數(shù)字電路英文版-第二單元講課教案課件

數(shù)字電路英文版PPT--第二單元數(shù)字電路英文版PPT--第二單元Weight[權(quán)]Carry[進(jìn)位]Remainder[余數(shù)]Quotient[商]Integer[整數(shù)]Fraction[小數(shù)]1’Complement[反碼]2’Complement[補(bǔ)碼]Format[格式]Precision[精度]Mantissa[尾數(shù)]Weight[權(quán)]Carry[進(jìn)位]KEYTERMSAlphanumeric:Consistingofnumerals,letters,andothercharacters.ASCII:AmericanStandardCodeforInformationInterchange;themostwidelyusedalphanumericcode.KEYTERMSAlphanumeric:ConsisBCD:Binarycodeddecimal;adigitalcodeinwhicheachofthedecimaldigits,0through9,isrepresentedbygroupoffourbits.Byte:Agroupofeightbits.Carry:Thedigitgeneratedwhenthesumoftwobinarydigitsexceeds1.BCD:Binarycodeddecimal;aComplement:Theinverseoroppositeofanumber.Decimal:Describesanumbersystemwithabaseoften.Digit:Asymbolusedtoexpressaquantity.Exponent:Thepartofafloating-pointnumberthatrepresentsthenumberofplacesthatthedecimalpointistobemoved.Complement:TheinverseoropFloating-pointnumber:Anumberrepresentationbasedonscientificnotationinwhichthenumberconsistsofanexponentandamantissa.Graycode:Anunweighteddigitalcodecharacterizedbyasinglebitchangebetweenadjacentcodenumberinasequence.Floating-pointnumber:AnumbHexadecimal:Describesanumbersystemwithabaseof16.Integer:Awholenumber.Leastsignificantbit(LSB):Generally,theright–mostbitinabinarywholenumberorcode.Mantissa:Themagnitudeofafloating-pointnumber.Hexadecimal:DescribesanumbMostsignificantbit(MSB):Theleft–mostbitinabinarywholenumberorcode.Octal:Describesanumbersystemwithabaseofeight.Overflow:Theconditionthatoccurswhenthenumberofbitsinasumexceedsthenumberofbitsineachofthenumbersadded.Mostsignificantbit(MSB):TParity:Inrelationtobinarycodes,theconditionofevennessoroddnessofthenumberof1sinacodegroup.Signbit:Theleft-mostbitofabinarynumberthatdesignateswhetherthenumberispositive(0)ornegative(1).Weight:Thevalueofadigitinanumberbasedonitspositioninthenumber.Parity:InrelationtobinaryYouarefamiliarwiththedecimalnumbersystembecauseyouusedecimalnumberseveryday.Althoughdecimalnumbersarecommonplace,theirweightedstructureisoftennotunderstood.§2.1DECIMALNUMBERSYouarefamiliarwithtInthissection,thestructureofdecimalnumbersisreviewed.Thisreviewwillhelpmoreeasilyunderstandthestructureofthebinary

numbersystem,whichisimportantincomputersanddigitalelectronics.Inthedecimalnumbersystemeachofthetendigits,0through9,representsacertainquantity.Statedantherway:Abase—10numbersystem.3.Inthissection,thestruEXAMPLE2-1Expressthenumber47asasumofthevaluesofeachdigit.SolutionThedigit4hasaweightof101,asindicatedbyitsposition.Thedigit7hasaweightof1,whichis100,asindicatedbyitsposition.47=(4X101)+(7X100)=(4X10)+(7X1)=40+7RelatedProblemDeterminethevalueofeachdigitin939.EXAMPLE2-1ExpressthenuThebinarynumbersystemissimplyanotherwaytorepresentquantities.Thebinarysystemislesscomplicatedthanthedecimalsystembecauseithasonlytwodigits.Itmayseemmoredifficultatfirstbecauseitisunfamiliartoyou.Thedecimalsystemwithitstendigitsisabase—tensystem;§2.2BINARYNUMBERS4.Thebinarynumbersystemthebinarysystemwithitstwodigitsisabase—twosystem.Thetwobinarydigits(bits)are1and0.Thepositionofa1or0inabinarynumberindicatesitsweight,orvaluewithinthenumber,justasthepositionofadecimaldigitdeterminesthevalueofthatdigit.Theweightsinabinarynumberarebasedonpowersoftwo.5.thebinarysystemwithCountingin

