姜书艳 数字逻辑设计及应用 4

DigitalLogicDesignandApplication(数字逻辑设计及应用)ReviewofChapter2

(第二章内容回顾)GeneralPositional-Number-SystemConversion(常用按位计数制的转换)AdditionandSubtractionofNon-decimalNumbers(非十进制的加法和减法)1ReviewofChapter2

(第二章内容回顾)RepresentationofNegativeNumbers

(负数的表示)Signed-Magnitude[符号－数值（原码）]ComplementNumberSystems(补码数制)

Radix–Complement(基数补码)

DiminishedRadix–Complement

[基数减1补码（基数反码）]DigitalLogicDesignandApplication(数字逻辑设计及应用)2ReviewofChapter2

(第二章内容回顾)BinarySigned-Magnitude,Ones’–Complement,andTwo’s–ComplementRepresentation(二进制的原码、反码、补码表示)

直接由补码(反码)求二进制数值的大小：最高位位权为-2n-1(-2n-1-1)(1011)2补=（）10DigitalLogicDesignandApplication(数字逻辑设计及应用)3ReviewofChapter2

(第二章内容回顾)Two’s–ComplementAdditionandSubtraction(二进制补码的加法和减法)Overflow（溢出）如果加法运算产生的和超出了数制表示的范围，则结果发生了溢出（Overflow）。如何判断溢出？

MSBCin

与Cout不同DigitalLogicDesignandApplication(数字逻辑设计及应用)4ReviewofChapter2

(第二章内容回顾)Howtorepresenta1-bitDecimalnumberwitha4-bitBinarycode(如何用4位二进制码表示1位十进制码)？——BinaryCodedDecimal(BCD码）(0.301)10=()8421BCDDigitalLogicDesignandApplication(数字逻辑设计及应用)5ReviewofChapter2

(第二章内容回顾)AdditionofBCDDigits(BCD数的加法)思考：两个BCD码与两个4位二进制数相加的区别?

DigitalLogicDesignandApplication(数字逻辑设计及应用)6DigitalLogicDesignandApplication(数字逻辑设计及应用)7ReviewofChapter2

(第二章内容回顾)AdditionofBCDDigits(BCD数的加法)思考：何时需要进行修正？

如果(X+Y)产生进位信号C或在1010~1111之间如何修正？——结果加6DigitalLogicDesignandApplication(数字逻辑设计及应用)8ReviewofChapter2

(第二章内容回顾)Graycode（格雷码）任意相邻码字间只有一位数位变化最高位的0和1只改变一次最大数回到0也只有一位码元不同DigitalLogicDesignandApplication(数字逻辑设计及应用)92.11Graycode（格雷码）DigitalLogicDesignandApplication(数字逻辑设计及应用)构造方法ReflectedCode（反射码）直接构造

Thebitsofann-bitbinarycordwordarenumberedfromrighttoleft,from0ton-1.[对n

位二进制的码字从右到左编号（0~n-1）]

BitiofaGray-codecodewordis0ifbitsiandi+1ofthecorrespondingbinarycodewordarethesame,elsebitiis1.(若二进制码字的第i位和第i+1位相同，则对应的葛莱码码字的第i

位为0，否则为1。)10ReviewofChapter2

(第二章内容回顾)DigitalLogicDesignandApplication(数字逻辑设计及应用)FrombinarynumbertoGraycodeThewidthissame,theMSBissame;Fromlefttoright,ifabitinbinarynumberissameasitsleftbit,thegraycodeis0,ifitisdifferent,thegraycodeis1.Examples:binarynumber:1001001001100011Graycode:110110110101001011ReviewofChapter2

(第二章内容回顾)构造方法异或（XOR）运算：相异为1，相同为0Gn=Bn

Bn=GnGn-1=Bn⊕Bn-1Bn-1=Gn⊕Gn-1……G0=B1⊕B0B0=Gn⊕Gn-1⊕…⊕G0DigitalLogicDesignandApplication(数字逻辑设计及应用)12Chapter3DigitalCircuits(数字电路)GiveaknowledgeoftheElectricalaspectsofDigitalCircuits(介绍数字电路中的电气知识)DigitalLogicDesignandApplication(数字逻辑设计及应用)13ConsidersomeQuestions

（思考几个问题）在模拟的世界中如何表征数字系统？如何将物理上的实际值映射为逻辑上的0和1？什么时候考虑器件的逻辑功能；什么时候考虑器件的模拟特性？DigitalLogicDesignandApplication(数字逻辑设计及应用)14DigitalLogicDesignandApplication(数字逻辑设计及应用)3.1LogicSignalsandGates

