Digital_circuit01

ModernElectronicTechniques(AnalogCircuitandDigitalCircuit)ZANG,Chunhua(臧春华)CollegeofElectronicandInformationEngineeringTextbooks1.数字设计----原理与实践(第四版影印版)DigitalDesign(Principles&Practices)(FourthEdition)JoneF.Wakerly高等教育出版社,2007年2.数字设计引论（第二版）臧春华、沈嗣昌、蒋璇高等教育出版社,2010年ThiscoursebelongstoYOUanditssuccessrestslargelywithYOUDonotbeafraidtoASKQUESTIONS.BEONTIMEHAVEFUNLearnCollectionToldTold&ShownTold,Shown&ExperienceRecallafter70%72%85%3weeksRecallafter10%32%65%3monthsIntroduction0.1DigitalInformationandCircuitDigitalInformationisdiscreteelementsofinformation,includingnumericandnonnumericinformation.DigitalCircuitsareelectronicequipment,whichcanprocessDigitalInformation.0.2DigitalElementDigitalelementusedindigitalcircuits,isjustswitchinreality.SodigitalcircuitsarealsocalledSwitchingCircuits.Element:Relay-ElectronTube-Transistor-IntegratedCircuit(IC)0.3DigitalSignalDiscreteelementsofinformationarerepresentedinadigitalsystembyphysicalquantities,voltageorcurrent,calledSignal.TrendofDigitalCircuits:Thefunctionisstronger;Thespeedisfaster;Thevolumeissmaller;Thepowerdissipationislower!DigitalcircuitDigitalcircuitSignalwithParallelmodeSignalwithSeriesmode1----HighLevelSignal;0----LowLevelSignal并行式串联方式0.4BooleanAlgebraBooleanAlgebra,calledLogicAlgebra,isanalgebradealingwithbinaryvariablesandlogicoperations.Itisthetheoreticalbaseofdigitalsystems.SodigitalcircuitsarealsocalledLogicCircuits.BasicLogicOperations:ANDORNOTBasiclogicoperationsrealizedbyswitchesANDORNOT0.5BasicLogicGatesElectroniccircuitsthatrealizelogicoperationsarecalledgates,whicharethebasicdevicesindigitalcircuits.GraphicSymbolsandTruthTablesofthegates:(ANSI/IEEEStandard91-1984)Chapter1NumberSystemsandCodes1.1NumberSystems1.DecimalNumbers•Usedindailylife;•It’sbaseorradixis10;•Representnumbersbystringsofdigits,(0,1,…,9)andadecimalpoint(alsocalledradixpoint),whereeachdigithasanassociateweight,apoweroftheradix10;•Thevalueofthenumberisthesumofeachdigitmultipliedbythecorrespondingpoweroftheradix10(alsocalledtheweightedsumofthedigits).Ex1-1724.5=7×102+2×101+4×100+5×10-1ForthebaseRsystem,anumberisrepresentedbystringsofdigits(0,1,…R-1)andaradixpoint.(An-1An-2…A0.A-1A-2…A-m)RPositionalNotation=(An-1×Rn-1+An-2×Rn-2+…A0×R0+A-1×R-1+A-2×R-2+…A-m×R-m)10PolynomialNotationInadditiontodecimal,threesystemsareusedindigitalcircuits:Binary,OctalandHexadecimal.Thelattertwosystemsaremainlyusedfordocumentation,becausetheyprovideconvenientshorthandrepresentationsformultibitsbinarynumbersinadigitalsystem.2.BinaryNumbers•Representnumbersbystringsofonlytwodigits,0and1,andaradixpoint;•It’sbaseorradixis2;•Thevalueofthenumberisthesumofeachdigitmultipliedbythecorrespondingpoweroftheradix2.Ex1-2(11101.101)2=1×24+1×23+1×22+1×20+1×2-1+1×2-3=(29.625)103.OctalandHexadecimalThereare8digits(0,1,2…,7)inoctalsystem,and16digits(0,1,2…,9,A,B,C,D,E,F)inhexadecimalsystem.EX1-3(35.5)8=3×81+5+5×8-1=(29.625)10EX1-4(1D.A)16=1×161+13+10×16-1=(29.625)104.ConversionfromDecimaltoOtherBases(1)ConversionOfDecimalIntegers:RadixDivision(tillquotient=0)EX1-5(29)10=(?)229÷2=14……..1LSB(LeastSignificantBit)14÷2=7………07÷2=3………..13÷2=1………..11÷2=0………..1MSB(MostSignificantBit)Thus(29)10=(11101)2EX1-6(29)10=(?)829÷8=3………53÷8=0………3Thus(29)10=(35)8EX1-7(29)10=(?)1629÷16=1………131÷16=0………1Thus(29)10=(1D)16(2)ConversionOfDecimalFractions:RadixMultiplication(tillthefraction=0.0orresultreachestheprecisionrequirement)EX1-8(0.625)10=(?)20.625×2=[1].25……1MSB0.25×2=[0].5………00.5×2=[1].0………..1LSBThus(0.625)10=(0.101)2EX1-9(0.625)10=(?)165.ConversionbetweenbaseAandbaseBwhenB=Ak(1)every3bitsofbinarynumberscorrespondto1bitofoctalnumbersEX1-10(11101.101)2=(?)8(011101.101)2(35.5)80.625×16=[10].0……10Thus(0.625)10=(0.A)2(2)every4bitsofbinarynumberscorrespondto1bitofhexadecimalnumbersEX1-11(11101.101)2=(?)16(00011101.1010)2(1D.A)16(1)AdditionRule:0+0=0,0+1=1,1+0=1,1+1=0(carry=1,Thatis1+1=10)Ex1-121101+1011=?1101+101111000Thus1101+1011=110005.BinaryArithmeticBinaryarithmeticoperationsareperformedusingthesameprocedureasdecimaloperations.(2)SubstractionRule:0-0=0,1-0=1,1-1=0,0-1=1(borrow=1,Thatis10-1=1)Ex1-131101-1011=?1101-10110010Thus1101-1011=0010(3)MultiplicationRule:0×0=0,0×1=0,1×0=0,1×1=1(sameastheANDoperation)Ex1-141011×101=?1011×101101100001011110111Thus1011×101=110111(4)DivisionEx1-15:1110111÷1001=?1101quotient100111101111001101110011011100110remainder1.2BinaryCodesAcodeisasystematicandpreferablystandardizeduseofagivensetofsymbolsforrepresentinginformation.BinaryCodesuseonlyBinarysymbols(0and1)torepresentinformation.Asetofn-bitstringsinwhichdifferentbitstringsrepresentdifferentnumbersorotherthingsiscalledacode.Aparticularcombinationofnbit-valuesiscalledacodeword.DecimalBinaryGray0000000001000100012001000113001100104010001105010101116011001017011101008100011009100111011010101111111011111012110010101311011011141110100115111110001.NaturalBinaryCodesandBinaryGrayCodes•ConstructionofGraycodes1bit2bits3bits0000001010011101110010110111101100Thefirst2ncodewordsofan(n+1)-bitGraycodeequalthecodewordsofann-bitGraycode,writteninorderwithaleading0appende