Code Communication |date=1953-03-17<!-- gdate --> |orig-date=1947-11-13<!-- fdate --> |publisher=[[Bell Telephone Laboratories, Incorporated]] |location=New York, USA |id={{US patent|2632058}}. Serial No. 785697 |url=https://patentimages.storage.googleapis.com/a3/d7/f2/0343f5f2c0cf50/US2632058.pdf |access-date=2020-08-05 |url-status=live |archive-url=https://web.archive.org/web/20200805094312/https://patentimages.storage.googleapis.com/a3/d7/f2/0343f5f2c0cf50/US2632058.pdf |archive-date=2020-08-05}} (13 pages)</ref> <ref name="Breckman_1953">{{cite book |author-first=Jack |author-last=Breckman |title=Encoding Circuit |date=1956-01-31<!-- gdate --> |orig-date=1953-12-31<!-- fdate --> |publisher=[[US Secretary of the Army]] |location=Long Branch, New Jersey, USA |id={{US patent|2733432}}. Serial No. 401738 |url=https://patentimages.storage.googleapis.com/46/90/d6/2ed9fb7a77e643/US2733432.pdf |access-date=2020-08-05 |url-status=live |archive-url=https://web.archive.org/web/20200805094857/https://patentimages.storage.googleapis.com/46/90/d6/2ed9fb7a77e643/US2733432.pdf |archive-date=2020-08-05}} (8 pages)</ref> <ref name="Ragland-Schultheis_1953">{{cite book |author-first1=Earl Albert |author-last1=Ragland |author-first2=Harry B. |author-last2=Schultheis, Jr. |title=Direction-Sensitive Binary Code Position Control System |date=1958-02-11<!-- gdate --> |orig-date=1953-10-16<!-- fdate --> |publisher=Bendix Aviation Corporation |location=North Hollywood, California, USA |id={{US patent|2823345}}. Serial No. 386524 |url=https://patentimages.storage.googleapis.com/ad/74/b1/2b0aa965d0c1df/US2823345.pdf |access-date=2020-08-05 |url-status=live |archive-url=https://web.archive.org/web/20200805095445/https://patentimages.storage.googleapis.com/ad/74/b1/2b0aa965d0c1df/US2823345.pdf |archive-date=2020-08-05}} (10 pages)</ref> <ref name="Domeshek-Reiner_1954">{{cite book |author-first1=Sol |author-last1=Domeshek |author-first2=Stewart |author-last2=Reiner |title=Automatic Rectification System |date=1958-06-24<!-- gdate --> |orig-date=1954-01-08<!-- fdate --> |publisher=[[US Secretary of the Navy]] |id={{US patent|2839974}}. Serial No. 403085 |url=https://patentimages.storage.googleapis.com/9d/bf/65/e676a661e1217e/US2839974.pdf |access-date=2020-08-05 |url-status=live |archive-url=https://web.archive.org/web/20200805100327/https://patentimages.storage.googleapis.com/9d/bf/65/e676a661e1217e/US2839974.pdf |archive-date=2020-08-05}} (8 pages)</ref> <ref name="Hulst_1957">{{cite book |title=Reflected binary code counter |author-first=George D. |author-last=Hulst |publisher=[[International Telephone and Telegraph Corporation]] (ITT) |location=Nutley, New Jersey, USA |date=1962-02-06<!-- gdate --> |orig-date=1957-11-15<!-- fdate --> |id={{US patent|3020481}}. Serial No. 696793 |url=https://patentimages.storage.googleapis.com/a2/e5/21/f5abbb073bf21c/US3020481.pdf |access-date=2020-08-06 |url-status=live |archive-url=https://web.archive.org/web/20200806210248/https://patentimages.storage.googleapis.com/a2/e5/21/f5abbb073bf21c/US3020481.pdf |archive-date=2020-08-06}} (5 pages)</ref> <ref name="Doran_2007">{{cite book |title=The Gray Code |series=CDMTCS Research Report Series |author-first=Robert "Bob" William |author-last=Doran |author-link=Robert William Doran |publisher=Centre for Discrete Mathematics and Theoretical Computer Science, [[University of Auckland]], New Zealand |date=March 2007 |id=CDMTCS-304 |url=https://www.cs.auckland.ac.nz/research/groups/CDMTCS//researchreports/304bob.pdf |access-date=2020-05-23 |url-status=live |archive-url=https://web.archive.org/web/20200522091749/https://www.cs.auckland.ac.nz/research/groups/CDMTCS//researchreports/304bob.pdf |archive-date=2020-05-22}} (25 pages)</ref> <ref name="Turvey_1956">{{cite web |title=Pulse-Count Coder |author-first=Frank P. |author-last=Turvey, Jr. |id={{US patent|2845617A}}. Serial No. 585494 |date=1958-07-29 |orig-date=1956-05-17 |publisher=[[International Telephone and Telegraph Corporation]] |location=Nutley, New Jersey, USA |url=https://patentimages.storage.googleapis.com/14/07/c6/404dafe27dc829/US2845617.pdf |access-date=2020-05-23 |url-status=live |archive-url=https://web.archive.org/web/20200523115811/https://patentimages.storage.googleapis.com/14/07/c6/404dafe27dc829/US2845617.pdf |archive-date=2020-05-23}} (5 pages)</ref> <ref name="Winder_1959">{{cite journal |title=Shaft Angle Encoders Afford High Accuracy |author-first=C. Farrell |author-last=Winder |journal=[[Electronic Industries (journal)|Electronic Industries]] |publisher=[[Chilton Company]] |volume=18 |number=10 |date=October 1959 |pages=76–80 |url=https://worldradiohistory.com/Archive-Tele-Tech/50s/Electronic-Industries-1959-10.pdf |access-date=2018-01-14 |archive-url=https://web.archive.org/web/20200928132232/https://worldradiohistory.com/Archive-Tele-Tech/50s/Electronic-Industries-1959-10.pdf |archive-date=2020-09-28 |quote-page=78 |quote=[…] The type of code wheel most popular in [[optical encoder]]s contains a cyclic binary code pattern designed to give a cyclic sequence of "on-off" outputs. The cyclic binary code is also known as the cyclic progression code, the reflected binary code, and the Gray code. This code was originated by [[G. R. Stibitz]], of [[Bell Telephone Laboratories]], and was first proposed for [[pulse-code modulation]] systems by [[Frank Gray (researcher)|Frank Gray]], also of BTL. Thus the name Gray code. The Gray or cyclic code is used mainly to eliminate the possibility of errors at code transition which could result in gross ambiguities. […]}}</ref> <ref name="Karnaugh_1953">{{cite journal |author-last=Karnaugh |author-first=Maurice |author-link=Maurice Karnaugh |title=The Map Method for Synthesis of Combinational Logic Circuits |journal=[[Transactions of the American Institute of Electrical Engineers, Part I: Communication and Electronics]] |volume=72 |issue=5 |pages=593–599 |date=November 1953 |orig-date=1953-04-23, 1953-03-17 |id=Paper 53-217 |doi=10.1109/TCE.1953.6371932 |s2cid=51636736 |url=http://philectrosophy.com/documents/The%20Map%20Method%20For%20Synthesis%20of.pdf |access-date=2017-04-16 |archive-url=https://web.archive.org/web/20170416232229/http://philectrosophy.com/documents/The%20Map%20Method%20For%20Synthesis%20of.pdf |archive-date=2017-04-16}} (NB. Also contains a short review by [[Samuel H. Caldwell]].)</ref> <ref name="Wakerly_1994">{{cite book |title=Digital Design: Principles & Practices |author-last=Wakerly |author-first=John F. |date=1994 |publisher=[[Prentice Hall]] |location=New Jersey, USA |isbn=0-13-211459-3 |pages=48–49, 222}} (NB. The two page sections taken together say that [[K-map]]s are labeled with Gray code. The first section says that they are labeled with a code that changes only one bit between entries and the second section says that such a code is called Gray code.)</ref> <ref name="Brown_2012">{{cite book |title=Boolean Reasoning – The Logic of Boolean Equations |chapter=3.9.2 Maps |author-first=Frank Markham |author-last=Brown |edition=<!-- 2012 -->reissue of 2nd |publisher=[[Dover Publications, Inc.]] |location=Mineola, New York, USA |date=2012 |orig-date=2003, 1990 |isbn=978-0-486-42785-0 |page=49 |quote-page=49 |quote=[…] Karnaugh's map orders the arguments of the discriminants according to the reflected binary code, also called the Gray code. […]}} (xii+291+3 pages) [https://web.archive.org/web/20170416231752/http://www2.fiit.stuba.sk/~kvasnicka/Free%20books/Brown_Boolean%20Reasoning.pdf 1st edition]</ref> <ref name="Händler_1958">{{cite book |title=Ein Minimisierungsverfahren zur Synthese von Schaltkreisen (Minimisierungsgraphen) |language=de |author-first=Wolfgang |author-last=Händler |author-link=Wolfgang Händler |publisher=[[Technische Hochschule Darmstadt]] |location=Potsdam, Germany |date=1958 |id=D 17 |type=Dissertation |url=https://books.google.com/books?id=D58TAQAAIAAJ}} (73 pages+app.) [https://www.tib.eu/de/suchen/id/TIBKAT%3A044782241/Ein-Minimisierungsverfahren-zur-Synthese-von-Schaltkreisen/]</ref> <ref name="Steinbuch-Wagner_1967">{{cite book |title=Taschenbuch der Nachrichtenverarbeitung |language=de |editor-first1=Karl W. |editor-last1=Steinbuch |editor-link1=Karl W. Steinbuch |editor-first2=Siegfried W. |editor-last2=Wagner |author-first1=Erich R. |author-last1=Berger |author-first2=Wolfgang |author-last2=Händler |author-link2=Wolfgang Händler |date=1967 |orig-date=1962 |edition=2 |publisher=[[Springer-Verlag OHG]] |location=Berlin, Germany |id=Title No. 1036 |lccn=67-21079 |pages=64, 1034–1035, 1036, 1038 |quote-page=64 |quote=[…] Übersichtlich ist die Darstellung nach ''[[Wolfgang Händler|Händler]]'', die sämtliche Punkte, numeriert nach dem ''Gray-Code'' […], auf dem Umfeld eines Kreises anordnet. Sie erfordert allerdings sehr viel Platz. […] |trans-quote=''Händler's'' diagram, where all points, numbered according to the ''Gray code'', are arranged on the circumference of a circle, is easily comprehensible. It needs, however, a lot of space.