Gray code: Difference between revisions

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Latest revision as of 07:10, 26 August 2025

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<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 |article-number=R25 |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=https://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 |publisher=[[IEEE Computer Society]] |isbn=978-0-8186-7502-7 |pages=178–181|s2cid=52837310 }}</ref>

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<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=https://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 |article-number=N19 |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 |article-number=R31 |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>

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<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 }}</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 |bibcode=2001ITIT...47.2587H |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>

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* {{cite web |title=Gray Code Fundamentals |work=Design How-To |at=Part 1 |author-first=Clive "Max" |author-last=Maxfield |date=2012-10-01 |orig-date=2011-05-28 |publisher=[[EETimes]] |url=https://www.eetimes.com/document.asp?doc_id=1278809 |access-date=2017-10-30 |url-status=live |archive-url=https://web.archive.org/web/20171030135842/https://www.eetimes.com/document.asp?doc_id=1278809 |archive-date=2017-10-30}} [https://www.eetimes.com/document.asp?doc_id=1278827<!-- https://web.archive.org/web/20171030140209/https://www.eetimes.com/document.asp?doc_id=1278827 --> Part 2] [https://www.eetimes.com/document.asp?doc_id=1278853<!-- https://web.archive.org/web/20171030140323/https://www.eetimes.com/document.asp?doc_id=1278853 --> Part 3]

* {{cite book |title=Hacker's Delight |title-link=Hacker's Delight |chapter=Chapter 13: Gray Code |author-first=Henry S. |author-last=Warren, Jr. |date=2013 |edition=2 |publisher=[[Addison Wesley]] – [[Pearson Education, Inc.]] |isbn=978-0-321-84268-8 |pages=311–317<!-- page 318 is blank -->}} (7 pages)

* {{cite journal |title=Computing Binary Combinatorial Gray Codes Via Exhaustive Search With SAT Solvers |author-last1=Zinovik |author-first1=Igor |author-last2=Kroening |author-first2=Daniel |author-last3=Chebiryak |author-first3=Yury |journal=[[IEEE Transactions on Information Theory]] |publisher=[[IEEE]] |volume=54 |issue=4 |date=2008-03-21 |pages=1819–1823 |doi=10.1109/TIT.2008.917695 |bibcode=2008ITIT...54.1819Z |hdl=20.500.11850/11304 |s2cid=2854180 |hdl-access=free}} (5 pages)

* {{cite journal |author-first=Joseph A. |author-last=O'Brien |title=Unit-Distance Binary-Decimal Code Translators |journal=[[IRE Transactions on Electronic Computers]] |volume=EC-6 |issue=2 |date=June 1957 |issn=0367-9950 |doi=10.1109/TEC.1957.5221585 |pages=122–123 |url=https://www.researchgate.net/publication/250929745 |access-date=2020-05-25}} (2 pages)

* {{cite magazine |title=A decimal Gray code – Easily converted for shaft position coding |author-first=K. G. |author-last=Barr |___location=Faculty of Natural Sciences, [[University of the West Indies]] |date=March 1981 |magazine=[[Wireless World]] |volume=87 |number=1542 |pages=86–87 |url=https://worldradiohistory.com/hd2/IDX-Site-Early-Radio/Archive-Wireless-World-IDX/80s/Wireless-World-1981-03-OCR-Page-0046.pdf |access-date=2020-07-28 |url-status=live |archive-url=https://web.archive.org/web/20200728093447/https://worldradiohistory.com/hd2/IDX-Site-Early-Radio/Archive-Wireless-World-IDX/80s/Wireless-World-1981-03-OCR-Page-0046.pdf |archive-date=2020-07-28}}