附英文阅读材料.docx

附英文阅读材料.docx

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附英文阅读材料

CHAPTERTWO

DataRepresentation

（选自M.MORRISMANO《COMPUTERSYSTEMARCHITECTURE》THIRDEDITION）

INTHISCHAPTER

2-1DataTypes

2-2Complements

2-3Fixed-PointRepresentation

2-4Floating-PointRepresentation

2-5OtherBinaryCodes

2-6ErrorDetectionCodes

2-1DataTypes

Binaryinformationindigitalcomputersisstoredinmemoryorprocessorregisters.Registerscontaineitherdataorcontrolinformation.Controlinformationisabitoragroupofbitsusedtospecifythesequenceofcommandsignalsneededformanipulationofthedatainotherregisters.Dataarenumbersandotherbinary-codedinformationthatareoperatedontoachieverequiredcomputationalresults.Inthischapterwepresentthemostcommontypesofdatafoundindigitalcomputersandshowhowthevariousdatatypesarerepresentedinbinary-codedformincomputerregisters.

Thedatatypesfoundintheregistersofdigitalcomputersmaybeclassifiedasbeingoneofthefollowingcategories:

（1）numbersusedinarithmeticcomputations,

（2）lettersofthealphabetusedindataprocessing,and（3）otherdiscretesymbolsusedforspecificpurposed.Alltypesofdata,exceptbinarynumbers,arerepresentedincomputerregistersinbinary-codedform.Thisisbecauseregistersaremadeupofflip-flopsandflip-flopsaretwo-statedevicesthatcanstoreonly1’sand0’s.Thebinarynumbersystemisthemostnaturalsystemtouseinadigitalcomputer.Butsometimesitisconvenienttoemploydifferentnumbersystems,especiallythedecimalnumbersystem,sinceitisusedbypeopletoperformarithmeticcomputations.

NumberSystems

Anumbersystemofbase,orradix,risasystemthatusesdistinctsymbolsforrdigits.Numbersarerepresenteedbyastringofdigitsymbols.Todeterminethequantitythatthenumberrepresents,itisnecessarytomultiplyeachdigitbyanintegerpowerofrandthenformthesumofallweighteddigits.Forexample,thedecimalnumbersystemineverydayuseemploystheradix10system.The10symbolsare0,1,2,3,4,5,6,7,8,and9.Thestringofdigits724.5isinterpretedtorepresentthequantity.

7102+2101+4100+510-1

thatis,7hundreds,plus2tens,plus4units,plus5tenths.Everydecimalnumbercanbesimilarlyinterpretedtofindthequantityitrepresents.

Thebinarynumbersystemusestheradix2.Thetwodigitsymbolsusedare0and1.Thestringofdigits101101isinterpretedtorepresentthequantity

125+024+123+122+021+120=45

Todistinguishbetweendifferentradixnumbers,thedigitswillbeenclosedinparenthesesandtheradixofthenumberinsertedasasubscript.Forexample,toshowtheequalitybetweendecimalandbinaryforty-fivewewillwrite（101101）2=（45）10

Besidesthedecimalandbinarynumbersystems,theoctal（radix8）andhexadecimal（radix16）areimportantindigitalcomputerwork.Theeightsymbolsoftheoctalsystemare0,1,2,3,4,5,6,and7.The16symbolsofthehexadecimalsystemare0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,andF.Thelastsixsymbolsare,unfortunately,identicaltothelettersofthealphabetandcancauseconfusionattimes.However,thisistheconventionthathasbeenadopted.Whenusedtorepresenthexadecimaldigits,thesymbolsA,B,C,D,E,Fcorrespondtothedecimalnumbers10,11,12,13,14,15,respectively.

Anumberinradixrcanbeconvertedtothefamiliardecimalsystembyformingthesumoftheweighteddigits.Forexample,octal736.4isconvertedtodecimalasfollows:

（736.4）8=782+381+680+48-1

=764+38+61+4/8=（478.5）10

TheequivalentdecimalnumberofhexadecimalF3isobtainedfromthefollowingcalculation:

（F3）16=F16+3=1516+3=（243）10

Conversionfromdecimaltoitsequivalentrepresentationintheradixrsystemiscarriedoutbyseparatingthenumberintoitsintegerandfractionpartsandconvertingeachpartseparately.Theconversionofadecimalintegerintoabaserrepresentationisdonebysuccessivedivisionsbyrandaccumulationoftheremainders.Theconversionofadecimalfractiontoradixrrepresentationisaccomplishedbysuccessivemultiplicationsbyrandaccumulationoftheintegerdigitssoobtained.Figure2-1demonstratestheseprocedures.

Theconversionofdecimal41.6875intobinaryisdonebyfirstseparatingthenumberintoitsintegerpart41andfractionpart.6875.Theintegerpartisconvertedbydividing41byr=2togiveanintegerquotientof20andaremainderof1.Thequotientisagaindividedby2togiveanewquotientandremainder.Thisprocessisrepeateduntiltheintegerquotientbecomes0.Thecoefficientsofthebinarynumberareobtainedfromtheremainderswiththefirstremaindergivingthelow-orderbitoftheconvertedbinarynumber.