}}</ref> <ref name="ISER_1">{{cite web |title=Informatik Sammlung Erlangen (ISER) |date=2012-03-13 |publisher=[[Friedrich-Alexander Universität]] |location=Erlangen, Germany |language=de |url=https://www.rrze.fau.de/wir-ueber-uns/kooperationen/iser.shtml |access-date=2017-04-12 |archive-url=https://web.archive.org/web/20170516154655/https://www.rrze.fau.de/wir-ueber-uns/kooperationen/iser.shtml |archive-date=2017-05-16}}</ref> <ref name="ISER_2">{{cite web |title=Informatik Sammlung Erlangen (ISER) – Impressum |date=2012-03-13 |publisher=[[Friedrich-Alexander Universität]] |location=Erlangen, Germany |language=de |url=http://www.iser.uni-erlangen.de:80/index.php?ort_id=327&tree=0 |access-date=2017-04-15 |url-status=live |archive-url=https://web.archive.org/web/20120226004316/http://www.iser.uni-erlangen.de/index.php?ort_id=327&tree=0 |archive-date=2012-02-26}}</ref> <ref name="Kautz_1958">{{cite journal |author-last=Kautz |author-first=William H. |author-link=William H. Kautz |title=Unit-Distance Error-Checking Codes |journal=[[IRE Transactions on Electronic Computers]] |issn=0367-9950 |volume=EC-7 |issue=2 |date=June 1958 |doi=10.1109/TEC.1958.5222529 |s2cid=26649532 |pages=179–180}} (2 pages)</ref> <ref name="Richards_1971">{{cite book |author-first=Richard Kohler |author-last=Richards |title=Digital Design |chapter=Snake-in-the-Box Codes |publisher=[[Wiley-Interscience]], [[John Wiley & Sons, Inc.]] |location=Ames, Iowa, USA |publication-place=New York, USA |date=January 1971 |isbn=0-471-71945-5 |lccn=73-147235 |pages=206–207}} (12+577+1 pages)</ref> <ref name="Sellers-Hsiao-Bearnson_1968">{{cite book |author-first1=Frederick F. |author-last1=Sellers, Jr.<!-- to be sync'ed with corresponding citeref --> |author-first2=Mu-Yue |author-last2=Hsiao |author-first3=Leroy W. |author-last3=Bearnson |title=Error Detecting Logic for Digital Computers |publisher=[[McGraw-Hill Book Company]] |location=New York, USA |edition=1st |oclc=439460 |lccn=68-16491 |pages=152–164 |date=November 1968}}</ref> <ref name="Lucal_1959">{{cite journal |author-first=Harold M. |author-last=Lucal |title=Arithmetic Operations for Digital Computers Using a Modified Reflected Binary |journal=[[IRE Transactions on Electronic Computers]] |volume=EC-8 |number=4 |pages=449–458 |date=December 1959 |issn=0367-9950 |doi=10.1109/TEC.1959.5222057 |s2cid=206673385 |url=https://ieeexplore.ieee.org/document/5222057}} (10 pages)</ref> <ref name="Spaulding_1954">{{cite web |title=Digital coding and translating system |author-first=Carl P. |author-last=Spaulding |publisher=Datex Corporation |location=Monrovia, California, USA |year=1965a<!-- necessary for proper citeref linking --> |date=1965-01-12<!-- gdate --> |orig-date=1954-03-09<!-- fdate --> |id={{US patent|3165731A}}. Serial No. 415058 |url=https://patentimages.storage.googleapis.com/7f/1d/09/6a9b1fa3e67cb8/US3165731.pdf |access-date=2018-01-21 |url-status=live |archive-url=https://web.archive.org/web/20200805101618/https://patentimages.storage.googleapis.com/7f/1d/09/6a9b1fa3e67cb8/US3165731.pdf |archive-date=2020-08-05}} (28 pages)</ref> <ref name="Spaulding_1965">{{cite book |title=How to Use Shaft Encoders |author-first=Carl P. |author-last=Spaulding |year=1965b<!-- necessary for proper citeref linking --> |date=1965-07-12 |publisher=Datex Corporation<!-- Datex Div, of Conrac Corp. / a subsidiary of Giannini Control Corp. --> |location=Monrovia, California, USA}} (85 pages)</ref> <ref name="Foss_1954_1">{{cite web |title=Control Systems |author-first=Frederic A. |author-last=Foss |date=1960-12-27<!-- gdate --> |orig-date=1954-12-17<!-- fdate --> |id={{US patent|2966670A}}. Serial No. 475945 |publisher=[[International Business Machines Corp]] |pages=Fig. 7, Fig. 8, Fig. 11 |no-pp=yes |url=https://patentimages.storage.googleapis.com/3d/a8/16/1dc616c432ca95/US2966670.pdf |access-date=2020-08-05 |url-status=live |archive-url=https://web.archive.org/web/20200621145238/https://patentimages.storage.googleapis.com/3d/a8/16/1dc616c432ca95/US2966670.pdf |archive-date=2020-06-21}} (14 pages) (NB. The author called his code 2*-4-2-1 (+9-±7-±3-±1) reflected<!-- -coded --> decimal code.)</ref> <ref name="Foss_1954_2">{{cite journal |title=The Use of a Reflected Code in Digital Control Systems |author-first=Frederic A. |author-last=Foss |date=December 1954 |journal=[[IRE Transactions on Electronic Computers]] |volume=EC-3 |issue=4 |issn=2168-1740 |doi=10.1109/IREPGELC.1954.6499244 |pages=1–6}} (6 pages)</ref> <ref name="O'Brien_1955">{{cite journal |author-first=Joseph A. |author-last=O'Brien |title=Cyclic Decimal Codes for Analogue to Digital Converters |journal=[[Transactions of the American Institute of Electrical Engineers, Part I: Communication and Electronics]] |location=Bell Telephone Laboratories, Whippany, New Jersey, USA |volume=75 |issue=2 |date=May 1956 |orig-date=1955-11-15, 1955-06-23 |issn=0097-2452 |doi=10.1109/TCE.1956.6372498 |id=Paper 56-21 |s2cid=51657314 |pages=120–122 |url=https://pdfslide.net/documents/cyclic-decimal-codes-for-analogue-to-digital-converters.html |access-date=2020-05-18 |archive-date=2020-05-18 |archive-url=https://web.archive.org/web/20200518075301/https://pdfslide.net/documents/cyclic-decimal-codes-for-analogue-to-digital-converters.html |url-status=dead }} (3 pages) (NB. This paper was prepared for presentation at the AIEE Winter General Meeting, New York, USA, 1956-01-30 to 1956-02-03.)</ref> <ref name="Tompkins_1956">{{cite journal |author-first=Howard E. |author-last=Tompkins |title=Unit-Distance Binary-Decimal Codes for Two-Track Commutation |date=September 1956 |orig-date=1956-07-16 |journal=[[IRE Transactions on Electronic Computers]] |issn=0367-9950 |volume=EC-5 |issue=3 |doi=10.1109/TEC.1956.5219934 |series=Correspondence |location=[[Moore School of Electrical Engineering]], [[University of Pennsylvania]], Philadelphia, Pennsylvania, USA |page=139 |url=https://dokumen.tips/documents/unit-distance-binary-decimal-codes-for-two-track-commutation.html |access-date=2020-05-18 |archive-date=2020-05-18 |archive-url=https://web.archive.org/web/20200518083051/https://dokumen.tips/documents/unit-distance-binary-decimal-codes-for-two-track-commutation.html |url-status=dead }} (1 page)</ref> <ref name="Glixon_1957">{{cite journal |date=March 1957 |title=Can You Take Advantage of the Cyclic Binary-Decimal Code? |author-first=Harry Robert |author-last=Glixon |journal=[[Control Engineering (magazine)|Control Engineering]] |issn=0010-8049 |publisher=[[Technical Publishing Company]], a division of Dun-Donnelley Publishing Corporation, [[Dun & Bradstreet Corp.]] |volume=4 |number=3 |pages=<!-- 3, -->87–91 |url=https://books.google.com/books?id=-_5IAQAAIAAJ}}<!-- https://web.archive.org/web/20180115014809/https://donmooreswartales.com/2010/05/12/harry-glixon/ https://books.google.com/books?id=-_5IAQAAIAAJ&q=cyclic+binary+code --> (5 pages)</ref> <ref name="Steinbuch_1962">{{cite book |title=Taschenbuch der Nachrichtenverarbeitung |language=de |editor-first=Karl W. |editor-last=Steinbuch |editor-link=Karl W. Steinbuch |date=1962 |edition=1 |publisher=[[Springer-Verlag OHG]] |location=Karlsruhe, Germany |publication-place=Berlin / Göttingen / New York |lccn=62-14511 |pages=71–74, 97, 761–764, 770, 1080–1081}}</ref> <ref name="Steinbuch-Weber-Heinemann_1974">{{cite book |title=Taschenbuch der Informatik – Band II – Struktur und Programmierung von EDV-Systemen |language=de |editor-first1=Karl W. |editor-last1=Steinbuch |editor-link1=Karl W. Steinbuch |editor-first2=Wolfgang |editor-last2=Weber <!-- |editor-link2=:de:Wolfgang Weber (Ingenieur)? --> |editor-first3=Traute |editor-last3=Heinemann |date=1974 |orig-date=1967 |edition=3 |volume=2 |series=Taschenbuch der Nachrichtenverarbeitung |publisher=[[Springer Verlag]] |location=Berlin, Germany |isbn=3-540-06241-6 |lccn=73-80607 |pages=98–100}}</ref> <ref name="Dokter-Steinhauer_1973">{{cite book |title=Digital Electronics |author-first1=Folkert |author-last1=Dokter |author-first2=Jürgen |author-last2=Steinhauer |chapter=2.4. Coding numbers in the binary system |date=1973-06-18 |series=Philips Technical Library (PTL) / Macmillan Education |publisher=[[The Macmillan Press Ltd.]] / [[N. V. Philips' Gloeilampenfabrieken]] |edition=Reprint of 1st English |location=Eindhoven, Netherlands |sbn=333-13360-9 |isbn=978-1-349-01419-4 |doi=10.1007/978-1-349-01417-0 |pages=32, 39, 50–53 |url=https://books.google.com/books?id=hlRdDwAAQBAJ |access-date=2020-05-11 |quote-page=53 |quote=[…] The [[#Datex|Datex code]] […] uses the [[#O'Brien II|O'Brien code II]] within each decade, and reflected decimal numbers for the decimal transitions. For further processing, code conversion to the natural decimal notation is necessary. Since the O'Brien II code forms a [[9s complement]], this does not give rise to particular difficulties: whenever the code word for the tens represents an odd number, the code words for the decimal units are given as the 9s complements by inversion of the fourth binary digit. […] }}{{Dead link|date=July 2023 |bot=InternetArchiveBot |fix-attempted=yes }} (270 pages)</ref> <ref name="Dokter-Steinhauer_1975">{{cite book |author-first1=Folkert |author-last1=Dokter |author-first2=Jürgen |author-last2=Steinhauer |title=Digitale Elektronik in der Meßtechnik und Datenverarbeitung: Theoretische Grundlagen und Schaltungstechnik |chapter=2.4.4.6. Einschrittige Kodes |language=de |series=Philips Fachbücher |publisher=[[Deutsche Philips GmbH]] |publication-place=Hamburg, Germany |volume=I |date=1975 |orig-date=1969 |edition=improved and extended 5th |isbn=3-87145-272-6 |pages=41, 48, 51, 58, 60–61}} (xii+327+3 pages)</ref> <ref name="Petherick_1953">{{cite book |author-first=Edward John |author-last=Petherick |title=A Cyclic Progressive Binary-coded-decimal System of Representing Numbers |date=October 1953 |type=Technical Note MS15 |publisher=[[Royal Aircraft Establishment]] (RAE) |location=Farnborough, UK}} (4 pages) (NB. Sometimes referred to as ''A Cyclic-Coded Binary-Coded-Decimal System of Representing Numbers''.)