(完整版)电气专业中英文对照翻译毕业设计论文

优秀论文审核通过未经允许切勿外传Chapter3DigitalElectronics3.1IntroductionAcircuitthatemploysanumericalsignalinitsoperationisclassifiedasadigitalcircuitputers,pocketcalculators,digitalinstruments,andnumericalcontrol(NC)equipmentarecommonapplicationsofdigitalcircuits.Practicallyunlimitedquantitiesofdigitalinformationcanbeprocessedinshortperiodsoftimeelectronically.Withoperationalspeedofprimeimportanceinelectronicstoday,digitalcircuitsareusedmorefrequently.Inthischapter,digitalcircuitapplicationsarediscussed.Therearemanytypesofdigitalcircuitsthatelectronics,includinglogiccircuits,flip-flopcircuits,countingcircuits,andmanyothers.Thefirstsectionsofthisunitdiscussthenumbersystemsthatarebasictodigitalcircuitunderstanding.TheremainderofthechapterintroducessomeofthetypesofdigitalcircuitsandexplainsBooleanalgebraasitisappliedtologiccircuits.3.2DigitalNumberSystemsThemostcommonnumbersystemusedtodayisthedecimalsystem,inwhich10digitsareusedforcounting.Thenumberofdigitsinthesystemiscalleditsbase(orradix).Thedecimalsystem，therefore，thecountingprocess.Thelargestdigitthatcanbeusedinaspecificplaceorlocationisdeterminedbythebaseofthesystem.Inthedecimalsystemthefirstpositiontotheleftofthedecimalpointiscalledtheunitsplace.Anydigitfrom0to9canbeusedinthisplace.Whennumbervaluesgreaterthan9areused,theymustbeexpressedwithtwoormoreplaces.Thenextpositiontotheleftoftheunitsplaceinadecimalsystemisthetensplace.Thenumber99isthelargestdigitalvaluethatcanbeexpressedbytwoplacesinthedecimalsystem.Eachplaceaddedtotheleftextendsthenumbersystembyapowerof10.Anynumbercanbeexpressedasasumofweightedplacevalues.Thedecimalnumber2583,forexample,isexpressedas(2×1000)+(5×100)+(8×10)+(3×1).Thedecimalnumbersystemiscommonlyusedinourdailylives.Electronically,thebinarysystem.Electronically,thevalueof0canbeassociatedwithalow-voltagevalueornovoltage.Thenumber1canthenbeassociatedwithavoltagevaluelargerthan0.Binarysystemsthatusethesevoltagevaluesaresaidto,thischapter.Thetwooperationalstatesofabinarysystem,1and0,arenaturalcircuitconditions.Whenacircuitisturnedoffortheoff,or0,state.Anelectricalcircuitthattheon，or1,state.ByusingtransistororICs，itiselectronicallypossibletochangestatesinlessthanamicrosecond.Electronicdevicesmakeitpossibletomanipulatemillionsof0sandisinasecondandthustoprocessinformationquickly.Thebasicprinciplesofnumberingusedindecimalnumbersapplyingeneraltobinarynumbers.Thebaseofthebinarysystemis2,meaningthatonlythedigits0and1areusedtoexpressplacevalue.Thefirstplacetotheleftofthebinarypoint,orstartingpoint，representstheunits，oris,location.Placestotheleftofthebinarypointarethepowersof2.Someoftheplacevaluesinbase2are2o=1,21=2,22=4,23=8,2?=16,25=32,and26=64.Whenbasesotherthan10areused,thenumbersshouldexample.Thenumber100?