(逻辑信号和门电路)HowtogettheHIGHandLOWVoltage(如何获得高、低电平)？HIGHto0or1(高电平对应0还是1)？VOUTVINVccR获得高、低电平的基本原理Positive(正逻辑)10Negative(负逻辑)101516SwitchesElectronicswitchesarethebasisofbinarydigitalcircuitsAswitchhasthreepartsSourceinput,andoutputCurrenttriestoflowfromsourceinputtooutputControlinputVoltagecontrolswhetherthatcurrentcanflow“off”“on”outputsourceinputoutputsourceinputcontrolinputcontrolinput1617SwitchesTheamazing(令人惊奇的）shrinking（逐渐减小的）switch1930s:Relays1940s:Vacuumtubes1950s:Discretetransistor1960s:Integratedcircuits(ICs)InitiallyjustafewtransistorsonICThentens,hundreds,thousands...relayvacuumtubediscretetransistorICquarter(toseetherelativesize)1718TheCMOSTransistorCMOStransistorBasicswitchinmodernICsSilicon--notquiteaconductororinsulator:

Semiconductor2.3gatesourcedrainoxideApositivevoltagehere...(a)ICpackageIC...attractselectronshere,turningthechannelbetweenthesourceanddrainintoaconductor1819TheCMOSTransistorCMOStransistorBasicswitchinmodernICsdoesnotconduct0conducts1gatenMOSdoesnotconduct1gatepMOSconducts02.31920Moore’sLawICcapacity（容量，集成度）doublingaboutevery18monthsforseveraldecadesKnownas“Moore’sLaw”afterGordonMoore,co-founderofIntelPredicted（预言）in1965predictedthatcomponentsperICwoulddoubleroughly（粗略地，大致上）everyyearorso20Moore’sLawForaparticular（特定的）numberoftransistors,theICareashrinksbyhalfevery18monthsConsiderhowmuchshrinkingoccursinjust10years(trydrawingit)Enablesincredibly（不能相信的，难以置信的）powerfulcomputationinincrediblytinydevices21Moore’sLawToday’sICsholdbillionsoftransistorsThefirstPentiumprocessor(early1990s)neededonly3millionAnIntelPentiumprocessorIChavingmillionsoftransistors223.1LogicSignalsandGates

(逻辑信号和门电路)DigitalLogicDesignandApplication(数字逻辑设计及应用)从物理的角度考虑电路如何工作，工作中的电气特性实际物理器件不可避免的时间延迟问题从逻辑角度输入、输出的逻辑关系

三种基本逻辑：与、或、非2324BooleanLogicGates

BuildingBlocksforDigitalCircuits

(BecauseSwitchesareHardtoWorkWith)“Logicgates”arebetterdigitalcircuitbuildingblocksthanswitches(transistors)Why?...2.4Abstraction（提取）reducescomplexity!2425BooleanAlgebraanditsRelationtoDigitalCircuitsTounderstandthebenefitsof“logicgates”vs.switches,weshouldfirstunderstandBooleanalgebra“Traditional”algebraVariablesrepresentrealnumbers(x,y)Operators（运算器）operateonvariables,returnrealnumbers(2.5*x+y-3)a2526BooleanAlgebraanditsRelationtoDigitalCircuitsBooleanAlgebraVariablesrepresent0or1onlyOperatorsreturn0or1onlyBasicoperatorsAND:aANDbreturns1onlywhenbotha=1andb=1OR:aORbreturns1ifeither(orboth)a=1orb=1NOT:NOTareturnstheoppositeofa(1ifa=0,0ifa=1)a261、BasicLogicFunction:AND

（基本逻辑运算：与）000010100111ABZLogicExpression

(逻辑表达式)Z=A·BSwitch:1-on,0-off(开关：1通,0断)Lamp:1-Light,0-out(灯:1亮,0不亮)Producea1outputifandonlyifitsinputsareall1(当且仅当所有输入全为1时，输出为1)TruthTable

(真值表)&ABZABZ（逻辑符号）ABZLogicCircuitDigitalLogicDesignandApplication(数字逻辑设计及应用)272、BasicLogicFunction:OR

