Summary of list of bits responses
- To: mathgroup at smc.vnet.net
- Subject: [mg28739] Summary of list of bits responses
- From: Raul Martinez <rmartinez at vrinc.com>
- Date: Fri, 11 May 2001 03:38:54 -0400 (EDT)
- Organization: Vista Research Inc
- Sender: owner-wri-mathgroup at wolfram.com
--------------D33AE880BD70BF074A1A13D4 To the Mathgroup, Murray Eisenberg posted a question about converting a list of bits into a string representing a binary number. Many solutions were offered (none by me), and I found the diversity so interesting that I've taken the liberty to compile a summary of the solutions with examples and some comments. Several of the proposed solutions were identical, and when duplicates were accounted for six solutions remained. The summary is contained in the attached Mathematica notebook. HTH, Raul Martinez Staff Scientist Vista Research, Inc. Sunnyvale, CA 94085 --------------D33AE880BD70BF074A1A13D4 filename="listtobits.nb" (************** Content-type: application/mathematica ************** Mathematica-Compatible Notebook This notebook can be used with any Mathematica-compatible application, such as Mathematica, MathReader or Publicon. The data for the notebook starts with the line containing stars above. 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For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info at wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. *******************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 4164, 156]*) (*NotebookOutlinePosition[ 4795, 178]*) (* CellTagsIndexPosition[ 4751, 174]*) (*WindowFrame->Normal*) Notebook[{ Cell[TextData[StyleBox["DATA", FontWeight->"Bold"]], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(listofbits = {0, 1, 1, 0, 1}\)], "Input"], Cell[BoxData[ \({0, 1, 1, 0, 1}\)], "Output"] }, Open ]], Cell["\<\ \tThe problem is to convert the above list of bits into a string \ corresponding to the appropriate binary number. \ \>", "Text"], Cell[TextData[StyleBox["Solution 1", FontWeight->"Bold"]], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(ToString[Flatten[listofbits]]\)], "Input"], Cell[BoxData[ \("{0, 1, 1, 0, 1}"\)], "Output"] }, Open ]], Cell[TextData[StyleBox["Solution 2", FontWeight->"Bold"]], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(StringJoin @@ \(ToString /@ listofbits\)\)], "Input"], Cell[BoxData[ \("01101"\)], "Output"] }, Open ]], Cell[TextData[StyleBox["Solution 3", FontWeight->"Bold"]], "Text"], Cell[CellGroupData[{ Cell[BoxData[{ \(Map[Apply[StringJoin, Map[ToString, #]] &, listofbits]\), "\[IndentingNewLine]", \(Map[Apply[StringJoin, Map[ToString, #]] &, {listofbits}]\)}], "Input"], Cell[BoxData[ \({0, 1, 1, 0, 1}\)], "Output"], Cell[BoxData[ \({"01101"}\)], "Output"] }, Open ]], Cell[TextData[StyleBox["Solution 4", FontWeight->"Bold"]], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(StringJoin[ToString /@ listofbits]\)], "Input"], Cell[BoxData[ \("01101"\)], "Output"] }, Open ]], Cell[TextData[StyleBox["Solution 5", FontWeight->"Bold"]], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(ToString[FromDigits[listofbits]]\)], "Input"], Cell[BoxData[ \("1101"\)], "Output"] }, Open ]], Cell[TextData[StyleBox["Solution 6", FontWeight->"Bold"]], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Apply[StringJoin, ToString /@ listofbits]\)], "Input"], Cell[BoxData[ \("01101"\)], "Output"] }, Open ]], Cell[TextData[{ StyleBox["REMARKS", FontWeight->"Bold"], "\n\t1. Solution 1 does not work.\n\t\n\t2. Solutions 2, 4, and 6 give the \ same correct answer, with the appropriate zero padding on the left.\n\t\n\t3. \ Solution 3 works only if the list of bits is contained in a list. The \ resulting correct string is also enclosed in a list.\n\t\n\t4. Solution 5 is \ correct but not zero-padded on the left.\n\t\n\t5. Solutions 2 and 4 seem to \ be identical except for the syntax. IMHO, these two are to be the most \ elegant solutions in the sense that they are the shortest." }], "Text"] }, FrontEndVersion->"4.1 for X", ScreenRectangle->{{0, 1280}, {0, 1024}}, WindowSize->{520, 600}, WindowMargins->{{150, Automatic}, {Automatic, 52}} ] (******************************************************************* Cached data follows. If you edit this Notebook file directly, not using Mathematica, you must remove the line containing CacheID at the top of the file. 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