Introduction
Thearithmeticunitiscomposedofarithmeticlogicunit(ALU),accumulator,statusregister,generalregistergroup,etc.Thebasicfunctionsofthearithmeticlogicunit(ALU)arethefourarithmeticoperationsofaddition,subtraction,multiplication,anddivision,logicaloperationssuchasAND,OR,NOT,XOR,andoperationssuchasshiftandcomplement.Whenthecomputerisrunning,theoperationandoperationtypesofthearithmeticunitaredeterminedbythecontroller.Thedataprocessedbythearithmeticunitcomesfromthememory;theprocessedresultdataisusuallysentbacktothememoryortemporarilystoredinthearithmeticunit.TogetherwiththeControlUnit,itformsthecorepartoftheCPU.
Basictheory
Data
Theprocessingobjectofthearithmeticunitisdata,sothedatalengthandcomputerdatarepresentationmethodhaveagreatimpactontheperformanceofthearithmeticunit.Inthe1970s,microprocessorsoftenused1,4,8,and16binarybitsasthebasicunitofprocessingdata.Mostgeneral-purposecomputersuse16,32,and64bitsasthearithmeticunittoprocessthedatalength.Anarithmeticunitthatcanprocessallbitsofadataatthesametimeiscalledaparallelarithmeticunit.Ifonlyonebitisprocessedatatime,itiscalledaserialarithmeticunit.Somearithmeticunitscanprocessseveralbitsatatime(usually6or8bits),andacompletedataisdividedintoseveralsegmentsforcalculation,whichiscalledaserial/parallelarithmeticunit.Thearithmeticunitoftenonlyhandlesdataofonelength.Somecanalsohandledataofseveraldifferentlengths,suchashalf-word-lengthoperations,double-word-lengthoperations,andquadruple-word-lengthoperations.Somedatalengthscanbespecifiedduringoperation,whichiscalledvariablewordlengthoperation.
Accordingtothedifferentrepresentationmethodsofdata,therecanbebinaryarithmetic,decimalarithmetic,hexadecimalarithmetic,fixed-pointintegerarithmetic,fixed-pointdecimalarithmetic,floating-pointarithmetic,etc.Accordingtothenatureofthedata,thereareaddresscalculatorsandcharactercalculators.
Itsmainfunctionistoperformarithmeticandlogicaloperations
Operation
Howmanyoperationsandoperatingspeedthearithmeticunitcanperform,markingtheabilityofthearithmeticunitStrengthorweaknessevenmarksthecapabilitiesofthecomputeritself.Themostbasicoperationofthearithmeticunitisaddition.Addinganumbertozeroisequivalenttosimplytransmittingthenumber.Complementingthecodeofonenumberandaddingittoanothernumberisequivalenttosubtractingthepreviousnumberfromthenextnumber.Subtracttwonumberstocomparetheirsize.
Leftandrightshiftisthebasicoperationofthearithmeticunit.Inasignednumber,thesigndoesnotmovebutonlythedatabitsareshifted,whichiscalledarithmeticshift.Ifthedatamovestogetherwithallthebitsofthesymbol,itiscalledalogicalshift.Ifthehighestbitandthelowestbitofthedataarelinkedtoperformalogicalshift,itiscalledacyclicshift.
ThelogicoperationofthearithmeticunitcanperformbitwiseAND,OR,XORoftwodata,andnegatethebitsofadata.Somearithmeticunitscanalsoperform16kindsoflogicoperationsofbinarycodes.
Multiplicationanddivisionoperationsaremorecomplicated.Manycomputerarithmeticunitscandirectlyperformtheseoperations.Themultiplicationoperationisbasedontheadditionoperation.Thepartialproductissuccessivelygeneratedbyoneorseveralbitsofthemultiplierdecodingcontrol,andthepartialproductisaddedtoobtaintheproduct.Thedivisionruleisoftenbasedonmultiplication,thatis,anumberoffactorsareselectedandmultipliedbythedivisorsothatitisapproximately1,andthesefactorsaremultipliedbythedividendtoobtainthequotient.Computersthatdonotperformmultiplicationanddivisionhardwarecanuseprogramstoachievemultiplicationanddivision,butthespeedismuchslower.Somearithmeticunitscanalsoperformcomplexoperationssuchasfindingthelargestnumberinabatchofdata,continuouslyperformingthesameoperationonabatchofdata,andfindingthesquareroot.
Operationmethod
Torealizetheoperationofthearithmeticunit,especiallythefourarithmeticoperations,areasonableoperationmethodmustbeselected.Itdirectlyaffectstheperformanceofthearithmeticunit,andisalsorelatedtothestructureandcostofthearithmeticunit.Inaddition,whenperformingnumericalcalculations,theeffectivedigitsoftheresultmaybelonger,andcertaineffectivedigitsmustbeintercepted,whichresultsintheroundingoftheleastsignificantdigits.Theselectedroundingrulealsoaffectstheaccuracyofthecalculationresult.Thefollowingfactorsshouldbefullyconsideredwhenchoosingacomputer'snumberrepresentationmethod:Thetypeofnumbertoberepresented(decimal,integer,realnumber,andcomplexnumber):Decideontherepresentationmethodandtherangeofvaluesthatmaybeencountered:Determinestorageandprocessingcapabilities.Numericalaccuracy:relatedtoprocessingpower;hardwarecostrequiredfordatastorageandprocessing:highorlowcost.
Twocommonlyusedformats:fixed-pointformat:fixed-pointformatallowsalimitedrangeofvalues,butrequiressimpleprocessinghardware;floating-pointformat:allowsalargerangeofvalues,butrequiresmorecomplexprocessinghardware.