</ref> <ref name="Petherick-Hopkins_1958">{{cite book |author-first1=Edward John |author-last1=Petherick |author-first2=A. J. |author-last2=Hopkins |title=Some Recently Developed Digital Devices for Encoding the Rotations of Shafts |date=1958 |type=Technical Note MS21 |publisher=[[Royal Aircraft Establishment]] (RAE) |location=Farnborough, UK}}</ref> <ref name="Baumgartner_1963">{{cite periodical |title=Digitizer als Analog-Digital-Wandler in der Steuer-, Meß- und Regeltechnik |periodical=Technische Mitteilungen |series=Relais, elektronische Geräte, Steuerungen |language=de |date=May 1963 |issue=13 |publisher=Franz Baumgartner (FraBa) |location=Cologne-Niehl, Germany |pages=1–2 |url=https://www.posital.com/media/posital_media/documents/TechnischeMitteilung_May1963.pdf |access-date=2020-05-21 |archive-url=https://web.archive.org/web/20200521211656/https://www.posital.com/media/posital_media/documents/TechnischeMitteilung_May1963.pdf |archive-date=2020-05-21 |quote-pages=1–2 |quote=[…] Die Firma Harrison Reproduction Equipment, Farnborough/England […] hat in jahrelanger Entwicklung in Zusammenarbeit mit der Britischen Luftwaffe und britischen Industriebetrieben den mechanischen Digitizer […] zu einer technischen Reife gebracht, die fast allen Anforderungen […] genügt. […] Um bei der dezimalen Entschlüsselung des verwendeten Binärcodes zu eindeutigen und bei der Übergabe von einer Dezimalstelle zur anderen in der Reihenfolge immer richtigen Ergebnissen zu kommen, wurde ein spezieller Code entwickelt, der jede Möglichkeit einer Fehlaussage durch sein Prinzip ausschließt und der außerdem durch seinen Aufbau eine relativ einfache Entschlüsselung erlaubt. Der Code basiert auf dem [[#Petherick|Petherick-Code]]. […]}} (4 pages)</ref> <ref name="Charnley-Bidgood-Boardman_1965">{{cite journal |title=The Design of a Pneumatic Position Encoder |author-first1=C. J. |author-last1=Charnley |author-first2=R. E. |author-last2=Bidgood |author-first3=G. E. T. |author-last3=Boardman |journal=IFAC Proceedings Volumes |publisher=The College of Aeronautics, Cranfield, Bedford, England |volume=2 |issue=3 |date=October 1965 |pages=75–88 |id=Chapter 1.5. |doi=10.1016/S1474-6670(17)68955-9 |url=https://ac.els-cdn.com/S1474667017689559/1-s2.0-S1474667017689559-main.pdf?_tid=f0c1e48e-f95b-11e7-ad9a-00000aab0f01&acdnat=1515956073_9006e89e176c6a840b5454c38525240b |access-date=2018-01-14 }}{{Dead link|date=October 2023 |bot=InternetArchiveBot |fix-attempted=yes }}</ref> <ref name="Wheeler_1969">{{cite book |title=Analog to digital encoder |author-first=Edwin L. |author-last=Wheeler |publisher=Conrac Corporation |location=New York, USA |date=1969-12-30<!-- gdate --> |orig-date=1968-04-05<!-- fdate --> |id={{US patent|3487460A}}. Serial No. 719026 (397812<!-- 1964-09-21 -->) |url=https://patentimages.storage.googleapis.com/f0/c0/60/9c3231f7e8ed44/US3487460.pdf |access-date=2018-01-21 |url-status=live |archive-url=https://web.archive.org/web/20200805102804/https://patentimages.storage.googleapis.com/f0/c0/60/9c3231f7e8ed44/US3487460.pdf |archive-date=2020-08-05 |quote-page=5<!-- of text, p. 8 in total -->, left column 9, rows 15–22 |quote=[…] The [[MOA-Gillham code|MOA-GILLHAM code]] is essentially the combination of the Gray code discussed thereinabove and the well known [[#Datex|Datex code]]; the Datex code is disclosed in U.S. Patent {{citeref|Spaulding|1965a|3,165,731|style=plain}}. The arrangement is such that the Datex code defines the bits for the units count of the encoder and the Gray code defines the bits for each of the higher order decades, the tens, hundreds, etc. […]}} (11 pages)</ref> <ref name="Bishup-Repeta-Giarrizzo_1963">{{cite web |title=Telemetering and supervisory control system having normally continuous telemetering signals |id=US3397386A |author-first1=Bernard W. |author-last1=Bishup |author-first2=Anthony A. |author-last2=Repeta |author-first3=Frank C. |author-last3=Giarrizzo |publisher=[[Leeds & Northrup|Leeds and Northrup Co.]] |date=1968-08-13 |orig-date=1963-04-03 |url=https://patents.google.com/patent/US3397386A/en}} [https://patentimages.storage.googleapis.com/c8/f3/cc/936fef75655a2c/US3397386.pdf]</ref> <ref name="Savage_1997">{{cite journal |author-first=Carla Diane |author-last=Savage |author-link=Carla Diane Savage |title=Long cycles in the middle two levels of the Boolean lattice |journal=[[Ars Combinatoria (journal)|Ars Combinatoria]] |issn=0381-7032 |volume=35 |issue=A |date=1997-01-16 |location=North Carolina State University, Raleigh, North Carolina, USA |s2cid=15975960 |citeseerx=10.1.1.39.2249 |pages=97–108 |url=http://citeseerx.ist.psu.edu/viewdoc/download;jsessionid=DACA73A3D791549CE05443B7948527EC?doi=10.1.1.39.2249&rep=rep1&type=pdf |access-date=2020-05-13 |url-status=live |archive-url=https://web.archive.org/web/20200513191647/http://citeseerx.ist.psu.edu/viewdoc/download;jsessionid=DACA73A3D791549CE05443B7948527EC?doi=10.1.1.39.2249&rep=rep1&type=pdf |archive-date=2020-05-13}} (15 pages)</ref> <ref name="Phillips_1998">{{cite web |title=Altitude – MODEC ASCII |author-first=Darryl |author-last=Phillips |date=2012-07-26 |orig-date=1998 |publisher=AirSport Avionics |url=http://www.airsport-corp.com/modecascii.txt |url-status=usurped |archive-url=https://web.archive.org/web/20120726003224/http://www.airsport-corp.com/modecascii.txt |archive-date=2012-07-26}}</ref> <ref name="Stewart_2010">{{cite web |title=Aviation Gray Code: Gillham Code Explained |date=2010-12-03 |author-first=K. |author-last=Stewart |publisher=Custom Computer Services (CCS) |url=http://www.ccsinfo.com/forum/viewtopic.php?p=140960#140960 |access-date=2018-01-14 |url-status=live |archive-url=https://web.archive.org/web/20180116184525/http://www.ccsinfo.com/forum/viewtopic.php?p=140960 |archive-date=2018-01-16}}</ref> <ref name="Leslie-Russell_1964">{{cite book |title=A cyclic progressive decimal code for simple translation to decimal and analogue outputs |author-first1=William "Bill" H. P. |author-last1=Leslie |author-first2=A. |author-last2=Russell |publisher=[[National Engineering Laboratory]] |location=East Kilbride, Glasgow, UK |date=1964 |type=Report |id=NEL Report 129}} (17 pages)</ref> <ref name="Russell_1964">{{cite journal |title=Some Binary Codes and a Novel Five-Channel Code |author-first=A. |author-last=Russell |date=August 1964 |journal=Control (Systems, Instrumentation, Data Processing, Automation, Management, incorporating Automation Progress)<!-- "Control" (London) is a predecessor of "Control and Instrumentation" (C&I), ISSN 0010-8022, formed in April 1969 by merger with "Measurement and Instrument Review" (M&I). --> |volume=8 |number=74 |series=Special Features |publisher=Morgan-Grampain (Publishers) Limited |publication-place=London, UK |pages=399–404 |url=https://books.google.com/books?id=jf4eAAAAMAAJ |access-date=2020-06-22}} (6 pages)</ref> <ref name="Leslie_1974">{{cite book |title=Proceedings of the Fourteenth International Machine Tool Design and Research Conference, 12–14 September 1973 |chapter=The work on NC at NEL |author-first=William "Bill" H. P. |author-last=Leslie |editor-first1=Franz |editor-last1=Koenigsberger |editor-first2=Stephen Albert |editor-last2=Tobias |publisher=[[The Macmillan Press Ltd]] |date=1974 |sbn=333-14913-0 |isbn=978-1-34901921-2 |lccn=73-16545 |pages=215–224 [215, 217] |doi=10.1007/978-1-349-01921-2_30 |url=https://books.google.com/books?id=bFVdDwAAQBAJ&pg=PA215 |chapter-url=https://link.springer.com/chapter/10.1007/978-1-349-01921-2_30 |access-date=2020-05-21 |archive-date=2022-04-07 |archive-url=https://web.archive.org/web/20220407160744/https://books.google.com/books?id=bFVdDwAAQBAJ&pg=PA215 |url-status=dead }}</ref> <ref name="Wightman_1972">{{cite book |author-first=Eric Jeffrey |author-last=Wightman |title=Instrumentation in Process Control |date=1972 |edition=1 |publisher=[[Butterworth & Co (Publishers) Ltd]] |publication-place=London, UK |isbn=0-408-70293-1 |chapter=Chapter 6. Displacement measurement |pages=122–123 |chapter-url=https://books.google.com/books?id=8WEhBQAAQBAJ&pg=PA122 |url=https://books.google.com/books?id=8WEhBQAAQBAJ |quote-page=122–123 |quote=[…] Other forms of code are also well known. Among these are the [[Royal Radar Establishment]] code; The [[Excess Three decimal code]]; [[Gillham code]] which is recommended by [[ICAO]] for automatic height transmission for [[air traffic control]] purposes; the [[Petherick code]], and the [[Leslie and Russell code]] of the [[National Engineering Laboratory]]. Each has its particular merits and they are offered as options by various encoder manufacturers. […]}} (12+367+5 pages)</ref> <ref name="Varec_1954">{{cite journal |title=…accurate liquid level metering – at ANY DISTANCE! |journal=Petroleum Refiner |volume=33 |number=9 |issn=0096-6517 |publisher=[[Gulf Publishing Company]] |date=September 1954 |type=Advertisement |page=368 |quote-page=368 |quote=[…] The complete dispatching operation, gauging, and remote control is integrated into one single unitized system when a "Varec" Pulse Code Telemetering System is installed. […] |url=https://books.google.com/books?id=B2Q7AAAAMAAJ&q=%22Varec+pulse+code%22}}</ref> <ref name="Whessoe_1993">{{cite book |title=Installation and Operations Manual for the Model 1900 Micro 4-Wire Transmitter |chapter=Encoder Pulse Format |publisher=[[Whessoe Varec, Inc.]] |location=Cypress, California, USA |id=33-08461 |date=January 1993 |orig-date=1991-07-01 |pages=04-4–04-8 |url=https://www.varec.com/web/wp-content/uploads/2018/05/IOM016_1900.pdf |access-date=2020-05-16 |url-status=live |archive-url=https://web.archive.org/web/20200516191438/https://www.varec.com/web/wp-content/uploads/2018/05/IOM016_1900.pdf |archive-date=2020-05-16}} (38 pages) (NB. Position 5 for "Inches" on page 04-8 should read "0111" rather than "1111".)</ref> <ref name="Emerson">{{cite book |title=Varec Model 1900 – Micro 4-Wire Transmitter (BSAP to Mark / Space Protocol (MSP)) – Application Notes |chapter=2.2.3.3 MSP Level Data Format |publisher=[[Emerson Electric]] |pages=11–14 |url=https://www.emerson.com/documents/automation/manuals-guides-application-notes-varec-model-1900-protocol-ras-en-133360.pdf |access-date=2020-05-16 |url-status=live |archive-url=https://web.archive.org/web/20200516183338/https://www.emerson.com/documents/automation/manuals-guides-application-notes-varec-model-1900-protocol-ras-en-133360.pdf |archive-date=2020-05-16}} (vi+33 pages)</ref> <ref name="Hoklas_1989">{{cite web |title=Abtastvorrichtung zur digitalen Weg- oder Winkelmessung |language=de |author-first=Archibald |author-last=Hoklas |publisher={{ill|VEB Schiffselektronik Johannes Warnke|de}} |via={{ill|DEPATIS|de}} |date=1989-09-06<!-- published --> |orig-date=1988-04-29<!-- filed --> |id=GDR Patent DD271603A1. WP H 03 M / 315 194 8 |url=https://depatisnet.dpma.de/DepatisNet/depatisnet/DD000000271603A1_all_pages.pdf?window=1&space=menu&content=download_doc_verify&action=download_doc&docid=DD000000271603A1&so=asc&sf=vn&firstdoc=0&struct=&Cl=2&Bi=1&Ab=1&De=2&Dr=5&Pts=&Pa=&We=&Sr=&Eam=&Cor=&Aa=&NrFaxPages=5&pdfpage=2&pdfmatrix=1x1&origin=pdf_window&verify_str=null<!-- https://depatisnet.dpma.de/DepatisNet/depatisnet/DD000000271603A1_all_pages.pdf?docid=DD000000271603A1 --> |access-date=2018-01-18 |archive-url=https://web.archive.org/web/20180118015239/https://depatisnet.dpma.de/DepatisNet/depatisnet/DD000000271603A1_all_pages.pdf?window=1&space=menu&content=download_doc_verify&action=download_doc&docid=DD000000271603A1&so=asc&sf=vn&firstdoc=0&struct=&Cl=2&Bi=1&Ab=1&De=2&Dr=5&Pts=&Pa=&We=&Sr=&Eam=&Cor=&Aa=&NrFaxPages=5&pdfpage=2&pdfmatrix=1x1&origin=pdf_window&verify_str=null |archive-date=2018-01-18}} [https://depatisnet.dpma.de/DepatisNet/depatisnet?action=bibdat&docid=DD000000271603A1] [https://depatisnet.dpma.de/DepatisNet/depatisnet?action=pdf&docid=DD000000271603A1]</ref> <ref name="Hoklas_2005_1">{{cite web |title=Gray code – Unit distance code |author-first=Archibald |author-last=Hoklas |date=2005 |url=http://www.ahok.de/en/hoklas-code.html |access-date=2018-01-15 |url-status=live |archive-url=https://web.archive.org/web/20180115012854/http://www.ahok.de/en/hoklas-code.html |archive-date=2018-01-15}}</ref> <ref name="Hoklas_2005_2">{{cite web |title=Gray-Kode – Einschrittiger Abtastkode |language=de |author-first=Archibald |author-last=Hoklas |date=2005 |url=http://www.ahok.de/dt/hoklas-code.html |access-date=2018-01-15 |url-status=live |archive-url=https://web.archive.org/web/20180115012827/http://www.ahok.de/dt/hoklas-code.html |archive-date=2018-01-15}}</ref> <ref name="Klinkowski_1964">{{cite web |title=Electronic Diode Matrix Decoder Circuits |author-first=James J. |author-last=Klinkowski |id={{US patent|3309695A}}. Serial No. 353845 |publisher=[[Burroughs Corporation]] |location=Detroit, Michigan, USA |date=1967-03-14 |orig-date=1964-03-23 |url=https://patentimages.storage.googleapis.com/71/6a/f4/044b43b93097e7/US3309695.pdf |access-date=2020-05-23 |url-status=live |archive-url=https://web.archive.org/web/20200523144819/https://patentimages.storage.googleapis.com/71/6a/f4/044b43b93097e7/US3309695.pdf |archive-date=2020-05-23}} (5 pages) [https://web.archive.org/web/20200805103732/https://patentimages.storage.googleapis.com/97/33/74/aec52610026e59/USRE26780.pdf<!-- https://patentimages.storage.googleapis.com/97/33/74/aec52610026e59/USRE26780.pdf -->]</ref> <ref name="Klinkowski_1966">{{cite web |title=Binary-coded decimal signal converter |author-first=James J. |author-last=Klinkowski |id={{US patent|3504363A}}. Serial No. 603926 |publisher=[[Burroughs Corporation]] |location=Detroit, Michigan, USA |date=1970-03-31 |orig-date=1966-12-22 |url=https://patentimages.storage.googleapis.com/65/d6/45/f7837c143fa3da/US3504363.pdf |access-date=2020-05-23 |url-status=live |archive-url=https://web.archive.org/web/20200523145655/https://patentimages.storage.googleapis.com/65/d6/45/f7837c143fa3da/US3504363.pdf |archive-date=2020-05-23}} (7 pages)</ref> <ref name="EDN_1967">{{cite journal |title=(([title unknown])) |journal=[[Electrical Design News]] |issn=0012-7515 |publisher=[[Rogers Publishing Company]] |date=1967 |volume=12 |pages=<!-- 44, 448? -->}} [https://books.google.com/books?id=MThAAQAAIAAJ&q=%22Watts+code%22+%22Excess-3+Gray+Code%22][https://books.google.com/books?id=MThAAQAAIAAJ&q=%22Watts+code%22+%22Excess-3+Gray+Code%22]</ref> <ref name="Toth-Zentai_1979">{{cite journal |title=Some Problems Of Angular Rotational Digital Converters |author-first=Györgyi |author-last=Tóth-Zentai |volume=23 |number=3–4 |journal=Periodica Polytechnica Electrical Engineering |date=1979-10-05 |pages=265–270 [266] |location=Department of Electronics Technology, Technical University, Budapest, Hungary |url=https://pp.bme.hu/ee/article/view/4838 |access-date=2020-05-23}} [https://pp.bme.hu/ee/article/download/4838/3943/] (6 pages) (NB. Shows a 6-digit Watts code.<!-- also mentions a scheme named V-logic -->)</ref> <ref name="Knuth_2014">{{cite book |author-last=Knuth |author-first=Donald Ervin |author-link=Donald Ervin Knuth |chapter=Enumeration and Backtracking / Generating all ''n''-tuples |title=The Art of Computer Programming, Volume 4A: Combinatorial Algorithms, Part 1 |volume=4A |edition=1 |title-link=The Art of Computer Programming |date=2014-09-12 |publisher=[[Addison-Wesley Professional]] |isbn=978-0-13348885-2 |pages=442–443<!-- list of pages incomplete --> |chapter-url=https://books.google.com/books?id=IkuEBAAAQBAJ}} (912 pages)</ref> <ref name="Heath_1961">{{cite journal |title=Pioneers Of Binary Coding |author-first=F.<!-- Fred? --> G. |author-last=Heath |journal=[[Journal of the Institution of Electrical Engineers]] |publisher=[[Institution of Engineering and Technology]] (IET) |location=[[Manchester College of Science and Technology]], Faculty of Technology of the [[University of Manchester]], Manchester, UK |volume=7 |issue=81 |date=September 1961 |doi=10.1049/jiee-3.1961.0300 |pages=539–541 |url=https://ieeexplore.ieee.org/document/5324416 |archive-url=https://web.archive.org/web/20200328084237/https://ieeexplore.ieee.org/document/5324416/ |url-status=dead |archive-date=28 March 2020 |access-date=2020-06-22}} (3 pages)</ref> <ref name="Cattermole_1969">{{cite book |author-first=Kenneth W. |author-last=Cattermole |title=Principles of pulse code modulation |edition=1 |publisher=[[Iliffe Books Ltd.]] / [[American Elsevier Publishing Company, Inc.]] |date=1969 |publication-place=London, UK / New York, USA |location=Harlow, Essex, UK |sbn=444-19747-8 |isbn=978-0-444-19747-4 |lccn=78-80432 |pages=245, 434 |quote-page=245 |quote=[…] <!-- This was devised by Elisha Gray at some time before 1878, for telegraph usage; in recent times it has been used in electron-beam coding tubes […], and is generally applicable to parallel coders in which all the digits are produced simultaneously. […] -->There seems to be some confusion about the attributation of this code, because two inventors named Gray have been associated with it. When I first heard the name I took it as referring to [[Elisha Gray]], and {{citeref|Heath|1961|Heath|style=plain}} testifies to his usage of it. Many people take it as referring to [[Frank Gray (researcher)|Frank Gray]] of [[Bell Telephone Laboratories]], who in 1947 first proposed its use in [[coding tube]]s: his patent is listed in the bibliography. <!-- This is a particular interesting example of [[multiple invention]]. Two British engineers, C. W. Earp and M. F. Wintle, rediscovered it independently within a few month of F. Gray, some seventy years after E. Gray. -->[…]}} (2+448+2 pages)<!-- (NB. At least Charles William Earp's and Malcolm Frank Wintle's patent US2568724 describes a different code used for PCM.) --></ref> <ref name="Edwards_2004">{{cite book |title=Cogwheels of the Mind: The Story of Venn Diagrams |author-first=Anthony William Fairbank |author-last=Edwards |author-link=Anthony William Fairbank Edwards |publisher=[[Johns Hopkins University Press]] |date=2004 |isbn=0-8018-7434-3 |location=Baltimore, Maryland, USA |pages=48, 50 |url=https://books.google.com/books?id=7_0Thy4V3JIC&pg=PA65}}</ref> <ref name="Goodall_1951">{{cite journal |author-first=William M. |author-last=Goodall |title=Television by Pulse Code Modulation |journal=[[Bell System Technical Journal]] |volume=30 |issue=1 |pages=33–49 |date=January 1951 |doi=10.1002/j.1538-7305.1951.tb01365.x}} (NB. Presented orally before the I.R.E. National Convention, New York City, March 1949.)</ref> <ref name="Bhat-Savage_1996">{{cite journal |author-first1=Girish S. |author-last1=Bhat |author-first2=Carla Diane |author-last2=Savage |author-link2=Carla Diane Savage |title=Balanced Gray Codes |journal=[[Electronic Journal of Combinatorics]] |date=1996 |volume=3 |url=https://www.combinatorics.org/ojs/index.php/eljc/article/view/v3i1r25/ |issue=1 |doi=10.37236/1249 |doi-access=free}}</ref> <ref name="Donohue_2003">{{cite web |author-first=Ryan |author-last=Donohue |title=Synchronization in Digital Logic Circuits |date=2003 |url=http://www.stanford.edu/class/ee183/handouts_spr2003/synchronization_pres.pdf |access-date=2018-01-15 |url-status=live |archive-url=https://web.archive.org/web/20180115012747/https://web.stanford.edu/class/ee183/handouts_spr2003/synchronization_pres.pdf |archive-date=2018-01-15}}</ref> <ref name="Mehta-Owens-Irwin_1996">{{cite book |author-last1=Mehta |author-first1=Huzefa |author-last2=Owens |author-first2=Robert Michael |author-last3=Irwin |author-first3=Mary Jane "Janie" |chapter=Some issues in gray code addressing |title=Proceedings of the Sixth Great Lakes Symposium on VLSI |date=1996-03-22 |issn=1066-1395 |doi=10.1109/GLSV.1996.497616 |chapter-url=https://ieeexplore.ieee.org/document/497616 |publisher=[[IEEE Computer Society]] |isbn=978-0-8186-7502-7 |pages=178–181|s2cid=52837310 }}</ref> <ref name="Su-Tsui-Despain_1994">{{cite report |title=Low Power Architecture Design and Compilation Techniques for High-Performance Processors |author-first1=Ching-Long |author-last1=Su |author-first2=Chi-Ying |author-last2=Tsui |author-first3=Alvin M. |author-last3=Despain |date=1994 |publisher=Advanced Computer Architecture Laboratory |id=ACAL-TR-94-01 |url=http://www.scarpaz.com/2100-papers/Power%20Estimation/su94-low%20power%20architecture%20and%20compilation.pdf |access-date=2020-12-17 |url-status=live |archive-url=https://web.archive.org/web/20200726170626/http://www.scarpaz.com/2100-papers/Power%20Estimation/su94-low%20power%20architecture%20and%20compilation.pdf |archive-date=2020-07-26}}</ref> <ref name="Guo-Parameswaran_2010">{{cite journal |author-first1=Hui |author-last1=Guo |author-first2=Sri |author-last2=Parameswaran |doi=10.1016/j.sysarc.2010.03.003 |volume=56 |issue=4–6 |date=April–June 2010 |title=Shifted Gray encoding to reduce instruction memory address bus switching for low-power embedded systems |journal=Journal of Systems Architecture |pages=180–190}}</ref> <ref name="Dietz_2002">{{cite web |author-first=Henry Gordon "Hank" |author-last=Dietz |title=The Aggregate Magic Algorithms: Gray Code Conversion |work=The Aggregate |publisher=Electrical and Computer Engineering Department, College of Engineering, [[University of Kentucky]] |date=2002 |url=http://aggregate.org/MAGIC/#Gray%20Code%20Conversion |access-date=2020-12-16 |url-status=live |archive-url=https://web.archive.org/web/20201216122620/http://aggregate.org/MAGIC/#Gray%2520Code%2520Conversion |archive-date=2020-12-16}}</ref> <ref name="Guan_1998">{{cite journal |title=Generalized Gray Codes with Applications |author-last=Guan |author-first=Dah-Jyh |journal=Proceedings of the National Scientific Council, Republic of China, Part A |volume=22 |date=1998 |pages=841–848 |citeseerx=10.1.1.119.1344}}</ref> <ref name="Suparta_2005">{{cite journal |author-first=I. Nengah |author-last=Suparta |title=A simple proof for the existence of exponentially balanced Gray codes |journal=[[Electronic Journal of Combinatorics]] |date=2005 |volume=12 |doi-access=free |doi=10.37236/1986}}</ref> <ref name="Flahive-Bose_2007">{{cite journal |author-first1=Mary Elizabeth |author-last1=Flahive |author-link1=Mary Elizabeth Flahive |author-first2=Bella |author-last2=Bose |title=Balancing cyclic ''R''-ary Gray codes |journal=[[Electronic Journal of Combinatorics]] |date=2007 |volume=14 |doi-access=free |doi=10.37236/949}}</ref> <ref name="Strackx-Piessens_2016">{{cite journal |author-first1=Raoul |author-last1=Strackx |author-first2=Frank |author-last2=Piessens |title=Ariadne: A Minimal Approach to State Continuity |journal=Usenix Security |date=2016 |volume=25 |url=https://distrinet.cs.kuleuven.be/software/sce/ariadne.html}}</ref> <ref name="Savage-Winkler_1995">{{cite journal |author-first1=Carla Diane |author-last1=Savage |author-link1=Carla Diane Savage |author-first2=Peter |author-last2=Winkler |author-link2=Peter Winkler |title=Monotone Gray codes and the middle levels problem |journal=[[Journal of Combinatorial Theory]] | series=Series A |date=1995 |volume=70 |issn=0097-3165 |pages=230–248 |issue=2 |doi=10.1016/0097-3165(95)90091-8|doi-access=free}}</ref> <ref name="Goddyn_1999">{{cite web |title=MATH 343 Applied Discrete Math Supplementary Materials |author-last=Goddyn |author-first=Luis |date=1999 |publisher=Department of Mathematics, [[Simon Fraser University]] |url=http://www.math.sfu.ca/~goddyn/Courses/343/supMaterials.pdf |archive-url=https://web.archive.org/web/20150217160033/http://people.math.sfu.ca/~goddyn/Courses/343/supMaterials.pdf |archive-date=2015-02-17}}</ref> <ref name="Sawada-Wong_2007">{{cite journal |author-first1=Joseph "Joe" |author-last1=Sawada |author-first2=Dennis Chi-Him |author-last2=Wong |title=A Fast Algorithm to generate Beckett–Gray codes |journal=Electronic Notes in Discrete Mathematics |volume=29 |pages=571–577 |date=2007 |doi=10.1016/j.endm.2007.07.091}}</ref> <ref name="Spedding_1994_1">{{cite patent |inventor-last=Spedding |inventor-first=Norman Bruce<!-- Industrial Research Limited --> |pubdate=1994-10-28 |title=A position encoder |country=NZ |number=264738}}{{failed verification|date=July 2015}}</ref> <ref name="Spedding_1994_2">{{cite web <!-- descriptive title: -->|title=The following is a copy of the provisional patent filed on behalf of Industrial Research Limited on 1994-10-28 – NZ Patent 264738 |author-first=Norman Bruce |author-last=Spedding |publisher=Industrial Research Limited |date=1994-10-28 |id=NZ Patent 264738 |url=http://www.winzurf.co.nz/Single_Track_Grey_Code_Patent/Single_track_Grey_code_encoder_patent.pdf |access-date=2018-01-14 |url-status=live |archive-url=https://web.archive.org/web/20171029205005/http://www.winzurf.co.nz/Single_Track_Grey_Code_Patent/Single_track_Grey_code_encoder_patent.pdf |archive-date=2017-10-29}}</ref> <ref name="Hiltgen-Paterson-Brandestini_1996">{{cite journal |title=Single-Track Gray Codes |author-last1=Hiltgen |author-first1=Alain P. |author-first2=Kenneth G. |author-last2=Paterson |author-first3=Marco |author-last3=Brandestini |journal=[[IEEE Transactions on Information Theory]] |volume=42 |issue=5 |date=September 1996 |pages=1555–1561 |doi=10.1109/18.532900 |zbl=857.94007 |url=https://ieeexplore.ieee.org/document/532900}}</ref> <ref name="Hiltgen-Paterson_2001">{{cite journal |title=Single-Track Circuit Codes |author-last1=Hiltgen |author-first1=Alain P. |author-first2=Kenneth G. |author-last2=Paterson |journal=[[IEEE Transactions on Information Theory]] |volume=47 |issue=6 |date=September 2001 |pages=2587–2595 |doi=10.1109/18.945274 |citeseerx=10.1.1.10.8218 |url=http://www.hpl.hp.com/techreports/2000/HPL-2000-81.pdf |access-date=2018-01-15 |url-status=live |archive-url=https://web.archive.org/web/20180115013155/http://www.hpl.hp.com/techreports/2000/HPL-2000-81.pdf |archive-date=2018-01-15}}</ref> <ref name="Etzion-Schwartz_1999">{{cite journal |title=The Structure of Single-Track Gray Codes |author-last1=Etzion |author-first1=Tuvi |author-first2=Moshe |author-last2=Schwartz |journal=[[IEEE Transactions on Information Theory]] |volume=IT-45 |issue=7 |date=November 1999 |orig-date=1998-05-17 |pages=2383–2396 |doi=10.1109/18.796379 |citeseerx=10.1.1.14.8333 |url=http://etzion.net.technion.ac.il/files/2016/02/P54.pdf |access-date=2018-01-15 |url-status=live |archive-url=https://web.archive.org/web/20180115022531/http://etzion.net.technion.ac.il/files/2016/02/P54.pdf |archive-date=2018-01-15 }} [https://www.cs.technion.ac.il/users/wwwb/cgi-bin/tr-info.cgi?1998/CS/CS0937 Technical Report CS0937 <!