（基本逻辑运算：或）LogicExpression(逻辑表达式)：Z=A+BABZ真值表ABZProducea1outputifanyinputis1

(只要有任何一个输入为1，输出就为1)≥1ABZABZ逻辑符号000011101111TruthTableLogicCircuitDigitalLogicDesignandApplication(数字逻辑设计及应用)28AZ0110真值表LogicExpression(逻辑表达式)：Y=A=A’AZRProduceanoutputvaluethatistheoppositeofitsinputvalue.(产生一个与输入相反的输出)UsuallycalledanInverter

（通常称为反相器）1ZAAZ(逻辑符号)DigitalLogicDesignandApplication(数字逻辑设计及应用)3、BasicLogicFunction:NOT

（基本逻辑运算：非）TruthTableLogicCircuit294、NANDandNORGates(与非和或非)NAND(与非)

LogicExpression

(逻辑表达式)：Z=(A·B)’

LogicCircuit(逻辑符号)：NOR(或非)

LogicExpression(逻辑表达式)：Z=(A+B)’

LogicCircuit

(逻辑符号)：&≥1DigitalLogicDesignandApplication(数字逻辑设计及应用)30DigitalLogicDesignandApplication(数字逻辑设计及应用)TruthTable(真值表)&≥1LogicalOperation(逻辑运算)

NAND(与非)

NOR(或非)

LogicCircuit(逻辑符号)

LogicExpression(逻辑表达式)

Y=(AžB)’‘

Y=(A+B)’‘AB

0

0

1

11

Y

1

1

1

0

Y

1

0

0

0

1003132BooleanAlgebraanditsRelationtoDigitalCircuitsDevelopedmid-1800’sbyGeorgeBooletoformalize（使成正式）

humanthoughtEx:“I’llgotolunchifMarygoesORJohngoes,ANDSallydoesnotgo.”LetFrepresentmygoingtolunch(1meansIgo,0Idon’tgo)Likewise（类似地）,mforMarygoing,jforJohn,andsforSallyThenF=(mORj)ANDNOT(s)3233ConvertingtoBooleanEquationsQ1.Afiresprinkler（洒水器）systemshouldspray（喷）waterifhighheatissensedandthesystemissettoenabled.Answer:LetBooleanvariablehrepresent“highheatissensed,”erepresent“enabled,”andFrepresent“sprayingwater.”

Thenanequationis:F=hANDe.a3334ConvertingtoBooleanEquationsQ2.Acaralarmshouldsoundifthealarmisenabled,andeitherthecarisshakenorthedoorisopened.Answer:Letarepresent“alarmisenabled,”srepresent“carisshaken,”drepresent“doorisopened,”andFrepresent“alarmsounds.”

Thenanequationis:F=aAND(sORd).a34RelatingBooleanAlgebratoDigitalDesignBooleanalgebra(mid-1800s)Boole’sintent:formalizehumanthoughtSwitches(1930s)Shannon(1938)DigitaldesignShowedapplicationofBooleanalgebratodesignofswitch-basedcircuitsFortelephoneswitchingandotherelectronicuses35DigitalLogicDesignandApplication(数字逻辑设计及应用)3.2LogicFamilies（逻辑系列）同一系列的芯片具有类似的输入、输出及内部电路特征，但逻辑功能不同。不同系列的芯片可能不匹配CMOS系列TTL逻辑系列36DigitalLogicDesignandApplication(数字逻辑设计及应用)3.3CMOSLogic(CMOS

逻辑)CMOSLogiclevels(COMS逻辑电平)5.0V3.5V1.5V0.0VATypicalLogicCircuit:5-VoltPowerSupply(典型的5V电源电压)OtherPower-SupplyVoltages:3.3,2.5or1.8Volts(其它电源电压：3.3V,2.5V或1.8V)Logic1(High)[逻辑1（高态）]Logic0(Low)[逻辑0（低态）]37DigitalLogicDesignandApplication(数字逻辑设计及应用)2、MOSTransistors(MOS晶体管)TwoTypes:N-ChannelandP-Channel(分为：N沟道和P沟道)Drain(漏极)Source(源极)Gate(栅极)Vgs+N-Channel(N沟道)Source(源极)Drain(漏极)Gate(栅极)

+VgsP-Channel(P沟道)38DigitalLogicDesignandApplication(数字逻辑设计及应用)2、MOSTransistors(MOS晶体管)TwoTypes:N-ChannelandP-Channel(分为：N沟道和P沟道)Source(源极)Drain(漏极)Gate(栅极)

+VgsP-Channel(P沟道)Usually(通常)：

Vgs

<=0

Vgs

=0

RdsVeryHigh

Off(截止状态)