Binary

DecimalNumber

BinaryNumber

01234567810119121314150000000100101100

0101

0110

0111

0100

1111

1110

1101

1100

1011

1010

1001

1000

6.CountinginBinaryDecimalAsyouhaveseeninabovetable,fourbitsarerequiredtocountfromzeroto15.Ingeneral,withnbitsyoucancountuptoanumberequalto2n–1.Largestdecimalnumber=2n–1ifn=5,25–1=32–1=31ifn=6,26–1=64–1=63

AsyouhaveseeninabovetablTheWeightingStructureofBinaryNumbersTheright-mostbitistheleastsignificantbitinabinarywholenumberandhasaweightof20=1.Theleft-mostbitisthemostsignificantbit;itsweightdependsonthesizeofbinarynumber.TheWeightingStructureofBinBinaryweightPositivePowerofTwoNegativePowerofTwo2827262524232221202-12-22-32-42-52-6

25612864321684211/2

1/41/81/161/321/64

0.50.25

0.1250.06250.031250.015625

BinaryweightBinary-to-DecimalConversionThedecimalvalueofanybinarynumbercanbefoundbyaddingtheweightsofallbitsthatare1anddiscardingtheweightsofallbitsthatare0.EXAMPLE2-3Convertthebinarywholenumber1101101todecimal.Weight:26252423222120

Binarynumber:11011011101101=26+

25+

23+

22+

20

=64+32+8+4+1=109RelatedProblemConvertthebinarynumber10010001todecimal.Binary-to-DecimalConversionInSection2—2youlearnedhowtoconvertabinarynumbertotheequivalentdecimalnumber.Nowyouwilllearntwowaysofconvertingfromadecimalnumbertoabinarynumber.§2.3DECIMAL–TO-BINARYCONVERSION7.InSection2—2youlearned1.Sum-of-WeightsMethodListofeightbinaryweight128,64,32,16,8,4,2,127,26,25,24,23,22,21,20

9=8+11001125=64+32+16+8+4+0+111111011.Sum-of-WeightsMethodEXAMPLE2-5Convertthefollowingdecimalnumberstobinary:(a)12(b)25(c)58(d)82Solution(a)12=8+4=23+221100(b)25=16+8+1=24+23+2011001(c)58=32+16+8+2=25+24+23+21

111010(d)82=64+16+2=26+24+211010010RelatedProblemConvertthedecimalnumber125tobinary.EXAMPLE2-5Convertthefol2.RepeatedDivision-by-2Method2120LSB260231211MSB0

2.RepeatedDivision-by-2MethBinaryarithmeticisessentialinalldigitalcomputersandinmanyothertypesofdigitalsystems.Tounderstanddigitalsystem,youmustknowthebasicsofbinaryaddition,subtraction,multiplication,anddivision.§2.4BINARYARITHMETIC8.Binaryarithmeticisess

Thissectionprovidesanintroductionthatwillbeexpandedinlatersections.Rememberinbinary1+1=10,not2.Rememberinbinary10-1=1,not9.ThissectionprovidesBinaryAdditionThefourbasicrulesforaddingbinarydigitsareasfollows:0+0=0Sumof0withacarryof00+1=1Sumof1withacarryof01+0=1Sumof1withacarryof01+1=10Sumof0withacarryof1BinaryAdditionEXAMPLE2-7Addthefollowingbinarynumbers:11+11(b)100+10(c)111+11Solution(a)113(b)1004(c)1117+11+3+10+2+11+311061106101010

RelatedProblemAdd1111and1100EXAMPLE2-7AddthefolloBinarySubtractionThefourbasicrulesforsubtractingbitsareasfollows:0-0=01-1=01-0=110-1=10–1withaborrowof1BinarySubtractionEXAMPLE2-8(9)Performthefollowingbinarysubtraction:11-01(b)11-10(c)101-011Solution(a)113(b)113(c)1015-01-1-10-2-11-31020110102