-- https://web.archive.org/web/20180115023816/https://www.cs.technion.ac.il/users/wwwb/cgi-bin/tr-info.cgi?1998/CS/CS0937 -->] {{Webarchive|url=https://web.archive.org/web/20181215171438/http://www.cs.technion.ac.il/users/wwwb/cgi-bin/tr-info.cgi?1998/CS/CS0937 |date=2018-12-15 }}</ref> <ref name="Sillke_1997">{{cite web |author-first=Torsten |author-last=Sillke |date=1997 |orig-date=1993-03-01 |title=Gray-Codes with few tracks (a question of Marco Brandestini) |url=http://www.mathematik.uni-bielefeld.de/~sillke/PROBLEMS/gray |access-date=2017-10-29 |url-status=live |archive-url=https://web.archive.org/web/20171029202303/https://www.math.uni-bielefeld.de/~sillke/PROBLEMS/gray |archive-date=2017-10-29}}</ref> <ref name="Etzion-Paterson_1996">{{cite journal |title=Near Optimal Single-Track Gray Codes |author-first1=Tuvi |author-last1=Etzion |author-first2=Kenneth G. |author-last2=Paterson |journal=[[IEEE Transactions on Information Theory]] |volume=IT-42 |issue=3 |pages=779–789 |date=May 1996 |doi=10.1109/18.490544 |citeseerx=10.1.1.14.1527 |url=http://etzion.net.technion.ac.il/files/2016/02/P36.pdf |access-date=2018-04-08 |url-status=live |archive-url=https://web.archive.org/web/20161030214251/http://etzion.net.technion.ac.il/files/2016/02/P36.pdf |archive-date=2016-10-30}}</ref> <ref name="Ruskey_2005">{{cite journal |title=A Survey of Venn Diagrams: Symmetric Diagrams |url=http://www.combinatorics.org/Surveys/ds5/VennSymmEJC.html |journal=[[Electronic Journal of Combinatorics]] |date=2005-06-18 |author-first1=Frank |author-last1=Ruskey |author-link1=Frank Ruskey |author-first2=Mark |author-last2=Weston |doi=10.37236/26 |doi-access=free |department=Dynamic Surveys}}</ref> <ref name="Alciatore-Histand_1999">{{cite book |author-last1=Alciatore |author-first1=David G. |author-first2=Michael B. |author-last2=Histand |title=Mechatronics |date=1999 |publisher=[[McGraw–Hill Education]] – Europe |isbn=978-0-07-131444-2 |url=http://mechatronics.colostate.edu/}}</ref> <ref name="Krishna_2008">{{cite web |author=Krishna |title=Gray code for QAM |date=2008-05-11 |url=http://www.dsprelated.com/showthread/comp.dsp/96917-1.php |access-date=2017-10-29 |url-status=live |archive-url=https://web.archive.org/web/20171029192539/https://www.dsprelated.com/showthread/comp.dsp/96917-1.php |archive-date=2017-10-29}}</ref> <ref name="Greferath_2009">{{cite book |editor-first1=Massimiliano |editor-last1=Sala |editor-first2=Teo |editor-last2=Mora |editor-first3=Ludovic |editor-last3=Perret |editor-first4=Shojiro |editor-last4=Sakata |editor-first5=Carlo |editor-last5=Traverso |title=Gröbner Bases, Coding, and Cryptography |url=https://archive.org/details/grbnerbasescodin00sala |url-access=limited |date=2009 |publisher=[[Springer Science & Business Media]] |isbn=978-3-540-93806-4 |chapter=An Introduction to Ring-Linear Coding Theory |author-first=Marcus |author-last=Greferath |page=[https://archive.org/details/grbnerbasescodin00sala/page/n226 220]}}</ref> <ref name="Hazewinkel-Sole_2016">{{cite book |chapter=Kerdock and Preparata codes |author-first=Patrick |author-last=Solé |title=[[Encyclopedia of Mathematics]] |editor-first=Michiel |editor-last=Hazewinkel |editor-link=Michiel Hazewinkel |publisher=[[Springer Science+Business Media]] |date=2016 |isbn=978-1-4020-0609-8 |chapter-url=https://www.encyclopediaofmath.org/index.php/Kerdock_and_Preparata_codes |url-status=live |archive-url=https://web.archive.org/web/20171029191032/https://www.encyclopediaofmath.org/index.php/Kerdock_and_Preparata_codes |archive-date=2017-10-29}}</ref> <ref name="Evans_1958">{{cite journal |title=(([title unknown])) |author-first=David Silvester |author-last=Evans |volume=10–12 |page=87 |journal=Transactions |publisher=Institute of Measurement and Control |date=1958 |url=https://books.google.com/books?id=mwJvieqKGFsC&q=%22Watts+code%22}} (NB. The Watts code was called W.R.D. code or Watts Reflected Decimal to distinguish it from other codes used at [[Hilger & Watts Ltd.]])</ref> <ref name="Evans_1960">{{cite book |title=Fundamentals of Digital Instrumentation |author-first=David Silvester |author-last=Evans |publisher=[[Hilger & Watts Ltd]] |location=London, UK |edition=1 |date=1960 |url=https://books.google.com/books?id=gpVNAAAAYAAJ |access-date=2020-05-24}} (39 pages)</ref> <ref name="Evans_1961">{{cite book |title=Digital Data: Their derivation and reduction for analysis and process control |chapter=Chapter Three: Direct Reading from Coded Scales |author-first=David Silvester |author-last=Evans<!-- M.I.E.E. --> |edition=1<!-- printed by J. W. Arrowsmith Ltd, Bristol, UK --> |publisher=[[Hilger & Watts Ltd]] / [[Interscience Publishers]] |location=London, UK |date=March 1961 |pages=18–23 |url=https://books.google.com/books?id=WOIJAAAAMAAJ |access-date=2020-05-24 |quote-page=20–23 |quote=[…] Decoding. […] To decode C.P.B. or [[#Watts|W.R.D.]] codes, a simple inversion rule can be applied. The readings of the higher tracks determine the way in which the lower tracks are translated. The inversion rule is applied line by line for the C.P.B. and for the W.R.D. it is applied decade by decade or line by line. Starting therefore with the top or slowest changing track of the C.P.B., if the result is odd (1) the next track value has to be inverted, i.e. 0 for 1 and 1 for 0. If, however, the first track is even (0), the second track is left as read, i.e. 0 for 0 and 1 for 1. Again, if the resultant reading of the second track is odd, the third track reading is inverted and so on. When an odd is changed to an even the line below is not inverted and when an even is changed to an odd the line below is inverted. The result of applying this rule to the pattern […] is the [[Pure binary code|pure binary]] (P.B.) pattern […] where each track or digit can be given a definite numerical value (in this instance 1, 2, 4, 8, etc.). […] Using the line-by-line inversion rule on the W.R.D. code produces [a] pattern [of [[Aiken code|1, 2, 4, 2 code]]] where again the digits can be given numerical values and summed decade by decade. The summing of the digits can be very useful, for example, in a high-speed scanning system; but in a parallel decoding system […], it is usual to treat each binary quartet or decade as an entity. In other words, if the first or more significant decade is odd, the second decade is rectified or complemented by inverting the D track and so on, the result being the repeating pattern of [rectified W.R.D. code]. This is an extremely easy thing to achieve since the only change required is the inversion of the meaning of the D track or complementing digit. […]}} (8+82 pages) (NB. The author does not mention Gray at all and calls the standard Gray code "Cyclic Permuted Binary Code" (C.P.B.), the book index erroneously lists it as "cyclic pure binary code".)</ref> <ref name="Newson_1965">{{cite book |title=Tables for the Binary Encoding of Angles |author-first=P. A. |author-last=Newson |location=[[United Kingdom Atomic Energy Authority]], Research Group, [[Atomic Energy Research Establishment]], Harwell, UK |date=1965 |edition=1 |publisher=[[H. M. Stationery Office]] |url=https://books.google.com/books?id=aUEgAQAAIAAJ |access-date=2020-05-24}} (12 pages)</ref> <ref name="Benjamin-Nicholls_1963">{{cite book |title=Measurement of Neutron Spectra by Semi-Automatic Scanning of Recoil Protons in Photographic Emulsions |chapter=3.2.2 Electromechanical Digitizers |author-first1=P. W. |author-last1=Benjamin |author-first2=G. S. |author-last2=Nicholls |location=[[United Kingdom Atomic Energy Authority]], [[Atomic Weapons Research Establishment]], UK |id=AWRE Report No. NR 5/63 |publisher=[[U.S. Department of Energy]] |date=1963 |pages=8–10, 19 |chapter-url=https://books.google.com/books?id=tD5YAAAAYAAJ&pg=PT4}} [https://web.archive.org/web/20200525193325/https://books.googleusercontent.com/books/content?req=AKW5QadxAC8d1K6TXnjLMOKRt0wxLI2XEnyvs5b7wXlxCaZ4XdYW6qcmagghi7O1TLA4DL5nybOmiY0ue2ljEH9L2NvnP6Z6vN54dNvpxHnCIK79h1xoamtO5-waq-mDh2BPHJE9eJkmkoUl7uyPvrbWd7gNM8gpQKbx82WI_3gYiZHy-aHdQGQAFOkacvI1Kf52lu4i8_cuMNYztfa--t2eGiIk5ku1bP7T7n378Q2rNZRCMz3JCXeT0EzYNMkJzlpYSiP2FiQ8] (23 pages)</ref> <ref name="Hollingdale_1958">{{cite book |title=Applications of Computers |chapter=Session 14. Data Processing |author-first=Stuart H. |author-last=Hollingdale |date=1958-09-19 |series=Atlas – Application of Computers, University of Nottingham 15–19 September 1958 |type=Conference paper |chapter-url=http://www.chilton-computing.org.uk/acl/literature/manuals/nottingham/p014.htm |url=http://www.chilton-computing.org.uk/acl/literature/manuals/nottingham/contents.htm |access-date=2020-05-25 |url-status=live |archive-url=https://web.archive.org/web/20200525151358/http://www.chilton-computing.org.uk/acl/literature/manuals/nottingham/p014.htm |archive-date=2020-05-25}}</ref> <ref name="Paul_1995">{{cite web |author-first=Matthias R. |author-last=Paul |title=Unterbrechungsfreier Schleifencode |language=de |trans-title=Continuous loop code |version=1.02 |url=http://www.uni-bonn.de/~uzs180/download/mpbcd102.zip |date=1995-08-10 |orig-date=1994 |access-date=2008-02-11 }}{{cbignore}} (NB. The author called this code {{lang|de|Schleifencode}} (English: "loop code"). It differs from Gray BCD code only in the encoding of state 0 to make it a cyclic unit-distance code for full-circle rotatory applications. Avoiding the all-zero code pattern allows for loop self-testing and to use the data lines for uninterrupted power distribution.)