Thefractionpartisconvertedbymultiplyingitbyr=2togiveanintegerandafraction.Thenewfraction（withouttheinteger）ismultipliedagainby2togiveanewintegerandanewfraction.Thisprocessisrepeateduntilthefractionpartbecomeszerooruntilthenumberofdigitsobtainedgivestherequiredaccuracy.Thecoefficientsofthebinaryfractionareobtainedfromtheintegerdigitswiththefirstintegercomputedbeingthedigittobeplacednexttothebinarypoint.Finally,thetwopartsarecombinedtogivethetotalrequiredconversion.

OctalandHexadecimalNumbers

Theconversionfromandtobinary,octal,andhexadecimalrepresentationplaysandimportantpartindigitalcomputers.Since23=8and24=16,eachoctaldigitcorrespondstothreebinarydigitsandeachhexadecimaldigitcorrespondstofourbinarydigits.Theconversionfrombinarytooctaliseasilyaccomplishedbypartitioningthebinarynumberintogroupsofthreebitseach.Thecorrespondingoctaldigitisthenassignedtoeachgroupofbitsandthestringofdigitssoobtainedgivestheoctalequivalentofthebinarynumber.Consider,forexample,a16-bitregister.Physically,onemaythinkoftheregisterascomposedof16binarystoragecells,witheachcellcapableofholdingeithera1ora0.Supposethatthebitconfigurationstoredintheregisterisasshowninfig.2-2.Sinceabinarynumberconsistsofastringof1’sand0’s,the16-bitregistercanbeusedtostoreanybinarynumberfrom0to216-1.Fortheparticularexampleshown,thebinarynumberstoredintheregisteristheequivalentofdecimal44899.Startingfromthelow-orderbit,wepartitiontheregisterintogroupsofthreebitseach（thesixteenthbitremainsinagroupbyitself）.Eachgroupofthreebitsisassigneditsoctalequivalentandplacedontopoftheregister.Thestringofoctaldigitssoobtainedrepresentstheoctalequivalentofthebinarynumber.

Conversionfrombinarytohexadecimalissimilarexceptthatthebitsaredividedintogroupsoffour.ThecorrespondinghexadecimaldigitforeachgroupoffourbitsiswrittenasshownbelowtheregisterofFig.2-2.Thestringofhexadecimaldigitssoobtainedrepresentsthehexadecimalequivalentofthebinarynumber.Thecorrespondingoctaldigitforeachgroupofthreebitsiseasilyrememberedafterstudyingthefirsteightentrieslistedintable2-1.Thecorrespondencebetweenahexadecimaldigitanditsequivalent4-bitcodecanbefoundinthefirst16entriesofTable2-2.

Table2-1listsafewoctalnumbersandtheirrepresentationinregistersinbinary-codedform.Thebinarycodeisobtainedbytheprocedureexplainedabove.Eachoctaldigitisassigneda3-bitcodeasspecifiedbytheentriesofthefirsteightdigitsinthetable.Similarly,Table2-2listsafewhexadecimalnumbersandtheirrepresentationinregistersinbinary-codedform.Herethebinarycodeisobtainedbyassigningtoeachhexadecimaldigitthe4-bitcodelistedinthefirst16entriesofthetable.

Comparingthebinary-codedoctalandhexadecimalnumberswiththeirbinarynumberequivalentwefindthatthebitcombinationinallthreerepresentationsisexactlythesame.Forexample,decimal99,whenconvertedtobinary,becomes1100011.Thebinary-codedoctalequivalentofdecimal99is001100011andthebinary-codedhexadecimalofdecimal99is01100011.Ifweneglecttheleadingzerosinthesethreebinaryrepresentations,wefindthattheirbitcombinationisidentical.Thisshouldbesobecauseofthestraightforwardconversionthatexistsbetweenbinarynumbersandoctalorhexadecimal.Thepointofallthisisthatastringof1’sand0’sstoredinaregistercouldrepresentabinarynumber,butthissamestringofbitsmaybeinterpretedasholdinganoctalnumberinbinary-codedform（ifwedividethebitsingroupsofthree）orasholdingahexadecimalnumberinbinary-codedform（ifwedividethebitsingroupsoffour）.

Theregistersinadigitalcomputercontainmanybits.Specifyingthecontentofregistersbytheirbinaryvalueswillrequirealongstringofbinarydigits.Itismoreconvenienttospecifycontentofregistersbytheiroctalorhexadecimalequivalent.Thenumberofdigitsisreducedbyone-thirdintheoctaldesignationandbyone-fourthinthehexadecimaldesignation.Forexample,thebinarynumber111111111111has12digits.Itcanbeexpressedinoctalsas7777（fourdigits）orinhexadecimalasFFF（threedigits）.Computermanualsinvariablychooseeithertheoctalorthehexadecimaldesignationforspecifyingcontentsofregisters.

Decimalrepresentation

Thebinarynumbersystemisthemostnaturalsystemforacomputer,butpeopleareaccustomedtothedecimalsystem.Onewaytosolvethisconflictistoconvertallinputdecimalnumbersintobinarynumbers,letthecomputerperformallarithmeticoperationsinbinaryandthenconvertthebinaryresultsbacktodecimalforthehumanusertounderstand.However,itisalsopossibleforthecomputertoperformarithmeticoperationsdirectlywithdecimalnumbersprovidedtheyareplacedinregistersinacodedform