电气专业毕业设计中英文对照翻译Word文档格式.docx

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3.2DigitalNumberSystems

Themostcommonnumbersystemusedtodayisthedecimalsystem,inwhich10digitsareusedforcounting.Thenumberofdigitsinthesystemiscalleditsbase（orradix）.Thedecimalsystem，therefore，hasabaseof10.

Numberingsystemshaveaplacevalue，whichreferstotheplacementofadigitwithrespecttoothersinthecountingprocess.Thelargestdigitthatcanbeusedinaspecificplaceorlocationisdeterminedbythebaseofthesystem.Inthedecimalsystemthefirstpositiontotheleftofthedecimalpointiscalledtheunitsplace.Anydigitfrom0to9canbeusedinthisplace.Whennumbervaluesgreaterthan9areused,theymustbeexpressedwithtwoormoreplaces.Thenextpositiontotheleftoftheunitsplaceinadecimalsystemisthetensplace.Thenumber99isthelargestdigitalvaluethatcanbeexpressedbytwoplacesinthedecimalsystem.Eachplaceaddedtotheleftextendsthenumbersystembyapowerof10.

Anynumbercanbeexpressedasasumofweightedplacevalues.Thedecimalnumber2583,forexample,isexpressedas（2×

1000）+（5×

100）+（8×

10）+（3×

1）.

Thedecimalnumbersystemiscommonlyusedinourdailylives.Electronically,however,itisratherdifficulttouse.Eachdigitofabase10systemwouldrequireaspecificvalueassociatedwithit,soitwouldnotbepractical.

3.2.1BinaryNumberSystem

Electronicdigitalsystemsareordinarilythebinarytype，whichhas2asitsbase.Onlythenumbers0or1areusedinthebinarysystem.Electronically,thevalueof0canbeassociatedwithalow-voltagevalueornovoltage.Thenumber1canthenbeassociatedwithavoltagevaluelargerthan0.Binarysystemsthatusethesevoltagevaluesaresaidtohavepositivelogic.Negativelogic,bycomparison,hasavoltageassignedto0andnovoltagevalueassignedto1.Positivelogicisusedinthischapter.

Thetwooperationalstatesofabinarysystem,1and0,arenaturalcircuitconditions.Whenacircuitisturnedofforhasnovoltageapplied，itisintheoff,or0,state.Anelectricalcircuitthathasvoltageappliedisintheon，or1,state.ByusingtransistororICs，itiselectronicallypossibletochangestatesinlessthanamicrosecond.Electronicdevicesmakeitpossibletomanipulatemillionsof0sandisinasecondandthustoprocessinformationquickly.

Thebasicprinciplesofnumberingusedindecimalnumbersapplyingeneraltobinarynumbers.Thebaseofthebinarysystemis2,meaningthatonlythedigits0and1areusedtoexpressplacevalue.Thefirstplacetotheleftofthebinarypoint,orstartingpoint，representstheunits，oris,location.Placestotheleftofthebinarypointarethepowersof2.Someoftheplacevaluesinbase2are2º

=1,2¹

=2,2²

=4,2³

=8,2⁴=16,25=32,and26=64.

Whenbasesotherthan10areused,thenumbersshouldhaveasubscripttoidentifythebaseused.Thenumber100₂isanexample.

Thenumber100₂（read“one,zero,zero,base2”）isequivalentto4inbase10,or410.Startingwiththefirstdigittotheleftofthebinarypoint,thisnumberhasvalue（0×

20）+（0×

21）+（1×

22）.Inthismethodofconversionabinarynumbertoanequivalentdecimalnumber，writedownthebinarynumberfirst.Startingatthebinarypoint，indicatethedecimalequivalentforeachbinaryplacelocationwherea1isindicated.Foreach0inthebinarynumberleaveablankspaceorindicatea0'

Addtheplacevaluesandthenrecordthedecimalequivalent.

Theconversionofadecimalnumbertoabinaryequivalentisachievedbyrepetitivestepsofdivisionbythenumber2.Whenthequotientisevenwithnoremainder,a0isrecorded.Whenthequotienthasaremainder.as1isrecorded.Thedivisionprocesscontinuesuntilthequotientis0.Thebinaryequivalentconsistsoftheremaindervaluesintheorderlasttofirst.

3.2.2Binary-codedDecimal（BCD）NumberSystem

Whenlargenumbersareindicatedbybinarynumbers，theyaredifficulttouse.Forthisreason，theBinary-CodedDecimal（BCD）methodofcountingwasdevised.Inthissystemfourbinarydigitsareusedtorepresenteachdecimaldigit.Toillustratethisprocedure，thenumber105，isconvertedtoaBCDnumber.Inbinarynumbers，10510=10001012.