</ref> <ref name="Klar_1970">{{cite book |title=Digitale Rechenautomaten – Eine Einführung |language=de |trans-title=Digital Computers – An Introduction |author-first=Rainer |author-last=Klar |publisher=[[Walter de Gruyter & Co.]] / {{ill|G. J. Göschen'sche Verlagsbuchhandlung|de|G. J. Göschen'sche Verlagsbuchhandlung}} |publication-place=Berlin, Germany |series=Sammlung Göschen |volume=1241/1241a |date=1970-02-01 |isbn=3-11-083160-0 |id=. Archiv-Nr. 7990709. |page=17 |edition=1 |url=https://books.google.com/books?id=QnqVDwAAQBAJ&pg=PA17 |access-date=2020-04-13 |url-status=live |archive-url=https://web.archive.org/web/20200601100645/https://books.google.de/books?id=QnqVDwAAQBAJ&pg=PA17&lpg=PA17&redir_esc=y |archive-date=2020-06-01}} (205 pages) (NB. A 2019 reprint of the first edition is available under {{ISBN|3-11002793-3|978-3-11002793-8}}. A reworked and expanded {{citeref|Klar|1989|4th edition|style=plain}} exists as well.)</ref> <ref name="Klar_1989">{{cite book |title=Digitale Rechenautomaten – Eine Einführung in die Struktur von Computerhardware |language=de |trans-title=Digital Computers – An Introduction into the structure of computer hardware |author-first=Rainer |author-last=Klar |publisher=[[Walter de Gruyter & Co.]] |publication-place=Berlin, Germany |series=Sammlung Göschen |volume=2050 |date=1989 |orig-date=1988-10-01 |isbn=3-11011700-2 |page=28 |edition=4th reworked}} (320 pages) (NB. The author called this code {{lang|de|Einheitsabstandscode}} (English: "unit-distance code"). By swapping two bit rows and inverting one of them, it can be transferred into the [[#O'Brien II|O'Brien code II]], whereas by swapping and inverting two bit rows, it can be transferred into the [[#Petherick|Petherick code]].)</ref> <ref name="Susskind_1958">{{cite book |title=Notes on Analog-Digital Conversion Techniques |chapter=III.F. Unit-Distance Codes / VI.E.2. Reflected Binary Codes |editor-first=Alfred Kriss |editor-last=Susskind<!-- born 1923-10-04, Coblenz (Göda), Germany, died 1988-12-10 Bethesda, Maryland, USA --> |author-first1=Alfred Kriss<!-- Patent US3487460A erroneously refers to Alfred Kriss Susskind as Alfred N. Susskind: https://patents.google.com/patent/US3487460A --> |author-last1=Susskind |author-first2=John Erwin |author-last2=Ward<!-- born 1920 --> |date=1958-03-28 |orig-date=1957, 1956 |edition=3 |publisher=[[Technology Press of the Massachusetts Institute of Technology]] / [[John Wiley & Sons, Inc.]] / [[Chapman & Hall, Ltd.]] |publication-place=New York, USA |location=Cambridge, Massachusetts, USA |series=Technology Books in Science and Engineering |volume=1 |pages=3-10–3-16 [3-13–3-16], 6-65–6-60 [6-60]}} (x+416+2 pages) (NB. The contents of the book was originally prepared by staff members of the [[MIT Servomechanisms Laboratory|Servomechanisms Laboraratory]], Department of Electrical Engineering, [[Massachusetts Institute of Technology|MIT]], for Special Summer Programs held in 1956 and 1957. Susskind's "reading-type code" is actually a minor variant of the code shown here with the two most significant bit rows swapped to better illustrate symmetries. Also, by swapping two bit rows and inverting one of them, the code can be transferred into the [[#Petherick|Petherick code]], whereas by swapping and inverting two bit rows, the code can be transferred into the [[#O'Brien II|O'Brien code II]].)</ref> <ref name="Kämmerer_1969">{{cite book |title=Digitale Automaten – Theorie, Struktur, Technik, Programmieren |language=de |author-first=Wilhelm |author-last=Kämmerer |author-link=:de:Wilhelm Kämmerer |editor-first1=Hans |editor-last1=Frühauf |editor-link1=:de:Hans Frühauf |editor-first2=Wilhelm |editor-last2=Kämmerer |editor-first3=Kurz |editor-last3=Schröder |editor-first4=Helmut |editor-last4=Winkler |chapter=II.15. Struktur: Informationsdarstellung im Automaten |edition=1 |date=May 1969 |publisher=[[Akademie-Verlag GmbH]] |publication-place=Berlin, Germany |location=Jena, Germany |volume=5 |id=License no. 202-100/416/69. Order no. 4666 ES 20 K 3. |series=Elektronisches Rechnen und Regeln |page=173 <!-- |url=https://books.google.com/books?id=jkcgAQAAIAAJ -->}} (NB. A second edition 1973 exists as well. Like {{citeref|Borucki|Dittmann|1971|Borucki and Dittmann|style=plain}}, but without naming it Glixon code, the author creates a 20-cyclic tetradic code from Glixon code and a Glixon code variant with inverted high-order bit.)</ref> <ref name="Borucki-Dittmann_1971">{{cite book |title=Digitale Meßtechnik: Eine Einführung |chapter=2.3 Gebräuchliche Codes in der digitalen Meßtechnik |language=de |author-first1=Lorenz |author-last1=Borucki |author-first2=Joachim |author-last2=Dittmann |date=1971 |orig-date=July 1970, 1966, Autumn 1965 |publisher=[[Springer-Verlag]] |publication-place=Berlin / Heidelberg, Germany |location=Krefeld / Karlsruhe, Germany |edition=2 |lccn=75-131547 |isbn=3-540-05058-2<!-- this is the ISBN printed in the book --> |id={{ISBN|978-3-642-80561-5}}<!-- this is for reprints of the 2nd edition --> |doi=10.1007/978-3-642-80560-8 |pages=10–23 [12–14]}} (viii+252 pages) [https://books.google.com/books?id=NwyCBwAAQBAJ&pg=PA15 1st edition] (NB. Like {{citeref|Kämmerer|1969|Kämmerer|style=plain}}, the authors describe a 6-bit 20-cyclic Glixon code.)</ref> <ref name="Chinal_1973">{{cite book |title=Design Methods for Digital Systems |chapter=3.3. Unit Distance Codes |author-first=Jean P. |author-last=Chinal |language=en |publisher=[[Akademie-Verlag]] / [[Springer-Verlag]] |publication-place=Berlin, Germany |location=Paris, France |translator-first=Alan |translator-last1=Preston |translator-first2=Arthur |translator-last2=Summer |date=January 1973 |edition=1st English |id=License No. 202-100/542/73. Order No. 7617470(6047) ES 19 B 1 / 20 K 3 |isbn=978-0-387-05871-9 |doi=10.1007/978-3-642-86187-1<!-- |chapter-doi=10.1007/978-3-642-86187-1_3 --> |page=50 |s2cid=60362404 |url=https://books.google.com/books?id=8FnxCAAAQBAJ |access-date=2020-06-21}} (xviii+506 pages) (NB. The French 1967 original book was named "Techniques Booléennes et Calculateurs Arithmétiques", published by {{ill|Éditions Dunod|fr}}.)</ref> <ref name="MIL_1991">{{cite book |title=Military Handbook: Encoders – Shaft Angle To Digital |publisher=[[United States Department of Defense]] |id=MIL-HDBK-231A |date=1991-09-30 |url=http://everyspec.com/MIL-HDBK/MIL-HDBK-0200-0299/download.php?spec=MIL_HDBK_231A.1809.pdf |access-date=2020-07-25 |url-status=live |archive-url=https://web.archive.org/web/20200725051128/http://everyspec.com/MIL-HDBK/MIL-HDBK-0200-0299/download.php?spec=MIL_HDBK_231A.1809.pdf |archive-date=2020-07-25}} (NB. Supersedes MIL-HDBK-231(AS) (1970-07-01).)</ref> <ref name="Powell_1968">{{cite book |title=A short note on useful codes for Fluidic Control Circuits |chapter=Codes particularly useful for analogue to digital conversions<!-- Petherick code / Modified Gray code --> |author-first=E. Alexander |author-last=Powell |date=June 1968 |id=CoA Memo 156 |publisher=[[College of Aeronautics, Cranfield|The College of Aeronautics]], Department of Production Engineering |publication-place=Cranfield, UK |s2cid=215864694 |pages=7, 9 |url=https://dspace.lib.cranfield.ac.uk/bitstream/handle/1826/9559/COA_Memo_156_June_1968.pdf |access-date=2020-12-15 |url-status=live |archive-url=https://web.archive.org/web/20201215124905/https://dspace.lib.cranfield.ac.uk/bitstream/handle/1826/9559/COA_Memo_156_June_1968.pdf |archive-date=2020-12-15}} (18 pages) (NB. The paper names the [[#Glixon|Glixon code]] ''modified Gray code'' and misspells [[Richard W. Hamming]]'s name<!-- as R. W. Hammering -->.)</ref> <ref name="Savard_2018">{{cite web |title=Decimal Representations |author-first=John J. G. |author-last=Savard |date=2018 |orig-date=2006 |work=quadibloc |url=http://www.quadibloc.com/comp/cp0203.htm |access-date=2018-07-16 |url-status=live |archive-url=https://web.archive.org/web/20180716101321/http://www.quadibloc.com/comp/cp0203.htm |archive-date=2018-07-16}}</ref> <ref name="Herter-Rote_2016">{{cite journal |title=Loopless Gray Code Enumeration and the Tower of Bucharest |author-first1=Felix |author-last1=Herter |author-first2=Günter |author-last2=Rote |publication-place=Berlin, Germany |orig-date=2018-08-09, 2017-12, 2017-08-09, 2016-04-22 |date=2018-11-14 |journal=[[Theoretical Computer Science (journal)|Theoretical Computer Science]] |issn=0304-3975 |volume=748 |arxiv=1604.06707<!