RelatedProblemSubtract100from111.Subtract101from110.EXAMPLE2-8(9)PerformthBinaryMultiplicationThefourbasicrulesformultiplyingbitsareasfollows:0×0=00×1=01×0=01×1=1Multiplicationisperformedwithbinarynumbersinthesamemanneraswithdecimalnumbers.BinaryMultiplicationEXAMPLE2-10Performthefollowingbinarymultiplications:(a)11×11(b)101×111Solution(a)113(b)1117×11×3×101×511911135+110001001+111100011EXAMPLE2-10PerformthefoRelatedProblemMultiply1101×1010(13×10=130)RelatedProblemMultiply11BinaryDivisionDivisioninbinaryfollowsthesameprocedureasdivisionindecimal.Performthefollowingbinarydivision:(a)110÷11(b)110÷10Solution(a)10211311√1103√610√1102√6

11610600001001000BinaryDivisionRelatedproblemDivide1100by100(12÷4=3)RelatedproblemDivide1100bThe1′scomplementandthe2′scomplementofabinarynumberareimportantbecausetheypermittherepresentationofnegativenumbers.Themethodof2′scomplementarithmeticiscommonlyusedincomputerstohandlenegativenumbers.§2.51’sAND2’sCOMPLEMENTSOFBINARYNUMBERS9.The1′scomplementandthe2′sFindingthe1’scomplementofaBinarynumber10110010Binarynumber

010011011’scomplement(touseparallelinverters,NOTgate)Findingthe1’scomplementofFindingthe2’sComplementofaBinaryNumber2’scomplement=(1’scomplement)+1EXAMPLE2-12Findthe2’scomplementof10110010.Solution10110010Binarynumber010011011’scomplement+1Add1

01001110

2’scomplementRelatedProblemDeterminethe2’scomplementof11001011.Findingthe2’sComplementofAnalternativemethodoffindingthe2’scomplementofabinarynumberisasfollows:1.StartattherightwiththeLSBandwritethebitsastheyareuptoandincludingthefirst1.2.Takethe1’scomplementsoftheremainingbits.AnalternativemethodoffindiEXAMPLE2-13Findthe2’scomplementof10111000usingthealternativemethod.Solution10111000Binarynumber1’scomplements010010002’scomplementoforiginalbitsThesebitsstaythesame.RelatedProblemFindthe2’scomplementof11000000.EXAMPLE2-13Findthe2’scFigure2--3Exampleofobtainingthe2’scomplementofanegativebinarynumber.ThomasL.Floyd

DigitalFundamentals,8eCopyright?2003byPearsonEducation,Inc.

UpperSaddleRiver,NewJersey07458

Allrightsreserved.Figure2--3ExampleofobtaDigitalsystem,suchasthecomputer,mustbeabletohandlebothpositiveandnegativenumbers.Asignedbinarynumberconsistsofbothsignandmagnitudeinformation.Thesignindicateswhetheranumberispositiveornegativeandthemagnitudeisthevalueofthenumber.§2.6SIGNEDNUMBERS10.Digitalsystem,suchasTherearethreewaysinwhichsignedintegernumberscanberepresentedinbinaryform:sign-magnitude,1′scomplement,and2′scomplement.Nonintegerandverylargeorsmallnumberscanbeexpressedinfloating-pointformat.11.TherearethreewaysTheleft-mostbitinasignalbinarynumberisthesignbit,whichtellsyouwhetherthenumberispositiveornegative.A0isforpositive,anda1isfornegative.000110012510011001-25