ToapplytheBCDconversionprocess，thebase10numberisfirstdividedintodigitsaccordingtoplacevalues.Thenumber10510givesthedigits1-0-5.Convertingeachdigittobinarygives0001-0000-0101BCD.Decimalnumbersupto99910maybedisplayedbythisprocesswithonly12binarynumbers.ThehyphenbetweeneachgroupofdigitsisimportantwhendisplayingBCDnumbers.

ThelargestdigittobedisplayedbyanygroupofBCDnumbersis9.Sixdigitsofanumber-codinggrouparenotusedatallinthissystem.Becauseofthis,theoctal（base8）andthehexadecimal（base16）systemsweredevised.DigitalcircuitsprocessnumbersinbinaryformbutusuallydisplaytheminBCD,octal,orhexadecimalform.

3.2.3OctalNumberSystem

Theoctal（base8）numbersystemisusedtoprocesslargenumbersbydigitalcircuits.Theoctalsystemofnumbersusesthesamebasicprinciplesasthedecimalandbinarysystems.

Theoctalnumbersystemhasabaseof8.Thelargestnumberusedinabase8systemis7.Theplacevaluesstartingattheleftoftheoctalpointarethepowersofeight:

80=1,81=8,82=64,83=512,84=4096,andsoon.

Theprocessofconvertinganoctalnumbertoadecimalnumberisthesameasthatusedinthebinary-to-decimalconversionprocess.Inthismethod,however,thepowersof8areusedinsteadofthepowersof2.Thenumberforchanging3828toanequivalentdecimalis25810.

ConvertinganoctalnumbertoanequivalentbinarynumberissimilartotheBCDconversionprocess.Theoctalnumberisfirstdividedintodigitsaccordingtoplacevalue.Eachoctaldigitisthenconvertedintoanequivalentbinarynumberusingonlythreedigits.

Convertingadecimalnumbertoanoctalnumberisaprocessofrepetitivedivisionbythenumber8.Afterthequotienthasbeendetermined，theremainderisbroughtdownastheplacevalue.Whenthequotientisevenwithnoremainder，a0istransferredtotheplaceposition.Thenumberforconverting409810tobase8is100028.

Convertingabinarynumbertoanoctalnumberisanimportantconversionprocessofdigitalcircuits.Binarynumbersarefirstprocessedataveryhighspeed.Anoutputcircuitthenacceptsthissignalandconvertsittoanoctalsignaldisplayedonareadoutdevice.

Assumethatthenumber1101001002istohechangedtoanequivalentoctalnumber.Thedigitsmustfirstbedividedintogroupsofthree，startingattheoctalpoint.Eachbinarygroupisthenconvertedintoanequivalentoctalnumber.Thesenumbersarethencombined，whileremainingintheirsamerespectiveplaces，torepresenttheequivalentoctalnumber.

3.2.4HexadecimalNumberSystem

Thehexadecimalnumbersystemisusedindigitalsystemstoprocesslargenumbervalues.Thebaseofthissystemis16，whichmeansthatthelargestnumberusedinaplaceis15.Digitsusedbythissystemarethenumbers0-9andthelettersA-F.ThelettersA-Pareusedtodenotethedigits10-15，respectively.Theplacevaluestotheleftofthehexadecimalpointarethepowersof16:

160=1，161=16，162=256,l63=4096，164=65536，andsoon.

Theprocessofchangingahexadecimalnumbertoadecimalnumberissimilartothatoutlinedforotherconversions.Initially，ahexadecimalnumberisrecordedinproperdigitalorder.Theplacevalues，orpowersofthebase，arethenpositionedundertherespectivedigitsinstep2.Instep3，thevalueofeachdigitisrecorded.Thevaluesinsteps2and3arethenmultipliedtogetherandadded.Thesumgivesthedecimalequivalentvalueofahexadecimalnumber.

Theprocessofchangingahexadecimalnumbertoabinaryequivalentisasimplegroupingoperation.Initially，thehexadecimalnumberisseparatedintodigits.Eachdigitisthenconvertedtoabinarynumberusingfourdigitspergroup.Thebinarygroupiscombinedtoformtheequivalentbinarynumber.

Theconversionofadecimalnumbertoahexadecimalnumberisachievedbyrepetitivedivision，aswithothernumbersystems.Inthisprocedurethedivisionisby16andremainderscanbeaslargeas15.

Convertingabinarynumbertoahexadecimalequivalentisthereverseofthehexadecimaltobinaryprocess.Initially，thebinarynumberisdividedingroupsoffourdigits，startingatthehexadecimalpoint.Eachnumbergroupisthenconvertedtoahexadecimalvalueandcombinedtoformthehexadecimalequivalentnumber.

3.3BinaryLogicCircuits

Indigitalcircuit-designapplicationsbinarysignalsarefarsuperiortothoseoftheoctal，decimal，orhexadecimalsystems.Binarysignalscanbeprocessedveryeasilythroughelectroniccircuitry，sincetheycanberepresentedbytwostablestatesofoperation.Thesestatescanbeeasilydefinedasonoroff,1or0，upordown，voltageornovolta