1.Fixed-pointnumberrepresentation:Fixed-pointmeansthatthepositionofthedecimalpointisfixed.Inordertofacilitateprocessing,itisgenerallydividedintofixed-pointpureintegersandpuredecimals.
2.Floating-pointnumberrepresentation:Becausetherangeofvaluestoberepresentedisverydifferent,whichbringsalotofinconveniencetostorageandcalculation,floating-pointarithmeticappears.
Floatingpointnotation,thatis,thepositionofthedecimalpointisfloating.Theideacomesfromscientificnotation.IEEE754floating-pointnumber(morespecial)floating-pointnumberstandardization:mainlytosolvetheproblemofnon-uniquenessofthesamefloating-pointnumberrepresentation.Specify,otherwisethemantissashouldbeshiftedleftorright.
Theconceptofmachinezero:themantissais0ortheordercodevalueislessthanthesmallestnumberthatcanberepresented.
3.Therepresentationmethodofdecimalnumberstring:Sincepeoplearemorefamiliarwithdecimal,itisnecessarytoincreasethesupportfordecimaloperationsinthecomputer.Twomethods:convertdecimalnumberintobinarynumberoperation,andthenchangefrombinarytodecimalwhenoutput.Directdecimalcalculation.Representationmethodofdirectoperation:stringform:usedfornon-numericalcalculationfield,compresseddecimalnumberstring:dividedintofixedlengthandvariablelength.Correspondingdecimalarithmeticunitandinstructionsupportarerequired.
4.Customdatarepresentation:markerdatarepresentation,descriptordatarepresentation.Difference:Theidentifierisconnectedtoeachdata,andthetwoarestoredtogetherinastorageunit,andthedescriptormustbestoredseparatelyfromthedata;inthedescriptorrepresentation,thedescriptorisaccessedfirst,andthenthedataisaccessed.Atleastonememoryaccessisadded;descriptionSymbolsarepartoftheprogram,notpartofthedata.Originalcode:Morenaturalnotation,thehighestbitrepresentsthesign,0ispositive,1isnegative.Advantages:simpleandeasytounderstand.Disadvantages:complexadditionandsubtractionoperations.Complement:Itisconvenientforadditionandsubtraction,andsubtractioncanbeconvertedtoaddition.Thecomplementofafixed-pointdecimal.Fixed-pointinteger'scomplement,inversecode:Introducedfortheconvenienceofcalculatingthecomplement.Complementthecodefromtheinversecode:thesymbolpositionis1,thebitsareinverted,andthelastbitisincreasedby1.Shiftcode:Itisusedtoexpresstheordercode.Itiseasytocomparethesizeoftwocodeshifts,whichisconvenientforordering.
ASCIIcodeinputcode:usedforChinesecharacterinput;Chinesecharacterstorage;fontcode:usedforChinesecharacterdisplay.Twomethodsofremainderprocessing:restoringremaindermethod:theoperationstepsareuncertain,thecontroliscomplicated,anditisnotsuitableforcomputeroperations.Alternateadditionandsubtractionmethod:Theremainderisnotrestored,thecalculationstepsaredetermined,anditissuitableforcomputeroperations.Logicalnumberconcept:unsignedbinarynumber.Fourlogicaloperations:logicalnegation,logicaladdition,logicalmultiplication,andlogicalexclusive.Multi-functionalarithmetic/logicoperationunit(ALU)Parallelcarry,twoproblemswithtravelingwavecarryadder/subtractor:longoperationtime,travelingwavecarryadder/subtractorcanonlycompleteadditionandsubtraction,butnotlogicaloperations,ThecontrolterminalMisusedtocontrolwhethertoperformarithmeticoperationsorlogicaloperations.Thedifferencebetweenthetwooperationsliesinwhetherthecarryisprocessed.WhenM=0,ithasnoeffectonthecarryandisanarithmeticoperation;whenM=1,thecarryisblockedanditisalogicaloperation.Inpositivelogic,"1"isrepresentedbyahighlevel,and"0"isrepresentedbyalowlevel,whilenegativelogicisjusttheopposite.Therelationshipbetweenlogicandnegativelogicisthatthe"and"ofpositivelogicbecomes"or"innegativelogic,thatis,+·exchange.
Internalbus,busclassification:internalbus,externalbus(systembus),communicationbus.Thebuscanbedividedintoone-waybusandtwo-waybus.Thebuswithlatchcanrealizebusmultiplexing.ThearithmeticunitincludeslogiccomponentssuchasALU,arraymultiplicationanddivisiondevices,registers,multiplexers,three-statebuffers,anddatabuses.ThedesignofthearithmeticunitmainlyrevolvesaroundhowtotransferoperandsandoperationresultsbetweentheALUandtheregisterandthedatabus.Therearethreestructuralformsofthearithmeticunit:asingle-busstructurearithmeticunit:Themaindisadvantageofthisstructureisthattheoperationprogressisrelativelyslow,butthecontrolcircuitisrelativelysimple.Thearithmeticunitwithdualbusstructure.Thearithmeticunitofthethree-busstructure:Thecharacteristicofthearithmeticunitofthethree-busstructureisfastoperationtime.