Theleft-mostbitinasignalInthesign-magnitudesystem,anegativenumberhasthesamemagnitudebitsasthecorrespondingpositivenumberbutthesignbitisa1ratherthan0.000110012510011001-25Inthesign-magnitude1’sComplementSystemPositivenumbersinthe1’scomplementsystemarerepresentedthesamewayasthepositivesign-magnitudenumbers.Negativenumbers,however,arethe1’scomplementsofthecorrespondingpositivenumbers.+2500011001000110011’scomplement-2510011001111001101’scomplement1’sComplementSystem2’sComplementSystemPositivenumbersinthe2’scomplementsystemarerepresentedthesamewayasinthesign-magnitudeand1’scomplementsystems.Negativenumbersarethe2’scomplementsofthecorrespondingpositivenumbers.+2500011001000110012’scomplement-2510011001111001112’scomplement2’sComplementSystemEXAMPLE2-14Expressthedecimalnumber-39asan8-bitnumberinthesign-magnitude,1’scomplement,and2’scomplement.Solution+3900100111-3910100111sign-M110110001’sCom110110012’sComRelatedProblemExpress+19and-19insign-magnitude,1’scomplement,and2’scomplement.EXAMPLE2-14ExpresstheRelatedProblemExpress+19and-19insign-magnitude,1’scomplement,and2’scomplement.Solution+1900010011-1910010011sign-M111011001’sCom111011012’sComRelatedProblemExpress+TheDecimalValueofSignedNumbersEXAMPLE2-15Determinethedecimalvalueofthissignedbinarynumberexpressedinsign-magnitude:10010101=-21RelatedProblemDeterminethedecimalvalueofthesign-magnitudenumber01110111.(11910)TheDecimalValueofSignedNuEXAMPLE2-16Determinethedecimalvalueofthissignedbinarynumbersexpressedin1’scomplement:(a)00010111(b)11101000Solution(a)23(b)-128+64+32+8=-24-24+1=-23RelatedProblemDeterminethedecimalvalueofthe1’scomplementnumber11101011.(-2010)EXAMPLE2-16DetermineEXAMPLE2-17Determinethedecimalvalueofthissignedbinarynumbersexpressedin2’scomplement:(a)01010110(b)10101010Solution(a)86(b)-128+32+8+2=-86

RelatedProblemDeterminethedecimalvalueofthe2’scomplementnumber11010111.(-4110)EXAMPLE2-17DetermineInthelastsection,youlearnedhowsignednumbersarerepresentedinthreedifferentsystems.Inthissection,youwilllearnhowsignednumbersareadded,subtracted,multiplied,anddivided.§2.7ARITHMETICOPERATIONSWITHSIGNEDNUMBERS12.Inthelastsection,youBecausethe2′scomplementsystemforrepresentingsignednumbersisthemostwidelyusedincomputersandmicroprocessor—basedsystems,thecoverageinthissectionislimitedto2′scomplementarithmetic.Theprocessescoveredcanbeextendedtotheothersystemsifnecessary.13.Becausethe2′scomplemenAddition1.Bothnumberspositive2.Positivenumberwithmagnitudelargerthannegativenumber3.Negativenumberwithmagnitudelargerthanpositivenumber4.BothnumbersnegativeAddition1.BothnumberspositBothnumberspositive:000001117+00000100+40000101111Positivenumberwithmagnitudelargerthannegativenumber:0000111115+11111010+-61000010019DiscardcarryBothnumberspositive:Negativenumberwithmagnitudelargerthanpositivenumber:0001000016+11101000+-2411111000-8Bothnumbersnegative:11111011-5+11110111+-9111110010-14DiscardcarryNegativenumberwithmagnitudeEXAMPLE2-19Addthesignednumbers:01000100,00011011,00001110,and00010010.Solution6801000100+27+000110119501011111+14+0000111010901101101+18+0001001012701111111EXAMPLE2-19AddthesignedRelatedProblemAdd00110011,10111111,and01100011.Thesearesignednumbers.5100110011-65+10111111-1411110010+99+0110001185101010101

DiscardcarryRelatedProblemAdd0011001Subtraction:Itisaspecialcaseofaddition.Thesignofapositiveornegativebinarynumberischangedbytakingits2’scomplement.Tosubtracttwosignednumbers,takethe2’scomplementofthesubtrahendandadd.Discardanyfinalcarrybit.Subtraction:EXAMPLE2-20Performeachofthefollowingsubtractionofthesignednumbers:(a)00001000–00000011(b)00001100–11110111(c)11100111–00010011(d)10001000–11100010Solution(a)Inthiscase,8–3=8+(-3)=500001000Minuend(+8)+111111012’sComofsubtrahendDiscardcarry100000101Difference(+5)EXAMPLE2-20Performeachof(b)Inthiscase,12–(-9)=12+9=2100001100Minuend(+12)+000010012’sComofsubtrahend(9)00010101Difference(+21)(c)Inthiscase,-25–(+19)=-25+(-19)=-4411100111Minuend(-25)+111011012’sComofsubtrahend(-19)Discardcarry111010100Difference(-44)(b)Inthiscase,12–(-9)=(d)Inthiscase,-120–(-30)=-120+30=-9010001000Minuend(-120)+000111102’sComofsubtrahend(30)10100110Difference(-90)RelatedProblemSubtract01000111from01011000(d)Inthiscase,-120–(-30)RelatedProblemSubtract01000111from01011000Inthiscase,88–71=88+(-71)=1701001000Minuend(88)+101110012’sComofsubtrahend(-71)Discardcarry