(read“one,zero,zero,base2”)isequivalentto4inbase10,or410.Startingwiththefirstdigittotheleftofthebinarypoint,thisnumberthismethodofconversionabinarynumbertoanequivalentdecimalnumber，writedownthebinarynumberfirst.Startingatthebinarypoint，indicatethedecimalequivalentforeachbinaryplacelocationwherea1isindicated.Foreach0inthebinarynumberleaveablankspaceorindicatea0'Addtheplacevaluesandthenrecordthedecimalequivalent.Theconversionofadecimalnumbertoabinaryequivalentisachievedbyrepetitivestepsofdivisionbythenumber2.Whenthequotientisevenwithnoremainder,a0isrecorded.Whenthequotientprocesscontinuesuntilthequotientis0.Thebinaryequivalentconsistsoftheremaindervaluesintheorderlasttofirst.3.2.2Binary-codedDecimal(BCD)NumberSystemWhenlargenumbersareindicatedbybinarynumbers，theyaredifficulttouse.Forthisreason，theBinary-CodedDecimal(BCD)methodofcountingwasdevised.Inthissystemfourbinarydigitsareusedtorepresenteachdecimaldigit.Toillustratethisprocedure，thenumber105，isconvertedtoaBCDnumber.Inbinarynumbers，ToapplytheBCDconversionprocess，thebase10numberisfirstdividedintodigitsaccordingtoplacevalues.Thenumber10510givesthedigits1-0-5.Convertingeachdisplayedbythisprocesswithonly12binarynumbers.ThebetweeneachgroupofdigitsisimportantwhendisplayingBCDnumbers.ThelargestdigittobedisplayedbyanygroupofBCDnumbersis9.Sixdigitsofanumber-codinggrouparenotusedatallinthissystem.Becauseofthis,theoctal(base8)andthebinaryformbutusuallydisplaytheminBCD,octal,orabase8systemis7.Theplacevaluesstartingattheleftoftheoctalpointarethepowersofeight:80=1,81=8,82=64,83=512,84=4096,andsoon.Theprocessofconvertinganoctalnumbertoadecimalnumberisthesameasthatusedinthebinary-to-decimalconversionprocess.Inthismethod,equivalentdecimalis25810.ConvertinganoctalnumbertoanequivalentbinarynumberissimilartotheBCDconversionprocess.Theoctalnumberisfirstdividedintodigitsaccordingtoplacevalue.Eachoctaldigitisthenconvertedintoanequivalentbinarynumberusingonlythreedigits.Convertingadecimalnumbertoanoctalnumberisaprocessofrepetitivedivisionbythenumber8.Afterthequotientdetermined，theremainderisbroughtdownastheplacevalue.Whenthequotientisevenwithnoremainder，a0istransferredtotheplaceposition.Thenumberforconverting409810tobase8is100028.Convertingabinarynumbertoanoctalnumberisanimportantconversionprocessofdigitalcircuits.Binarynumbersarefirstprocessedataveryoutputcircuitthenacceptsthissignalandconvertsittoanoctalsignaldisplayedonareadoutdevice.mustfirstbedividedintogroupsofthree，startingattheoctalpoint.Eachbinarygroupisthenconvertedintoanequivalentoctalnumber.Thesenumbersarethencombined，whileremainingintheirsamerespectiveplaces，torepresenttheequivalentoctalnumber.3.2.4HexadecimalNumberSystemThedigitalsystemstoprocesslargenumbervalues.Thebaseofthissystemis16，whichmeansthatthelargestnumberusedinaplaceis15.Digitsusedbythissystemarethenumbers0-9andthelettersA-F.ThelettersA-Pareusedtodenotethedigits10-15，respectively.Theplacevaluestotheleftofthe.Theprocessofchangingaproperdigitalorder.Theplacevalues，orpowersofthebase，arethenpositionedundertherespectivedigitsinstep2.Instep3，thevalueofeachdigitisrecorded.Thevaluesinsteps2and3arethenmultipliedtogetherandadded.Thesumgivesthedecimalequivalentvalueofa.Initially，theconvertedtoabinarynumberusingfourdigitspergroup.Thebinarygroupiscombinedtoformtheequivalentbinarynumber.Theconversionofadecimalnumbertoa，aswithothernumbersystems.Inthisprocedurethedivisionisby16andremainderscanbeaslargeas15.Convertingabinarynumbertoagroupsoffourdigits，startingattheconvertedtoadigitalcircuit-designapplicationsbinarysignalsarefarsuperiortothoseoftheoctal，decimal，orbeprocessedveryeasilythroughelectroniccircuitry，sincetheycanberepresentedbytwostablestatesofoperation.Thesestatescanbeeasilydefinedasonoroff,1，orup0ordown，voltageornovoltage，rightorleft，oranyothertwo-conditionstates.Theremustbenoin-betweenstate.Thesymbolsusedtodefinetheoperationalstateofabinarysystemareveryimportant.Inpositivebinarylogic，thestateofvoltage，on，true，oraletterdesignation(suchasA)isusedtodenotetheoperationalstate1.Novoltage，off，false，andtheletterAarecommonlyusedtodenotethe0condition.Acircuitcanbesettoeitherstateandwillremaininthatstateuntilitiscausedtochangeconditions.Anyelectronicdevicethatcanbesetinoneoftwooperationalstatesorconditionsbyanoutsidesignalissaidtobebistable.Relays，lamps，switches，transistors,diodesandICsmaybeusedforthispurpose.Abistabledevice.Byusingmanyofthesedevices，itispossibletobuildanelectroniccircuitthatwillmakedecisionsbasedupontheappliedinputsignals.Theoutputofthiscircuitisadecisionbasedupontheoperationalconditionsoftheinput.Sincetheapplicationofbistabledevicesindigitalcircuitsmakeslogicaldecisions，theyarecommonlycalledbinarylogiccircuits.Ifweweretodrawacircuitdiagramforsuchasystem，includingalltheresistors，diodes，transistorsandinterconnections，wewouldfaceanoverwhelmingtask,andanunnecessaryone.Anyonewhoreadthecircuitdiagramwouldintheirmindgroupthecomponentsintostandardcircuitsandthinkintermsofthe"system"functionsoftheindividualgates.Forthisreason，wedesignanddrawdigitalcircuitwithstandardlogicsymbols.Threebasiccircuitsofthistypeareusedtomakesimplelogicdecisions.ThesearetheANDcircuit,ORcircuit,andtheNOTcircuit.Electroniccircuitsdesignedtoperformlogicfunctionsarecalledgates.Thistermreferstothecapabilityofacircuittopassorblockspecificdigitalsignals.Thelogic-gatesymbolsareshowninFig.3-1.ThesmallcircleattheoutputofNOTgateindicatestheinversionofthesignal.Mathematically，thisactionisdescribedasA=.Thuswithoutthesmallcircle，therectanglewouldrepresentanamplifier(orbuffer)withagainofunity.AnANDgatethe1statesimultaneously，thentherewillbea1attheoutput.TheANDgateinFig.3-1producesonlya1out-putwhenAandBareboth1.Mathematically，thisactionisdescribedasA·B=C.Thisexpressionshowsthemultiplicationoperation.AnORgateFig.3-1producesawheneitherorbothinputsarel.Mathematically，thisactionisdescribedasA+B=C.ThisexpressionshowsORaddition.Thisgateisusedtomakelogicdecisionsofwhetherornota1appearsateitherinput.AnIF-THENtypeofsentenceisoftenusedtodescribethebasicoperationofalogicstate.Forexample，iftheinputsappliedtoanANDgateareall1，thentheoutputwillbe1.Ifa1isappliedtoanyinputofanORgate，thentheoutputwillbe1.IfaninputisappliedtoaNOTgate，thentheoutputwillbetheoppositeorinverse.ThelogicgatesymbolsinFig.3-1showonlytheinputandoutputconnections.Theactualgates，whenwiredintoadigitalcircuit,wouldpin14and7.3.4CombinationLogicGatesWhenaNOTgateiscombinedwithanANDgateoranORgate，itiscalledacombinationlogicgate.ANOT-ANDgateiscalledaNANDgate，whichisaninvertedANDgate.MathematicallytheoperationofaNANDgateisAB=·.AcombinationNOT-OR，orNOR，gateproducesanegationoftheORfunction.MathematicallytheoperationofaNORgateisA+B=.A1appearsattheoutputonlywhenAis0andBis0.ThelogicsymbolsareshowninFig.3-3.ThebaroverCdenotestheinversion，ornegativefunction，ofthegate.Thelogicgatesdiscussed.Inactualdigitalelectronicapplications，solid-statecomponentsareordinarilyusedtoaccomplishgatefunctions.Booleanalgebraisaspecialformofalgebrathatwasdesignedtoshowtherelationshipsoflogicoperations.Thinformofalgebraisideallysuitedforanalysisanddesignofbinarylogicsystems.ThroughtheuseofBooleanalgebra，itispossibletowritemathematicalexpressionsthatdescribespecificlogicfunctions.Booleanexpressionsaremoremeaningfulthancomplexwordstatementsororelaboratetruthtables.ThelawsthatapplytoBooleanalgebraareusedtosimplifycomplexexpressions.Throughthistypeofoperationitmaybepossibletoreducethenumberoflogicgatesneededtoachieveaspecificfunctionbeforethecircuitsaredesigned.InBooleanalgebrathevariablesofanequationareassignedbylettersofthealphabet.Eachvariablethenexistsinstatesof1or0accordingtoitscondition.The1，ortruestate，isnormallyrepresentedbyasinglelettersuchasA，BorC.Theoppositestateorconditionisthendescribedas，or0false，andisrepresentedbyorA’.Thisisdescribedas，NOTAnegatedA，orAcomplemented.Booleanalgebraissomewhatdifferentfromconventionalalgebrawithrespecttomathematicaloperations.TheBooleanoperationsareexpressedasfollows:Multiplication:AANDB，AB，,A·BORaddition:AORB.A+BNegation，orcomplementing:NOTA，，A’AssumethatadigitallogiccircuitonlyCisonbyitselforwhenA，BandCareallonexpressiondescribesthedesiredoutput.Eight(23)differentcombinationsofA，B，andCexistinthisexpressionbecausetherearethree，inputs.Onlytwoofthosecombinationsshouldcauseasignalthatwillactuatetheoutput.Whenavariableisnoton(0)，itisexpressedasanegatedletter.Theoriginalstatementisexpressedasfollows:With，AB，andConorwithAoff,Boff,andCon，anoutput(X）willoccur:ABC+C=XAtruthtableillustratesifthisexpressionisachievedornot.Table3-1showsatruthtableforthisequation.First，ABCisdeterminedbymultiplyingthethreeinputstogether.A1appearsonlywhenthe，AB，andCinputsareall1.NextthenegatedinputsAandBaredetermined.ThentheproductsofinputsC，A，andBarelisted.ThenextcolumnshowstheadditionofABCandC.Theoutputofthisequationshowsthatoutput1isproducedonlywhenCis1orwhenABCis1.AlogiccircuittoaccomplishthisBooleanexpressionisshowninFig.3-4.Initiallytheequationisanalyzedtodetermineitsprimaryoperationalfunction.Step1showstheoriginalequation.Theprimaryfunctionisaddition，sinceitinfluencesallpartsoftheequationinsomeway.Step2showstheprimaryfunctionchangedtoalogicgatediagram.Step3showsthebranchpartsoftheequationexpressedbylogicdiagram，withANDgatesusedtocombineterms.Step4completestheprocessbyconnectingallinputstogether.Thecirclesatinputs，ofthelowerANDgateareusedtoachievethenegativefunctionofthesebranchparts.ThegeneralrulesforchangingaBooleanequationintoalogiccircuitdiagramareverysimilartothoseoutlined.Initiallytheoriginalequationmustbeanalyzedforitsprimarymathematicalfunction.Thisisthenchangedintoagatediagramthatisinputtedbybranchpartsoftheequation.Eachbranchoperationisthenanalyzedandexpressedingateform.Theprocesscontinuesuntilallbranchesarecompletelyexpressedindiagramformmoninputsarethenconnectedtogether.3.5TimingandStorageElementsDigitalelectronicsinvolvesanumberofitemsthatarenotclassifiedasgates.Circuitsordevicesofthistypetheoperationofasystem.Includedinthissystemaresuchthingsastimingdevices，torageelements，counters，decoders，memory，andregisters.Truthtablessymbols，operationalcharacteristics，andapplicationsoftheseitemswillbepresentedanICchip.Theinternalconstructionofthechipcannotbeeffectivelyaltered.Operationiscontrolledbytheapplicationofanexternalsignaltotheinput.Asarule，verylittleworkcanbedonetocontroloperationotherthanalteringtheinputsignal.ThelogiccircuitsinFig.3-4arecombinationalcircuitbecausetheoutputrespondsimmediatelytotheinputsandthereisnomemoryWhen.memoryisapartofalogiccircuit，thesystemiscalledsequentialcircuitbecauseitsoutputdependsontheinputplusitsaninputsignalisapplied.Abistablemultivibrator，inthestrictsense，isaflip-flop.Whenitisturnedon，itassumesaparticularoperationalstate.Itdoesnotchangestatesuntiltheinputisaltered.Aflip-flopoppositepolarity.Twoinputsareusuallyneededtoalterthestateofaflip-flop.Avarietyofnamesareusedfortheinputs.Thesevaryagreatdealbetweendifferentflip-flops.1.R-Sflip-flopsFig.3-5showslogiccircuitconstructionofanR-Sflip-flop.ItisconstructedfromtwoNANDgates.TheoutputofeachNANDprovidesoneoftheinputsfortheotherNAND.RstandsfortheresetinputandSrepresentsthesetinput.ThetruthtableandlogicsymbolareshowninFig.3-6.Noticethatthetruthtableissomewhatmorecomplexthanthatofagate.Itshows,forexample，theappliedinput,previousoutput，andresultingoutput.TounderstandtheoperationofanR-Sflip-flop，wemustfirstlookatthepreviousoutputs.Thisisthestatusoftheoutputbeforeachangeisappliedtotheinput.ThefirstfouritemsofthepreviousoutputsareQ=1and=0.ThesecondfourstatesthiscaseoftheinputtoNANDSis0andthatis0，whichimpliesthatbothinputstoNANDRare1.Bysymmetry，thelogiccircuitwillalsostablewithQ0and1.IfnowRmomentarilybecomes0，theoutputofNANDR，，willrisetoresultinginNANDSberealizedbya0atS.TheoutputsQandareunpredictablewhentheinputsRandSare0states.Thiscaseisnotallowed.Seldomwouldindividualgatesbeusedtoconstructaflip-flop，ratherthanoneofthespecialtypesfortheflip-floppackagesonasinglechipwouldbeusedbyadesigner.Avarietyofdifferentflip-flopsareusedindigitalelectronicsystemstoday.Ingeneral，eachflip-floptypeR-S-Tflip-flopforexample.isatriggeredR-Sflip-flop.ItwillnotchangestateswhentheRandSinputsassumeavalueuntilatriggerpulseisapplied.Thiswouldpermitalargenumberofflip-flopstochangestatesallatthesametime.Fig.3-7showsthelogiccircuitconstruction.ThetruthtableandlogicsymbolareshowninFig.3-8.TheRandSinputarethusactivewhenthesignalatthegateinput(T)is1.Normally，suchtiming，orsynchronizing，signalsaredistributedthroughoutadigitalsystembyclockpulses，asshowninFig.3-9.Thesymmetricalclocksignalprovidestwotimeseachperiod.Thecircuitcanbedesignedtotriggerattheleadingortrailingedgeoftheclock.Thelogicsymbolsforedgetriggerflip-flopsareshowninFig.3-10.2.J-Kflip-flopsAnotherveryimportantflip-flopunpredictableoutputstate.TheJandKinputsadditiontothis，J-Kflip-flopsmayemploypresetandpreclearfunctions.Thisisusedtoestablishsequentialtimingoperations.Fig.3-11showsthelogicsymbolandtruthtableofaJ-Kflip-flop.3.5.2CountersAflip-flopbeusedinswitchingoperations，anditcancountpulses.seriesofinterconnectedflip-flopsisgenerallycalledaregister.Eachregistercanstoreonebinarydigitorbitofdata.Severalflip-flopsconnectedformacounter.Countingisafundamentaldigitalelectronicfunction.Foranelectroniccircuittocount，anumberofthingsmustbeachieved.Basically，thecircuitmustbesuppliedwithsomeformofdataorinformationthatissuitableforprocessing.Typically，electricalpulsesthatturnonandoffareappliedtotheinputofacounter.Thesepulsesmustinitiateastatechangeinthecircuitwhentheyarereceived.Thecircuitmustalsobeabletorecognizewhereitisincountingsequenceatanyparticulartime.Thisrequiressomeformofmemory.Thecountermustalsobeabletorespondtothenextnumberinthesequence.Indigitalelectronicsystemsflip-flopsareprimarilyusedtoachievecounting.Thistypeofdeviceiscapableofchangingstateswhenapulseisapplied，outputpulse.Thereareseveraltypesofcountersusedindigitalcircuitrytoday.Probablythemostcommonoftheseisthebinarycounter.Thisparticularcounterisdesignedtoprocesstwo-stateorbinaryinformation.J-Kflip-flopsarecommonlyusedinbinarycounters.RefernowtothesingleJ-Kflip-flopofFig.3-11.Initstogglestate，thisflip-flopiscapableofachievingcounting.First，assumethattheflip-flopisinitsresetstate.ThiswouldcauseQtobe0andQtobe1.Normally，weareconcernedonlywithQoutputincountingoperations.Theflip-flopisnowconnectedforoperationinthetogglemode.JandKmustbothbemadethe1state.Whenapulseisappliedtothe，Torclock，input，Qchangesto1.Thismeansthatwithonepulseapplied，a1isgeneratedintheoutput.Theflip-flopthenextpulsearrives，Qresets，orchangesto0.Essentially，thismeansthattwoinputpulsesproduceonlyoneoutputpulse.Thisisadivide-by-twofunction.Forbinarynumbers，countingisachievedbyanumberofdivide-by-twoflip-flops.Tocountmorethanonepulse，additionalflip-flopsmustbeemployed.Foreachflip-flopaddedtothecounter，itscapacityisincreasedbythepowerof2.Withoneflip-flopthemaximumcountwas20，or1.Fortwoflip-flopsitwouldcounttwoplaces，suchas20and21.Thiswouldreachacountof3orabinarynumberof11.Thecountwouldbe00，01，10，andThecounterwouldthenclearandreturnto00.Ineffect,thiscountsfourstatechanges.Threeflip-flopswouldcountthreeplaces，or20，21，and22.Thiswouldpermitatotalcountofeightstatechanges.Thebinaryvaluesare000，001，010，011，100，101，110and111.Themaximumcountisseven，or111.Fourflip-flopswouldcountfourplaces，or20，21，22，and23.Thetotalcountwouldmake16statechanges.Themaximumcountwouldbe15，orthebinarynumber1111.Eachadditionalflip-flopwouldcausethistoincreaseonebinaryplace.河南理工大学电气工程及其自动化专业中英双语对照翻译。中文翻译：第三章数字电子技术3.1介绍采用了数字信号的电路称为数字电路。电脑、袖珍计算器,数字仪器、数控设备常见的数字电路的应用。几乎无限数量的数字信息电子可以在很短的时间处理。如今，在电子学中，运算速度是最重要的性能之一，因此数字电路更加频繁地被使用。在这一章,对数字电路的应用进行了讨论。有许多类型的数字电路应用在电子技术中,包括逻辑电路、触发器电路,计数电路,和许多其他内容。这个单元的第一节主要讨论了对数字电路系统基本数量的理解。其余的章节介绍了数字电路的类型以及阐述了布尔代数在逻辑电路中的应用。3.2数字编号系统当今使用的最常见的数字系统是十进制系统中，其中每10位计一次数。在该系统中的位数被称为基（或基数）。十进制系统具有10个基。编码系统都有一个数位值，与其它系统相比它指的是在计算过程中的一个数字位置。在一个数位或位置我们所能使用的最大的数字是由该系统的基所决定的。在十进制系统中，小数点左侧第一个位置叫做个位。在个位可以使用从0～9的任一数字。当要使用比9大的数值时，就必须用两个或更多的数位来表示。在十进制系统中，个位左侧的下一个位置是十位，数字99是两个数位所能表示的最大值。加到左侧的每一个数位把数字系统扩展为10的次幂。任何数量可以表示为加权处的值的总和。十进制数2583，例如，可以表示为（2×1000）+（5×100）+（8×10）+（3×1）。在我们的日常生活中常用十进制数字系统。然而，电子它是很难使用的。一个是十进制数字系统中的每个数字都需要特定的值与其相关联，所以它是不切合实际的。3.2.1二进制数字系统通常电子数字系统的二进制类型,2作为它的基。只有0或1的数字在二进制中使用。电子为0的值可以用低电压值或没有电压相关联。数字1可以与一个电压值大于0的内容相关联。这些电压值用二进制表示的是正逻辑。相对地,负逻辑电压分配到0,没有电压值的分配给1。本章采用正逻辑。一个二进制有两种操作状态，1和0，是自然循环条件。当电路被关断或已不施加电压时，它处于关闭或0状态。已施加电压的电路处于导通，或1状态。通过使用晶体管或集成电路，在不到一微秒的时间内能够改变电路状态。电子设备有可能会操纵百万的0，并且是在第二，从而快速地处理信息。编号用于小数的基本原则适用于一般二进制数字。二进制的基是2,这意味着只有数字0和1是用来表达的价值。首先左边的二元观点,或起点,代表单位,或位置。二进制的左边点的地方是2的幂。一些地方的值在基2，2o=1,21=2,22=4、23=8,2?=16,25=32,26=64。当基不是10被使用时，数字应该有一个下标来标识基，数字100?就是一个例子。数量100?(读“零,零,基数2”)相当于4在基数10内或410。从第一位二进制左边的点,这个数字相当于(0×20)+(0×21)+(1×22)。一个二进制数等效转换为十进制数的方法,首先写下二进制数。从二进制的小数点开始，当指数为1时，对于每一位二进制位置空间给出了十进制等效值。二进制数值中每个0保留了一空白空间或指数为0。按权表达式展开然后记录十进制数。在一个十进制数转换为二进制数相当于由2部重复步骤实现。当商没有余数时用0来记录。当商余数时用1来记录。开方过程继续进行，直到商为0。从而等效二进制数按照由后到前的顺序来写。3.2.2二进制编码的十进制(BCD)数字系统当大量用二进制数表示,他们很难使用。因为这个原因,二-十进制(BCD)设计的计算方法。在此系统中四个二进制数字是用来表示每一个十进制数字。为了说要应用的BCD转换过程中，基10首先根据位值分为数字。数10510给出的数字1-0-5。每个数字转换为二进制给出了0001-0000-0101BCD）。十进制数高达99910可通过此过程中，只有12位二进制数来显示。显示BCD数字时，每组数字之间的连字符是非常重要的。通过任何一组BCD数的要显示的最大数字是9。不使用六位数的数编码组在所有在这个系统中。正因为如此，八进制（基为8）和十六进制（基为16）系统进行了设计。以二进制形式的数字电路处理数字，但通常它们显示在BCD码，八进制或十六进制形式。3.2.3八进制数字系统八进制（基8）数字系统通常用于数字电路中来处理大量数据运算。数字的八进制系统使用相同的基本原则与十进制和二进制系统相似。八进制数系统的基8。八进制数字系统中最大的数字是7。位置值从左边的八进制值都是8的次幂:80=1,81=8,82=64,83=512,84=4096,等等。转换一个八进制数的十进制数