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1、CHAPTERTWODataRepresentation(选口M.MORRISMANO《COMPUTERSYSTEMARCHITECTURE》THIRDEDITION)INTHISCHAPTER2-12-22-32-42-52-6DataTypesComplementsFixed-PointRepresentationFloating-PointRepresentationOtherBinaryCodesErrorDetectionCodes2-1DataTypesThebinarynumbersystemusesthe
2、radix2.Thetwodigitsymbolsusedare0and1.Thestringofdigits101101isinterpretedtorepresentthequantity1x25+0x24+1x234-1x22+0x21+1x2°=45Todistinguishbetweendifferentradixnumbers,thedigitswillbeenclosedinparenthesesandtheradixofthenumberinsertedasasubscript.Forexample,to
3、showtheequalitybetweendecimalandbinaryforty-fivewewillwrite(101101)2=(45))oBesidesthedecimalandbinarynumbersystems,theoctal(radix8)andhexadecimal(radix16)areimportantindigitalcomputerwork.Theeightsymbolsoftheoctalsystemare0丄2,3,4,5,6,and7.The16symbolsofthehexadec
4、imalsystemarc0」23,4,5,6,7,&9,A,B,CQ,E,andEThelastsixsymbolsarc,unfortunately,identicaltothelettersofthealphabetandcancauseconfusionattimes・However,thisistheconventionthathasbeenadopted.Whenusedtorepresenthexadecimaldigits,thesymbolsA,B,C,D,E,Fcorrespondtothedecim
5、alnumbers10,11,12,13,14,15respectively.Anumberinradixrcanbeconvertedtothefamiliardecimalsystembyformingthesumoftheweighteddigits.Forexample,octal736.4isconvertedtodecimalasfollows:(736.4h=7x82+3x81+6x8°+4x8'1=7x64+3x8+6x1+4/8=(478.5)1()Theequivalentdecimalnumbero
6、fhexadecimalF3isobtainedfromthefollowingcalculation:(F3)16=FX16+3=15x16+3=(243)10Conversionfromdecimaltoitsequivalentrepresentationintheradixrsystemiscarriedoutbyseparatingthenumberintoitsintegerandfractionpartsandconvertingeachpartseparately.Theconversionofadeci
7、malintegerintoabaserrepresentationisdonebysuccessivedivisionsbyrandaccumulationoftheremainders・Theconversionofadecimalfractiontoradixrrepresentationisaccomplishedbysuccessivemultiplicationsbyrandaccumulationoftheintegerdigitssoobtained・Figure2-1demonstratesthesep
8、rocedures.Fieure7.1Conversionofdecimal41・6875intobinary.Intes^r■■41Fraction■0.6875410.68752012IOO1.37505Ox2210.75001o恢2O11.5000x2•lToboo«nlo-■(1OIOOI>2