Structure
Thearithmeticunitincludesthreeparts:register,executionpartandcontrolcircuit.Thereare3registersinatypicalarithmeticunit:thereceivingregisterthatreceivesandsavesoneoperand;theaccumulationregisterthatsavestheotheroperandandtheresultoftheoperation;themultiplierregisterthatsavesthemultiplierorquotientwhenmultiplyinganddividingoperations.Executioncomponentsincludeanadderandvarioustypesofinputandoutputgates.Thecontrolcircuitsendsoutdifferentcontrolsignalsaccordingtoacertaintimesequence,sothatthedataenterstheregisterortheadderthroughthecorrespondinggatecircuittocompletethespecifiedoperation.Inordertoreducetheaccesstothememory,thearithmeticunitsofmanycomputershavemoreregisterstostoreintermediatecalculationresultssothattheycanbedirectlyusedasoperandsinsubsequentcalculations.Inordertoincreasethecalculationspeed,somelargecomputershavemultiplearithmeticunits.Theycanbedifferenttypesofarithmeticunits,suchasfixed-pointadders,floating-pointadders,multipliers,etc.,ortheycanbethesametypeofarithmeticunits.Thecompositionofthearithmeticunitisdeterminedbythedesignideasanddesignrequirementsofthewholemachine,anddifferentarithmeticmethodswillleadtodifferentcompositionofthearithmeticunit.However,becausethebasicfunctionsofthearithmeticunitsarethesame,andtheiralgorithmsareroughlythesame,thearithmeticunitsofdifferentmachinesaresimilar.Thearithmeticunitismainlycomposedofarithmeticlogiccomponents,generalregistergroupandstatusregister.1.ThearithmeticlogicunitALU.ALUmainlycompletesfixed-pointarithmeticoperations,logicaloperationsandvariousshiftoperationsonbinaryinformation.Arithmeticoperationsmainlyincludefixed-pointaddition,subtraction,multiplicationanddivisionoperations.LogicaloperationsmainlyincludelogicalAND,logicalOR,logicalexclusiveORandlogicalNOToperations.Theshiftoperationmainlycompleteslogicalleftandrightshifts,arithmeticleftandrightshiftsandothershiftoperations.Insomemachines,ALUalsoneedstocompletenumericalcomparison,changenumericalsign,calculatetheaddressofoperandinmemory,etc.ItcanbeseenthatALUisapowerfulcombinationallogiccircuit,sometimescalledamulti-functiongenerator,anditisthecorecomponentofthearithmeticunit.Thenumberofdatabits(iewordlength)thatALUcanhandledependsonthemachine.Forexample,intheZ80single-boardcomputer,theALUis8bits;intheIBMPC/XTandATmachines,theALUis16bits;inthe386and486microcomputers,theALUis32bits.ALUhastwodatainputterminalsandonedataoutputterminal.Theinputandoutputdatawidth(thatis,thenumberofbits)isthesameasthedatawidthprocessedbyALU.
2.Thearithmeticunitofthemachinedesignedbythegeneralregistersethasasetofgeneralregisters.Itismainlyusedtosavetheoperandsparticipatingintheoperationandtheresultoftheoperation.Earlymachinesonlydesignedaregistertostoreoperands,operationresults,andperformshiftoperations
.Becauseitcanbeusedtostorerepeatedlyaccumulateddata,itisoftencalledanaccumulator.Allgeneralregisterscanbeusedasaccumulators.Thedataaccessspeedofgeneralregistersisveryfast,generallyadozennanoseconds(μs).IfbothoperandsofALUcomefromregisters,theoperationspeedcanbegreatlyimproved.General-purposeregisterscanbeusedasspecialregistersatthesametime,includingtheaddressusedtocalculatetheoperand(usedtoprovidetheformaladdressoftheoperand,andthenformaneffectiveaddresstoaccessthemainmemoryunit).Forexample,itcanbeusedasindexregister,programcounter(PC),stackpointer(SP),etc.Itmustbenotedthatdifferentmachinesusethissetofregistersandthenumberofsettingsisdifferent.
3.StatusregisterThestatusregisterisusedtorecordtheresultstatusofarithmetic,logicoperationortestoperation.Inprogramdesign,thesestatesareusuallyusedasthejudgmentconditionsofconditionaltransferinstructions,sotheyarealsocalledconditioncoderegisters.Generally,thefollowingstatusbitsareset:
1)Zeroflagbit(Z):Whentheoperationresultis0,theZpositionis"1";whenitisnot0,itissetto"0";
2)Negativeflagbit(N):Whentheoperationresultisnegative,theNpositionis"1";whenitispositive,itissetto"0";
3)Overflowflagbit(V):Whentheoperationresultoverflows,theVpositionis"1";whenthereisnooverflow,itissetto"0";
4)Carryorborrowflag(C):Whendoingaddition,iftheoperationresultisthehighestThesignificantbit(forsignednumbers,thesignbit;forunsignednumbers,thehighestbitofthevalue),whenacarryoccursforward,theCpositionis"1";whenthereisnocarry,itissetto"0".Whendoingsubtraction,ifitisnotenoughtosubtract,andthemostsignificantbithasaborrowforward(thereisnocarryforwardatthistime),theCpositionis"1";whenthereisnoborrow(thatis,thereisacarrygeneration),theCpositionis"0".Inadditiontotheabovestates,thestatusregisterisoftenprovidedwithsomeflagbitsthatsaveinformationaboutinterruptsandmachineworkingstates(userstateorcorestate)(itshouldbenotedthatthecontentandflagsymbolsspecifiedbydifferentmachinesarenotexactlythesame),soastobetimelyReflecttheworkingstatusofthemachinerunningtheprogram,sosomemachinescallit"programstatusword"or"processorstatusword"(ProcessorStatusWord,PSW).