-- 24 pages --> |s2cid=4014870 |doi=10.1016/j.tcs.2017.11.017 |pages=40–54 |url=https://page.mi.fu-berlin.de/rote/Papers/pdf/Loopless+Gray+code+enumeration+and+the+Tower+of+Bucharest.pdf<!-- 18 pages --> |access-date=2020-12-16 |url-status=live |archive-url=https://web.archive.org/web/20201216150701/https://page.mi.fu-berlin.de/rote/Papers/pdf/Loopless+Gray+code+enumeration+and+the+Tower+of+Bucharest.pdf |archive-date=2020-12-16}} [https://web.archive.org/web/20201216230211/https://arxiv.org/pdf/1604.06707.pdf] (15/18/19/24 pages)</ref> <ref name="Strang-Dammann-Roeckl-Plass_2009">{{cite conference |title=Using Gray codes as Location Identifiers |author-first1=Thomas |author-last1=Strang |author-first2=Armin |author-last2=Dammann |author-first3=Matthias |author-last3=Röckl<!-- also written as: Roeckl --> |author-first4=Simon |author-last4=Plass |work=6. GI/ITG KuVS Fachgespräch Ortsbezogene Anwendungen und Dienste |language=en, de |date=October 2009 |publisher=Institute of Communications and Navigation<!-- Institut für Kommunikation und Navigation -->, [[German Aerospace Center]]<!-- Deutsches Zentrum für Luft‐ und Raumfahrt e.V. --> (DLR) |publication-place=Oberpfaffenhofen, Germany |citeseerx=10.1.1.398.9164<!-- https://web.archive.org/web/20201216232905/https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.398.9164&rep=rep1&type=pdf --> |access-date=2020-12-16 |url-status=live |url=http://elib.dlr.de/60489/3/paper.pdf |archive-url=https://web.archive.org/web/20150501063457/http://elib.dlr.de/60489/3/paper.pdf |archive-date=2015-05-01}} (5/8 pages) [https://web.archive.org/web/20201216231728/https://elib.dlr.de/60489/2/Strang_Thomas.pdf] *{{cite web |author=Thomas Strang |display-authors=etal |date=October 2009 |title=Using Gray codes as Location Identifiers |website=ResearchGate |type=Abstract |url=https://www.researchgate.net/publication/225003251 |archive-url=https://web.archive.org/web/20200903200722/https://www.researchgate.net/profile/Simon_Plass/publication/225003251_Using_Gray_codes_as_Location_Identifiers/links/02e7e53a733e49b2f6000000/Using-Gray-codes-as-Location-Identifiers.pdf |archive-date=2020-09-03 |language=de, en}}</ref> <ref name="Goldberg_1989">{{cite book |title=Genetic Algorithms in Search, Optimization, and Machine Learning |author-first=David Edward |author-last=Goldberg |author-link=David Edward Goldberg |publisher=[[Addison-Wesley]] |publication-place=Reading, Massachusetts, USA |edition=1 |date=1989|bibcode=1989gaso.book.....G }}</ref> <ref name="Froehlich-Kent_1991">{{cite book |title=The Froehlich/Kent Encyclopedia of Telecommunications: Volume 2 - Batteries to Codes-Telecommunications |editor-first1=Fritz E. |editor-last1=Froehlich |editor-first2=Allen |editor-last2=Kent |editor-link2=Allen Kent |editor-first3=Carolyn M. |editor-last3=Hall |chapter=Baudot, Jean Maurice Emile |author-first=Andrew J. |author-last=Butrica |publisher=[[Marcel Dekker Inc.]] / [[CRC Press]] |date=1991-06-21 |volume=2 |isbn=0-8247-2901-3 |lccn=90-3966 |pages=31–34 |chapter-url=https://books.google.com/books?id=l3Rn_VefKaoC&pg=PA31 |access-date=2020-12-20 |quote-page=31 |quote=[…] A Baudot prototype (4 years in the making) was built in 1876. The transmitter had 5 keys similar to those of a piano. Messages were sent in a special 5-element code devised by Baudot […]}}</ref> <ref name="Fischer_2000">{{cite web |title=The Evolution of Character Codes, 1874–1968 |author-first=Eric N. |author-last=Fischer |date=2000-06-20 |id=ark:/13960/t07x23w8s |url=https://archive.org/details/enf-ascii |access-date=2020-12-20 |quote=[…] In 1872, [Baudot] started research toward a telegraph system that would allow multiple operators to transmit simultaneously over a single wire and, as the transmissions were received, would print them in ordinary alphabetic characters on a strip of paper. He received a patent for such a system on June 17, 1874. […] Instead of a variable delay followed by a single-unit pulse, Baudot's system used a uniform six time units to transmit each character. […] his early telegraph probably used the six-unit code […] that he attributes to [[Edward Davy|Davy]] in an 1877 article. […] in 1876 Baudot redesigned his equipment to use a five-unit code. Punctuation and digits were still sometimes needed, though, so he adopted from [[David Edward Hughes|Hughes]] the use of two special letter space and figure space characters that would cause the printer to shift between cases at the same time as it advanced the paper without printing. The five-unit code he began using at this time […] was structured to suit his keyboard […], which controlled two units of each character with switches operated by the left hand and the other three units with the right hand. […]}} [https://web.archive.org/web/20180919020435/http://index-of.es/Varios-2/ASCII%20The%20Evolution%20of%20Character%20Codes.pdf][https://archive.org/details/enf-ascii]</ref> <ref name="MacMillan_2010">{{cite web |title=Codes that Don't Count - Some Printing Telegraph Codes as Products of their Technologies (With Particular Attention to the Teletypesetter) |author-first=David M. |author-last=MacMillan |work=lemur.com |location=Mineral Point, Wisconsin, USA |version=Revision 3 |date=2010-04-27 |orig-date=2010-04-25, 2010-04-23 |url=http://www.circuitousroot.com/artifice/telegraphy/tty/codes/index.html |access-date=2020-12-20 |url-status=live |archive-url=https://web.archive.org/web/20201218233813/http://www.circuitousroot.com/artifice/telegraphy/tty/codes/index.html |archive-date=2020-12-18}}</ref> <ref name="ITU_1909">{{cite book |title=Convention télégraphique internationale de Saint-Pétersbourg et Règlement et tarifs y annexés, Revision de Lisbonne, 1908 / Extraits de la publication: Documents de la Conférence télégraphique internationale de Lisbonne |language=fr |date=1909 |orig-date=1908 |location=Lisbon, Portugal |publication-place=Berne, Switzerland |publisher=[[Bureau Internationale de L'Union Télégraphique]]}}</ref> <ref name="ITU_1933_FR">{{cite book |title=Règlement télégraphique annexé à la convention internationale des télécommunications - protocol finale audit règlement - Madrid, 1932 |language=fr |chapter=Chapter IX. Signaux de transmission, Article 35. Signaux de transmission des alphabets télegraphiques internationaux 'nos 1 et 2, signaux d.u code Morse, de l'appareil Hughes et de l'appareil Siemens |location=Madrid, Spain |publication-place=Berne, Switzerland |publisher=[[Bureau Internationale de L'Union Télégraphique]] |date=1933 |orig-date=1932 |pages=31–40 [33] |url=http://search.itu.int/history/HistoryDigitalCollectionDocLibrary/4.5.43.fr.201.pdf |access-date=2020-12-21 |url-status=live |archive-url=https://web.archive.org/web/20201221011133/http://search.itu.int/history/HistoryDigitalCollectionDocLibrary/4.5.43.fr.201.pdf |archive-date=2020-12-21}} (1+188 pages) [https://web.archive.org/web/20201221012741/https://www.itu.int/en/history/Pages/PlenipotentiaryConferences.aspx?conf=4.5]</ref> <ref name="ITU_1933_EN">{{cite book |title=Telegraph Regulations Annexed To The International Telecommunication Convention - Final Protocol To The Telegraph Regulations - Madrid 1932 |chapter=Chapter IX. Transmission Signals. Article 35. Transmission Signals of the International Telegraph Alphabets Nos. 1 and 2, Morse Code Signals and Signals of the Hughes and Siemens Instruments. |language=en, fr |date=1933 |orig-date=1932 |id=43-152-2 / 18693 |pages=32–40 [34] |publisher=General Post Office / [[His Majesty's Stationery Office]] |location=London, UK |url=http://search.itu.int/history/HistoryDigitalCollectionDocLibrary/4.5.43.en.101.pdf |access-date=2020-12-21 |url-status=live |archive-url=https://web.archive.org/web/20201221011748/http://search.itu.int/history/HistoryDigitalCollectionDocLibrary/4.5.43.en.101.pdf |archive-date=2020-12-21}} (1+2*120+26 pages) [https://web.archive.org/web/20201221012741/https://www.itu.int/en/history/Pages/PlenipotentiaryConferences.aspx?conf=4.5]</ref> <ref name="Zeman-Fischer_1877">{{cite journal |title=Einige neuere Vorschläge zur mehrfachen Telegraphie: A. Absatzweise vielfache Telegraphie |language=de |date=1877 |journal=[[:de:Polytechnisches Journal|Dingler's Polytechnisches Journal]] |editor-first1=Johann |editor-last1=Zeman |editor-first2=Ferdinand |editor-last2=Fischer |publication-place=Augsburg, Germany |publisher=[[:de:J. G. Cotta'sche Buchhandlung|J. G. Cotta'sche Buchhandlung]] |volume=226 |pages=499–507 |url=http://dingler.culture.hu-berlin.de/article/pj226/ar226125 |access-date=2020-12-21 |url-status=live |archive-url=https://web.archive.org/web/20201221163504/http://dingler.culture.hu-berlin.de/article/pj226/ar226125 |archive-date=2020-12-21 |quote-page=499 |quote=[…] Der um die Mitte des J[ahres] 1874 patenti[e]rte, ebenfalls dem [[Henry Highton|Highton]]'schen verwandte Typendrucker des französischen Telegraphen-Verwaltungsbeamten Baudot wurde bei seiner 1875 patenti[e]rten Weiterentwicklung in einen fünffachen umgewandelt […]}}</ref> }}
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