100010001Difference(-90)RelatedProblemSubtract01Thehexadecimalnumbersystemhassixteendigitsandisusedprimarilyasacompactwayofdisplayingorwritingbinarynumbersbecauseitisveryeasytoconvertbetweenbinaryandhexadecimal.Asyouareprobablyaware,longbinarynumbersaredifficulttoreadandwritebecauseitiseasytodroportransposeabit.§2.8HEXADECIMALNUMBERS14.ThehexadecimalnumbersysSincecomputersandmicroprocessorsunderstandonly1sand0s,itisnecessarytousedthesedigitswhenyouprogramin“machinelanguage.”Imaginewritingasixteenbitinstructionforamicroprocessorsystemin1sand0s.Itismuchmoreefficienttousehexadecimaloroctal;octalnumbersarecoveredinSection2—9.Hexadecimaliswidelyusedincomputerandmicroprocessorapplication.15.SincecomputersandmicDecimalBinaryHexadecimal00000010001120010230011340100450101560110670111722.Decimal

DecimalBinaryHexadecimal810008910019101010A111011B121100C131101D141110E151111FDecimalCountinginHexadcimal0to9A,B,C,D,E,F,10,11,12,13,14,15,16,17,18,19,1A,1B,1C,1D,1E,1F,20,21,22,23,24,25,26,27,28,29,2A,2B,2C,2D,2E,2F,30,31,32,….CountinginHexadcimalEXAMPLE2-24Convertthefollowingbinarynumberstohexadecimal:(a)1100101001010111(b)111111000101101001Solution(a)1100101001010111(b)00111111000101101001CA573F169RelatedProblemConvertthebinarynumber1001111011110011100tohexadecimal.EXAMPLE2-24ConvertthefoRelatedProblemConvertthebinarynumber1001111011110011100tohexadecimal.Solution

010011110111100111004F79CRelatedProblemConverttheHexadecimal-to-BinaryConversionToreversetheprocessEXAMPLE2-25Determinethebinarynumbersforthefollowinghexadecimalnumbers:(a)10A416(b)CF8E16(c)974216Solution(a)10A4

(b)CF8E10000101001001100111110001110Hexadecimal-to-BinaryConversi(c)97421001011101000010RelatedProblemConvertthehexadecimalnumber6BD3tobinary.Solution6BD3110101111010011(c)974Hexadecimal-to-DecimalConversionOnewaytofindthedecimalequivalentofahexadecimalnumberistofirstconvertthehexadecimalnumbertobinaryandthenconvertfrombinarytodecimal.Hexadecimal-to-DecimalConversEXAMPLE2-26Convertthefollowinghexadecimalnumberstodecimal:(a)1C16(b)A8516Solution(a)1C00011100=24+23+22=16+8+4=2810(b)A85

101010000101=211+29+27+22+20

=2048+512+128+4+1=269310EXAMPLE2-26Convertthef數(shù)字電路英文版--第二單元講課教案課件數(shù)字電路英文版--第二單元講課教案課件Likethehexadecimalsystem,theoctalsystemprovidesaconvenientwaytoexpressbinarynumbersandcodes.However,itisusedlessfrequentlythanhexadecimalinconjunctionwithcomputersandmicroprocessorstoexpressbinaryquantitiesforinputandoutputpurposes.§2.9OCTALNUMBERS16.LikethehexadecimaTheOCTALnumbersystemiscomposedofeightdigits,whichare0,1,2,3,4,5,6,7Tocountabove7,beginanothercolumnandstartover:10,11,12,13,14,15,16,17,20,21andsoon.Abase—8numbersystem.17.TheO