Performanceindicators
1.Machinewordlength,machinewordlengthreferstothebasicdigitsofthedatainvolvedintheoperation.Itdeterminesthenumberofbitsofregisters,arithmeticunitsanddatabuses,whichdirectlyaffectsthepriceofhardware.Thewordlengthindicatestheaccuracyofthecalculation.Inordertocoordinateaccuracyandcost,andmeetvariousrequirements,manycomputersallowvariablewordlengthcalculations,suchashalfwordlength,fullwordlength,anddoublewordlength.Sincethenumbersandinstructioncodesareplacedinthemainmemory,thewordlengthandtheinstructioncodelengthoftenhaveacorrespondingrelationship,andthewordlengthalsoaffectsthestrengthoftheinstructionsystemfunction.Computerwordlengthsrangefrom4bits,8bits,16bits,32bitsto64bits.Themachinewordlengthcancontainoneormorebytes.Inordertoensureaccuracy,themachineusedforscientificcomputingneedsalongwordlength;fordataprocessingandindustrialcontrolmachines,awordlengthof16or32bitscanmeettherequirements.
2.ComputingspeedItisoneofthemainindicatorsofacomputer.Thetimerequiredforthecomputertoperformdifferentcalculationsandoperationsmaybedifferent,sotherearedifferentcalculationmethodsforthecalculationspeed.Generally,theaveragespeedisusuallyexpressedbytheaveragenumberofinstructionsthatcanbeexecutedperunitoftime.Forexample,acomputeroperatingspeedof1milliontimespersecondmeansthatthemachinecanexecuteanaverageof1millioninstructionsinonesecond(ie1MIPS).Sometimestheweightedaveragemethod(thatis,calculationbasedontheexecutiontimeofeachinstructionandthepercentageoftheinstructioninalloperations)isusedtoexpresstheequivalentspeed.
Functionclassification
Thebasicfunctionofthearithmeticunitistocompletetheprocessingofvariousdata,suchasthefourarithmeticoperations,logicaloperationssuchasAND,OR,negation,arithmeticandlogicshiftBitmanipulation,comparingvalues,changingsigns,calculatingmainmemoryaddresses,etc.Theregisterinthearithmeticunitisusedtotemporarilysavethedataparticipatingintheoperationandtheintermediateresultoftheoperation.Correspondingcomponentsarealsosetinthearithmeticunittorecordthecharacteristicsoftheresultofanoperation,suchaswhetheritoverflows,thesignbitoftheresult,whethertheresultiszero,andsoon.Therearemanytypesofarithmeticunitsusedbycomputers,andtherearedifferentclassificationmethodsfromdifferentperspectives.Fromtherepresentationofthedecimalpoint,itcanbedividedintofixed-pointarithmeticandfloating-pointarithmetic.Thefixed-pointarithmeticunitcanonlyperformfixed-pointnumberoperations,andischaracterizedbyasmallerrangerepresentedbythemachinenumber,butasimplerstructure.Floatingpointarithmetichasstrongfunctions,whichcanperformoperationsonbothfloating-pointnumbersandfixed-pointnumbers.Thenumberrepresentationrangeisverylarge,butthestructureisquitecomplicated.Fromthecarrysystem,itisdividedintobinaryarithmeticanddecimalarithmetic.Generally,computersusebinaryarithmeticunits.Ascomputersarewidelyusedinbusinessanddataprocessing,moreandmoremachineshaveexpandedthefunctionsofdecimalarithmetic,sothatthearithmeticunitscanperformbothbinaryanddecimalarithmetic.Thearithmeticunitinthecomputerneedstohavethefunctionofcompletingavarietyofarithmeticoperations,sovariousalgorithmsmustbeintegratedtodesignacompletearithmeticcomponent.Floatingpointarithmeticunit
1.Thegeneralstructureoffloatingpointarithmeticunit
Floatingpointarithmeticcanberealizedbytwolooselyconnectedfixed-pointarithmeticcomponents:namelyTheordercodecomponentandthemantissacomponent,thegeneralstructureofthefloatingpointarithmeticunit,themantissacomponentisessentiallyageneralfixed-pointarithmeticunit,whichisrequiredtoimplementfourbasicarithmeticoperationsofaddition,subtraction,multiplication,anddivision.Amongthem,threesingle-wordlongregistersareusedtostoretheoperands:ACistheaccumulator,MQisthemultiplierregister,andDRisthedataregister.ACandMQcanalsobeconnectedtoformadouble-wordlongregisterAC-MQthatshiftsleftandright.Paralleladderisusedtocompletetheprocessingof
intodata.ItsinputcomesfromACandDR,andtheresultissentbacktoAC.TheMQregisterstoresthemultiplierduringmultiplicationandthequotientduringdivision,soitiscalledthemultiplierregister.DRisusedtostorethemultiplicandordivisor,andtheresult(productorquotientandremainder)isstoredinAC-MQ.Inthefourarithmeticoperations,thetypicalmethodsofusingtheseregistersareasfollows:
OperationcategoryregisterrelationshipadditionAC+DR→ACsubtractionAC-DR→ACmultiplicationDR×MQ→AC－MQdivisionAC÷DR→AC－MQ
Fortheordercodecomponent,aslongasitcanperformordercodeaddition,subtractionandcomparisonoperations.InFigure2-21,theorderpartoftheoperandisplacedinregistersE1andE2,whichareconnectedtotheparalleladderforcalculation.Theordercodecomparisonrequiredforfloating-pointadditionandsubtractionisrealizedthroughE1-E2,andtheresultofthesubtractionisputintothecounterE,andthenaccordingtothesignofE,itisdeterminedwhichordercodeislarger.Beforethemantissaisaddedorsubtracted,amantissaneedstobeshifted.ThisiscontrolledbythecounterE.ThepurposeistoreducethevalueofEto0inorder.EachtimeEissubtractedby1,thecorrespondingmantissaisshiftedtotherightby1bit.Oncethemantissaisfinishedathighspeed,theycanbeprocessedaccordingtotheusualfixed-pointmethod.TheordercodevalueoftheoperationresultisstillputinthecounterE.
