Gray code: Difference between revisions

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<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=[((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>