(*********************************************************************** Mathematica-Compatible Notebook This notebook can be used on any computer system with Mathematica 4.0, MathReader 4.0, or any compatible application. The data for the notebook starts with the line containing stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). 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Knuth. \"Generating All Possibilities\", ", StyleBox["The Art of Computer Programming, Volumen 4, prefasc\[IAcute]culo \ 2a", FontSlant->"Italic"], ", [en l\[IAcute]nea], [versi\[OAcute]n del 31 de marzo de 2005]\n<", ButtonBox["http://www-cs-faculty.stanford.edu/~knuth/news.html>\n<", ButtonData:>{ URL[ "http://www-cs-faculty.stanford.edu/~knuth/news.html"], None}], ButtonBox["http://www-cs-faculty.stanford.edu/~knuth/", ButtonData:>{ URL[ "http://www-cs-faculty.stanford.edu/~knuth/fasc3a.ps.gz"], None}], StyleBox["fasc2a.ps.gz>", ButtonBoxOptions->{ButtonData:>{ URL[ "http://www-cs-faculty.stanford.edu/~knuth/fasc3a.ps.gz"], None}}], ButtonBox["\n", ButtonData:>{ URL[ "http://www-cs-faculty.stanford.edu/~knuth/news.html"], None}, ButtonStyle->"Hyperlink"] }], "Reference"], Cell[TextData[{ "[2] Gonzalo Mena Mendoza. \"", StyleBox["C\[OAcute]digo Binario Gray\"", FontVariations->{"CompatibilityType"->0}], ", [en l\[IAcute]nea], [consulta 20 de abril de 2005]\n<", ButtonBox["http://mena.com.mx/gonzalo/maestria/algor/CodigoBinarioGray.nb>", ButtonData:>{ URL[ "http://www-cs-faculty.stanford.edu/~knuth/news.html"], None}] }], "Reference"] }, Open ]], Cell[CellGroupData[{ Cell["Introducci\[OAcute]n", "SectionFirst"], Cell[TextData[{ "\tSe puede identificar la posici\[OAcute]n de un disco rotatorio que ha \ sido dividido en ", Cell[BoxData[ \(TraditionalForm\`2\^n\)]], " partes utilizando n sensores, cada uno de los cuales tiene que distinguir \ entre el blanco y el negro de la pista conc\[EAcute]ntrica correspondiente." }], "Text", TextAlignment->Left, TextJustification->0], Cell["\<\ La siguiente figura muestra el resultado deseado. Del lado izquierdo ese \ encuentra el disco para el \[OAcute]rden lexicogr\[AAcute]fico de n = 4; y \ del lado derecho, el disco del c\[OAcute]digo binario Gray respectivo[1].\ \>", "Text"], Cell[GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgGoo09Yoo`00VWoo00=_Nd8@7>L00PaS00LDYAcW8@P@Q2DYBW96<@0D Ool02DHa000Noig_DHa7>LHaRU: >Li:DU[fKg]oofLi@Q0]JaAoo`09MkeW>G>LCWGNm01Aoo`03 36=>Lgoo0?moofUoo`035:E:DWoo00Ioo`04LiaS65:D@Q0BOol03EJe48A2 43g_@Q0mkd8@?Nm243g_@Q0@Q7OM019oo`03248Q27OM09]oo`00V7oo00Ec W6Lfmk00Moo`03F]HaS7oo01Eoo`05Mkd@Q7>L34=W>@0FOol01`00 7>LYBSg_CW=Nmfmk0?moofEoo`0>5:De[GooOomg_FNhHaP0EOol210402a246:HHaQcW8@PU:BU:>Li:DUkgKg/0ogooH7oo00H< Ha24>Nh]JbDY8@P27>L25:D011245:E2<5[F4Goo00=F]Cg_Ool027oo00GOMTGoo002I Ool00b48E[Eoo`07Ool017_nG_LicTHa5Goo00E_NgNmOomoofLi01Eoo`08 48@]Jf]JE[E242U:6:HDQ@8HaP8Pj08YB_mooemoo`80008HYP0:5:D@Q2TZ >LiBU6l00=oo`08Mke[FU[FBU8YBQ24G_M_Nbmoo`03 5:E6Lh0ogooH7oo00D48BU:DYAS>7_N 00Eoo`03DYA1l7oo02moo`8DY@03Noioogoo009oo`07LkaS64YB=Jd@Q2e[ 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Generaci\[OAcute]n de las series binarias 2. Construcci\[OAcute]n de las pistas conc\[EAcute]ntricas 3. Separaci\[OAcute]n de las pistas 4. Separaci\[OAcute]n de los sectores 5. Generaci\[OAcute]n de las etiquetas radiales.\ \>", "Text", TextJustification->1], Cell[CellGroupData[{ Cell["Series Binarias", "Subsection"], Cell[CellGroupData[{ Cell["Orden Lexicogr\[AAcute]fico", "Subsubsection"], Cell[BoxData[ \(OrdenLexicogr\[AAcute]fico[n_] := \ IntegerDigits[Range[0, 2\^n - 1], 2, n]\)], "Input", CellLabel->"In[149]:="], Cell[CellGroupData[{ Cell[BoxData[ \(OrdenLexicogr\[AAcute]fico[3]\)], "Input", CellLabel->"In[150]:="], Cell[BoxData[ \({{0, 0, 0}, {0, 0, 1}, {0, 1, 0}, {0, 1, 1}, {1, 0, 0}, {1, 0, 1}, {1, 1, 0}, {1, 1, 1}}\)], "Output", CellLabel->"Out[150]="] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["C\[OAcute]digo Gray", "Subsubsection"], Cell["\<\ Se puede definir el C\[OAcute]digo Gray de la siguiente manera recursiva [2]:\ \ \>", "Text"], Cell[BoxData[{ \(C\[OAcute]digoGray[0] := {{}}\), "\[IndentingNewLine]", \(C\[OAcute]digoGray[n_] := Join[\[IndentingNewLine]Map[Prepend[#, 0] &, C\[OAcute]digoGray[n - 1]], \[IndentingNewLine]Map[Prepend[#, 1] &, Reverse[C\[OAcute]digoGray[n - 1]]]\[IndentingNewLine]]\)}], "Input",\ CellLabel->"In[151]:="], Cell[CellGroupData[{ Cell[BoxData[ \(C\[OAcute]digoGray[3]\)], "Input", CellLabel->"In[153]:="], Cell[BoxData[ \({{0, 0, 0}, {0, 0, 1}, {0, 1, 1}, {0, 1, 0}, {1, 1, 0}, {1, 1, 1}, {1, 0, 1}, {1, 0, 0}}\)], "Output", CellLabel->"Out[153]="] }, Open ]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Pistas", "Subsection"], Cell[TextData[{ "El problema principal consiste en dibujar las pistas codificadoras conc\ \[EAcute]ntricas. El disco de divide en ", Cell[BoxData[ \(TraditionalForm\`2\^n\)]], " sectores, uno por elemento de la serie s. Para cada sector se dibujan n \ secciones de pista, cada una de las secciones corresponde a un d\[IAcute]gito \ del elemento en cuesti\[OAcute]n. El d\[IAcute]gito m\[AAcute]s significativo \ corresponde a la pista m\[AAcute]s interna.El 1 se representa con negro y el \ 0 con blanco. 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