2.Pointcoprocessor,80x87isaspecialarithmeticoperationprocessordesignedandproducedbyIntelCorporationforprocessingfloating-pointnumbersandotherdataarithmeticoperationsandavarietyoffunctioncalculations.Becausetheirarithmeticoperationsarecarriedoutwith80x86CPU,theyarealsocalledcoprocessors.Wetake80x87asanexampletodiscussthecompositionoffloating-pointarithmeticcomponents.Themainfunctionsofthefloating-pointcoprocessorareasfollows:(1)ItcanworkasynchronouslyandinparallelwiththesupportingCPUchip.80x87isequivalenttoanI/Ocomponentof386.Ithasitsowninstructions,butitcannotbeusedalone.Itcanonlybeusedasacoprocessorofthe386mainCPUtooperate.Becausetherealworkofreadingandwritingmainmemoryisnotdoneby80x87,butby386.Iftheinstructionreadbythe386fromthemainmemoryisan80x87floating-pointarithmeticinstruction,theysendtheinstructionto80x87inoutputmode,andafter80x87receivesit,itdecodesandperformsfloating-pointarithmetic.Duringtheoperationofthe80x87,the386cantakeanotherinstructiontoexecute,thusachievingparallelwork.Ifthe386fetchesanother80x87instructionwhilethe80x87isexecutingthefloating-pointarithmeticinstruction,the80x87rejectsitbygivinga"busy"signsignal,causingthe386tosuspendsendingcommandstothe80x87.Onlyafter80x87completesthefloatingpointoperationandcancelsthe"busy"signsignal,the386canperformasendingoperation.(2)Theinternalstructureofhigh-performance80-bitwordlength,thereare880-bitwordlengthregistergroupsmanagedbystack.80x87uses80-bittemporaryrealnumbersandother6datatypestoperformautomaticconversionwhenfetchingnumbersfromthememoryandwritingnumberstothememory.Alldataarerepresentedintheformof80-bittemporaryrealnumbersin80x87.Therefore,80x87hasan80-bitinternalstructure,andthereareeight80-bitword-lengthregistergroupsmanagedina"first-in-last-out"manner,alsoknownastheregisterstack.Theseregisterscanworkinastackmode.Atthistime,thetopofthestackisusedasanaccumulator;itisalsopossibletodirectlyaccessanyregisteraccordingtotheregisternumber.(3)Theformatoffloating-pointnumbersisinfullcompliancewiththeinternationalstandardsestablishedbyIEEE.(4)Itcanprocess7kindsofdataincludingbinaryfloating-pointnumbers,binaryintegersanddecimalnumberstrings.The7datatypesarerepresentedintheregisterasfollows:shortinteger(32-bitinteger)S31-bit(two'scomplement)longinteger(64-bitinteger)S63-bit(two'scomplement)shortrealnumber(32-bitfloatingpoint)SExponentmantissa(23bits)Longrealnumber(64-bitfloatingpointnumber)SExponentmantissa(52bits)Temporaryrealnumber(80-bitfloatingpointnumber)SExponentmantissa(64bits)Decimalnumberstring(decimal18bits)S－－d17d16...d1d0.HereSisasignbit,0standsforpositiveand1standsfornegative.Thebasevalueofthethreefloating-pointnumbersis2.Theordercodevalueisexpressedbyashiftcode,andthemantissaisexpressedbytheoriginalcode.Therearethreetypesofmantissa:32-bit,64-bit,and80-bit.Itisnotonlyafloatingpointarithmeticunit,butalsoincludesallthecontrolcircuitsneededtoperformdataoperations.Asfarastheoperationpartisconcerned,therearepartsthatprocesstheexponentpartofthefloatingpointnumberandthepartthatprocessesthemantissapart,aswellastheshiftoperationthatacceleratestheshiftoperation.Positionercircuits,whichareconnectedtoeight80-bitword-lengthregisterstacksthroughtheexponentbusandthedecimalbus.(5)InternalerrormanagementfunctionInordertoensurethecorrectexecutionoftheoperation,the80x87alsosetsupthree16-bitword-lengthregisters,namelythefeatureregister,thecontrolwordregisterandthestatusregister.Thecharacteristicregisteruseseverytwobitstoindicatethestatusofeachregisterintheregisterstack,thatis,whenthecharacteristicvalueis00-11fourcombinations,itindicatesthatthecorrespondingregisterhascorrectdata,datais0,dataisillegal,andthereisnodata.Thecontrolwordregisterisusedtocontroltheinternaloperationofthe80x87.PCistheprecisioncontrolbitfield(2bits):00is24bits,01isspare,10is53bits,and11is64bits.RCistheroundingcontrolbitfield(2bits):00isroundingtothenearest,01isroundedinthe-direction,10isroundedinthe+direction,and11isroundedto0.ICistheinfinitycontrolbit:whenthebitis0,+and-aretreatedasthesamevalue,andwhenthebitis1,+and-arenottreatedasthesamevalue.Thelower6bitsofthecontrolregisterareusedasabnormalinterruptmaskbits:IMisillegalprocessing,DMisillegaloperand,ZMis0asthedivisor,OMisoverflow,UMisunderflow,andPMisprecisiondecrease.Thestatuswordregisterisusedtoindicatethe80x87resultprocessing.Forexample,whenthe"busy"flagis1,itmeansthatafloating-pointarithmeticinstructionisbeingexecuted,andifitis0,itmeansthatthe80x87isidle.Thelower6bitsofthestatusregisterindicate6typesofabnormalerrors,whicharethesameasthelower6bitsofthecontrolregister.Whenthecontrolregisterbitis0(unmasked)andthestatusregisterbitis1,aninterruptrequestisgeneratedduetoanabnormalerror.
3.Thefloating-pointarithmeticunitintheCPU,PentiumCPUincludesthefloating-pointarithmeticunitinthechip.Floating-pointarithmeticcomponentsadoptpipelinedesign.Theinstructionexecutionprocessisdividedinto8pipelines.Thefirst4stagesareinstructionprefetch(DF),instructiondecoding(D1),addressgeneration(D2),operandfetching(EX),whicharecompletedintheU,Vpipeline;thelast4stagesareexecution1(X1),execution2(X2),theresultiswrittenbacktotheregisterfile(WF),errorreport(ER),completedinthefloatingpointcalculator.Undernormalcircumstances,afloating-pointoperationinstructioniscompletedbytheVpipeline.Thefloating-pointunithasspecialadders,multipliersanddividersforfloating-point,andaregisterfilecomposedof880-bitregisters,andtheinternaldatabusis80-bitwide.Therefore,thefloating-pointunitcansupportfloating-pointnumbersinsingle-precisionanddouble-precisionformatsoftheIEEE754standard.Inaddition,an80-bitfloatingpointnumbercalledatemporaryrealnumberisalsoused.Forfloating-pointfetching,addition,multiplicationandotheroperations,newalgorithmsareusedandimplementedbyhardware,andtheexecutionspeedismorethan10timesthatof80486.
Development
Inthe5thcenturyBC,theChineseinventedtheabacus,whichiswidelyusedincommercialtrade.Theabacusisconsideredtheearliestcomputerandhasbeenusedtoday.Insomeaspects,thecomputingpoweroftheabacusexceedsthatofthecomputer,andtheaspectoftheabacusreflectsthewisdomoftheChinesepeople.
Itwasnotuntilthe17thcenturythatcomputingequipmentmadethesecondmajoradvancement.In1642,FrenchmanBlaisePascal(1623-1662)inventedtheautomaticcarryadder,calledPascalene.In1694,theGermanmathematicianGottfriedWilhemvonLeibniz(1646-1716)improvedPascalinesothatitcouldcalculatemultiplication.Later,FrenchmanCharlesXavierThomasdeColmarinventedacalculatorthatcanperformfourarithmeticoperations.ThetrueoriginofmoderncomputerscomesfromCharlesBabbage,aBritishmathematicsprofessor.CharlesBabbagefoundthattherearemanyerrorsintheusualcomputingequipment.WhenstudyinginCambridge,hethoughtthatasteamenginecouldbeusedforcalculations.Atfirst,hedesignedthedifferenceenginetocalculatethenavigationtable.Later,hefoundthatthedifferenceenginewasonlyaspecialpurposemachine,sohegaveuptheoriginalresearchandbegantodesignananalysismachinethatincludedthebasiccomponentsofmoderncomputers.(AnalyticalEngine)
AlthoughBabbage’ssteam-poweredcomputerwasnotcompletedintheend,itisstillveryprimitivebytoday’sstandards.However,itoutlinesthebasicfunctionsofmoderngeneral-purposecomputersandisaconceptualbreakthrough..
Inthefollowingyears,manyengineersmadeimportantprogressinotherareas.TheAmericanHermanHollerith(1860-1929)inventedtheperforatedsheetcomputerbasedontheprincipleofthejacquardloom.Andbringitintothecommercialfieldtoestablishacompany.
Thedevelopmenthistoryofmoderncomputers
Thefirstgenerationofelectronictubecomputers(1946-1957)
February15,1946,ENIAC(ElectronicNumericalIntegratorandComputer)wasmadepublicinPhiladelphia.ENIACrepresentsamilestoneinthehistoryofcomputerdevelopment.Italsohasparallelcomputingcapabilitiesthroughrewiringprogrammingbetweendifferentparts.ENIACisjointlydevelopedbytheUSgovernmentandtheUniversityofPennsylvania.Ituses18,000tubes,70,000resistors,5millionsolderjoints,consumes160kilowattsofpower,andhasacalculationspeedof5,000operationspersecond.Thefirstgenerationofcomputersischaracterizedbyoperatinginstructionsthatareprogrammedforspecifictasks.Eachmachinehasitsowndifferentmachinelanguage,itsfunctionsarelimited,anditsspeedisslow.Anotherobviousfeatureistheuseofvacuumtubesandmagneticdrumstostoredata.
Thesecond-generationtransistorcomputer(1957-1964)
In1948,thetransistorwasinventedtoreplacethebulkyelectronictube.Thevolumeoftheequipmentcontinuestodecrease.In1956,transistorswereusedincomputers,andtransistorsandmagneticcorememoryledtothesecondgenerationofcomputers.Thesecond-generationcomputersaresmallinsize,fastinspeed,lowinpowerconsumption,andmorestableinperformance.In1960,thereweresomesecond-generationcomputersthatweresuccessfullyusedinbusiness,universities,andgovernmentdepartments.Second-generationcomputersreplacedelectrontubeswithtransistors,andsomepartsofmoderncomputers:printers,tapes,disks,memory,operatingsystems,andsoon.Theprogramsstoredinthecomputermakethecomputeradaptableandcanbeusedmoreeffectivelyforcommercialpurposes.Duringthisperiod,moreadvancedlanguagessuchasCOBOLandFORTRANappearedtomakecomputerprogrammingeasier.Newprofessions(programmers,analysts,andcomputersystemsexperts)andtheentiresoftwareindustrywereborn.
Thethird-generationintegratedcircuitcomputer(1964-1972)
In1958,TexasInstrumentsengineerJackKilbyinventedtheintegratedcircuit(IC),combiningthreeelectroniccomponentsintoasmallOnasmallsiliconchip.Morecomponentsareintegratedonasinglesemiconductorchip,andcomputersbecomesmaller,consumelesspower,andarefaster.Thedevelopmentofthisperiodalsoincludedtheuseofoperatingsystems,whichenabledthecomputertorunmanydifferentprogramssimultaneouslyunderthecontrolandcoordinationofthecentralprogram.
Thefourth-generationlarge-scaleintegratedcircuitcomputer(1972-present)
Large-scaleintegratedcircuit(LSI)canaccommodatehundredsofcomponentsonachip.Bythe1980s,verylargescaleintegratedcircuits(VLSI)containedhundredsofthousandsofcomponentsonachip,andlater(ULSI)expandedthenumbertothemillions.Theabilitytoaccommodatesuchanumberofcomponentsonacoin-sizedchipmakesthesizeandpriceofthecomputercontinuetodecline,whilethefunctionalityandreliabilitycontinuetoincrease.Inthemid-1970s,computermanufacturersbegantobringcomputerstoordinaryconsumers.Atthistime,minicomputershadsoftwarepackageswithfriendlyinterfaces,programsfornon-professionals,andthemostpopularwordprocessingandspreadsheetprograms.In1981,IBMintroducedpersonalcomputers(PCs)foruseinhomes,offices,andschools.Thecompetitionofpersonalcomputersinthe1980scausedpricestocontinuetofall,thenumberofmicrocomputerscontinuedtoincrease,andcomputerscontinuedtoshrinkinsize.TheAppleMacintoshseries,whichcompeteswiththeIBMPC,waslaunchedin1984.TheMacintoshprovidesafriendlygraphicalinterfacethatuserscaneasilyoperatewithamouse.
ChronicleofChronicles
In1666,SamuelMorlandintheUnitedKingdominventedamechanicalcountingmachinethatcancalculateadditionsandsubtractions.
In1673,GottfriedLeibnizmadeasteppedcylindricalreelcountingmachinecalled"SteppedReckoner".ThiscalculatorcanmultiplyrepeatednumbersandautomaticallyAddittotheadder.
In1694,theGermanmathematician,GottfriedLeibniz,improvedPascaleneofPascaleandcreatedamachinethatcancalculatemultipliers.Itisstilloperatedbygearsanddials.
In1773,Philipp-Matthausmanufacturedandsoldasmallnumberofcomputingmachinesaccurateto12bits.
In1775,ThethirdEarlofStanhopeinventedamultiplicationcalculatorsimilartoLeibniz.
In1786,J.H.Muellerdesignedadifferentialengine,butunfortunatelytherewasnofundingtomakeit.
In1801,Joseph-MarieJacquard'sloomusedsequentialpunchcardstocontroltheweavingpattern.
In1854,GeorgeBoolepublished"AnInvestigationoftheLawsofThought",whichisaboutsymbolsandlogicalreasons,whichlaterbecamethebasicconceptofcomputerdesign.
In1858,atelegraphlinecrossedtheAtlanticforthefirsttimeandprovidedseveraldaysofservice.
In1861,atelegraphlineacrossthecontinentconnectedtheAtlanticandPacificcoasts.
In1876,AlexanderGrahamBellinventedthetelephoneandobtainedapatent.
From1876to1878,BaronKelvinmanufacturedanovertoneanalyzerandtidepredictor.
In1882,WilliamS.Burroughsquithisjobasabankclerkandfocusedontheinventionoftheadder.
In1889,HermanHollerith'selectricwatchmakingmachineperformedwellinthecompetitionandwasusedinthe1890census.HermanHollerithusestheconceptoftheJacquardloomforcalculations.Heusesacardtostoredataandtheninjectstheresultsintothemachinetocompile.Thismachineenabledthecensusresultsthatwouldhavetakentenyearstobeobtainedinjustsixweeks.
In1893,thefirstfour-functioncalculatorwasinvented.
In1895,GuglielmoMarconisentabroadcastsignal.
In1896,HollerithestablishedtheTabulatingMachineCompany(TabulatingMachineCompany).
In1901,thepunchkeyappeared,andtherewereveryfewchangesinthefollowinghalfacentury.
In1904,JohnA.Flemingobtainedthepatentforvacuumdiodes,whichestablishedthefoundationforradiocommunication.
In1906,LeedeForedtaddedadiodewithathirdvalveinFelmingandcreatedathree-electrodevacuumtube.
In1907,recordmusicformedthefirstofficialradiostationinNewYork.
In1908,BritishscientistCampbellSwintondescribedtheelectronicscanningmethodandpredictedtheuseofcathoderaytubestomaketelevisions.
In1911,Hollerith'swatchcompanymergedwithtwoothercompaniestoformtheComputerTabulatingRecordingCompany(C-T-R),awatchmakingandrecordingcompany.Butin1924,itwasrenamedInternationalBusinessMachineCorporation(IBM).
In1911,theDutchphysicistKamerlinghOnnesdiscoveredsuperconductivityinLeidenUnversity.
In1931,VanneverBushinventedacountingmachinethatcansolvedifferenceprograms.Thismachinecansolvesomecomplicateddifferenceprogramsthatmakemathematiciansandscientistsheadaches.
In1935,IBM(InternationalBusinessMachineCorporation)introduced"IBM601",whichisapunchcardmachinewitharithmeticcomponentsandamultiplierthatcanbecalculatedin1second.Itplaysagreatroleinscientificandcommercialcalculations.Atotalof1,500unitsweremanufactured.
In1937,AlanTuringcameupwiththeconceptofa"UniversalMachine",whichcanexecuteanyalgorithm,formingabasicconceptof"computability".TheconceptofTuringisbetterthanotherinventionsofthesametypebecauseitusestheconceptofsymbolprocessing.
InNovember1939,JohnVincentAtannsoffandJohnBerrybuilta16-bitadder.Itisthefirstmachinetocalculatewithvacuumtubes.
In1939,ZuseandSchreyercreated"V2"[latercalledZ2].ThismachineusesZ1'smechanicalstorage,plusanewarithmeticcomponentusingRelayLogic..ButwhenZusefinishedthedraft,theplanwasinterruptedforayear.
In1939-40,Schreyercompleteda10-digitadderwithavacuumtubeandamemorywithaneonlamp(neonlight).
InJanuary1940,atBellLabs,SamuelWilliamsandStibitzcompletedamachinethatcancalculatecomplexnumbers,calledthe"ComplexNumberCalculator",whichwaslaterrenamedthe"CircuitBreaker"CountingmachinemodelI(ModelIRelayCalculator)".Itusestelephoneswitchpartsaslogiccomponents:145circuitbreakersand10barswitches.Thenumbersarerepresentedby"Plus3BCD".InSeptemberofthesameyear,theteletypeetypewasinstalledinamathconferenceandwasconnectedtoNewYorkbyNewHampshire.
In1940,ZusefinallycompletedZ2.Itworkedbetterthanbutnottooreliable.
Inthesummerof1941,AtanasoffandBerrycompletedacalculatordesignedtosolvethesystemofsimultaneouslinearequations(systemofsimultaneouslinearequations),whichwaslatercalled"ABC(Atanasoff-BerryComputer)".Thereare6050-bitmemoriesinstalledontworotatingdrumsintheformofcapacitors(capacitories),andtheclockspeedis60Hz.
InFebruary1941,Zusecompleted"V3"(latercalledZ3),whichwasthefirstcountingmachinethatcouldbeprogrammedinoperation.Italsousesfloatingpointoperations,witha7-bitexponent,a14-bitmantissa,andasign.Thememorycanstore64words,so1400breakersareneeded.Ithasmorethan1200arithmeticandcontrolcomponents,andtheprogramming,inputandoutputarethesameasZ1.InJanuary1943,HowardH.Aikencompleted"ASCCMarkI"(AutomaticSequence-ControlledCalculatorMarkI),alsoknownas"HawardMarkI".Thismachineis51feetlong,weighs5tons,andismadeupof750,000parts.Ithas72accumulators,eachwithitsownarithmeticunit,anda23-digitregister.
InDecember1943,TommyFlowersandhisteamcompletedthefirst"Colossus".Ithad2,400vacuumtubesusedaslogiccomponents,and5papertapeloopreaders(readers),eachEachcanwork5000characterspersecond.
In1943,undertheleadershipofJohnBrainered,ENIACbeganresearch.JohnMauchlyandJ.PresperEckertareresponsiblefortheimplementationofthisplan.
Thefirstelectronicdigitalintegralcalculator(ENIAC)wasbuiltintheUnitedStatesin1946v.
In1947,theAmericanSocietyofCalculators(ACM)wasestablished.
In1947,BritaincompletedthefirststoragevacuumtubeO1948BellTelephoneCompanydevelopedintoasemiconductor.
In1949,Britaincompletedtheconstructionofthe"DelayedStorageElectronicAutomaticCalculator"(EDSAC)
In1950,theterm"automation"wasfirstusedintheautomotiveindustry.
In1951,theMassachusettsInstituteofTechnologymadeamagneticcore
In1952,thefirst"storedprogramcalculator"wasborn.
In1952,thefirstlarge-scalecomputersystemIBM701announcedthecompletionofitsconstruction.
In1952,thefirstsignlanguagetranslationmachinewasinvented.
In1954,thefirstsemiconductorcomputerwassuccessfullydevelopedbyBellTelephoneCompany.
In1954,thefirstgeneral-purposedataprocessorIBM650wasborn.
In1955,thefirstlarge-scalecomputerIBM705usingamagneticcorewasbuilt.
In1956,IBMlaunchedthescientific704computer.In1957,theprogramminglanguageFORTRANcameout.
In1959,thefirstsmallscientificcalculatorIBM620wassuccessfullydeveloped.
In1960,thedataprocessingsystemIBM1401wassuccessfullydeveloped.
In1961,theprogramminglanguageCOBOLcameout.
In1961,thefirstsub-systemcomputerwasdesignedandcompletedbytheMassachusettsInstituteofTechnology.
In1963,theBASIClanguagecameout.
In1964,thethird-generationcomputerIBM360serieswasmade.
In1965,AmericanDigitalEquipmentCorporationlaunchedthefirstminicomputerPDP-8.
In1969,IBMsuccessfullydevelopeda90-columncardmachineandsystem--3computersystem.
In1970,theIBMsystem1370computerserieswasmade.
In1971,theUniversityofIllinoisdesignedtheIllinoisIVsupercomputer.
In1971,thefirstmicroprocessor4004wassuccessfullydevelopedbyIntelCorporation.
In1972,microprocessorsubstratesbegantobemass-producedandsold.
In1973,thefirstfloppydiskwassuccessfullydevelopedbyIBM.In1975,ATARI-8800microcomputercameout.
In1977,KomodorCompanydeclaredthatthecompletecombinationmicrocomputerPET-2001wassuccessfullydeveloped.
In1977,theTRS-80microcomputerwasborn.
In1977,theApple-IItypemicrocomputerwasborn.
In1978,verylargescaleintegratedcircuitsbegantobeused.
In1978,bubblememorywasusedincommercialcomputersforthesecondtime.
In1979,Sharpannouncedtheproductionofthefirstportablemicrocomputer.
In1982,microcomputersbegantospread,andalargenumberofthementeredschoolsandhomes.
In1984,theJapanesecomputerindustrystartedtodevelopthe"fifthgenerationcomputer"---computerwithartificialintelligence