Vgs

Rds

On(导通状态)39DigitalLogicDesignandApplication(数字逻辑设计及应用)2、MOSTransistors(MOS晶体管)TheGateofaMOStransistorhasaveryhighimpedance（阻抗）.[Overmegohm(106ohms)][MOS晶体管栅极阻抗非常高（>兆欧）]Regardlessofgatevoltage(无论栅电压如何)

Almostnocurrentflowsfromthegatetosource,orfromthegatetodrain.(栅－源、栅－漏之间几乎没有电流)

（Leakage（漏出）Current,Lessthanmicroampere(漏电流,

A,10-6A）TheGateisCapacitively（容性地）coupledtothesourceanddrain

(栅极与源和漏极之间有容性耦合)

Thepowerneedtochargeanddischargethiscapacitance（电容）oneachinputsignaltransitionaccountsforanontrivial（非平凡的）portionofacircuit’spowerconsumption(信号转换时，电容充放电，功耗较大).40DigitalLogicDesignandApplication(数字逻辑设计及应用)MOS管的基本开关电路vI+–vO–+iD+VDDRDDGS只要电路参数选择合理输入低，截止，输出高输入高，导通，输出低41DigitalLogicDesignandApplication(数字逻辑设计及应用)3、BasicCMOSInverterCircuit

(基本的CMOS反相器)FunctionalBehavior

(工作原理)1、VIN=0.0VVGSN=0.0V，

TnOff(截止)VGSP=VIN–VDD=–5.0V，

TpOn(导通)VOUT

VDD=5.0VVDD=+5.0VVOUTVINTpTn423、BasicCMOSInverterCircuit

(基本的CMOS反相器)2、VIN=VDD=5.0VVGSN=5.0V

TnOn(导通)VGSP=VIN–VDD=0.0V

TpOff(截止)VOUT

0VDD=+5.0VVOUTVINTpTnDigitalLogicDesignandApplication(数字逻辑设计及应用)4344NOTgatex01F1010F1x0(a)10F0x1(b)Whentheinputis0Whentheinputis10110timeFx44DigitalLogicDesignandApplication(数字逻辑设计及应用)4、CMOSNAND(CMOS与非门)

FunctionalBehavior

(工作原理)：1、EitherInputLow,(A、B至少有一个为低),ThenEitherT1,T3Off(T1、T3至少有一个截止)EitherT2,T4On(T2、T4至少有一个导通)ZisHigh[Z为高

VDD）]VDD=+5.0VZABT1T2T4T3454、CMOSNANDGate(CMOS与非门)2、BothInputsHigh(A、B都为高),ThenBothT1,T3On(T1、T3都导通)BothT2,T4Off(T2，T4都截止)

ZisLow[Z为低（

0V）]VDD=+5.0VZABT1T2T4T3DigitalLogicDesignandApplication(数字逻辑设计及应用)465、CMOSNORGate(CMOS或非门)FunctionalBehavior

(工作原理)：1、BothInputsLow(A、B都为低),ThenBothT1、T3Off(T1、T3都截止)BothT2,T4On(T2，T4都导通)ZisHigh[Z为高（

VDD）]VDD=+5.0VZABT1T2T4T3DigitalLogicDesignandApplication(数字逻辑设计及应用)475、CMOSNORGate(CMOS或非门)FunctionalBehavior

(工作原理)：2、EitherInputHigh(A、B至少有一个为高)ThenEitherT1、T3On(T1、T3至少有一个导通)EitherT2,T4Off(T2、T4至少有一个截止)ZisLow[Z为低（0V）]VDD=+5.0VZABT1T2T4T3DigitalLogicDesignandApplication(数字逻辑设计及应用)4849BuildingCircuitsUsingGatesRecall（回想）themotion-in-darkexampleTurnonlamp(F=1)whenmotionsensed(a=1)andnolight(b=0)F=aANDNOT(b)4950BuildingCircuitsUsingGatesBuildusinglogicgates,ANDandNOT,asshownWejustbuiltourfirstdigitalcircuit!5051Example:SeatBeltWarningLightSystemDesigncircuitforwarninglightSensorss=1:seatbeltfastened（系紧）k=1:keyinsertedCaptureBooleanequationseatbeltnotfastened,andkeyinsertedw=NOT(s)ANDk5152Example:SeatBeltWarningLightSystemConvertequationtocircuitTimingdiagramillustratescircuitbehaviorWesetinputstoanyvaluesOutputsetaccordingtocircuitaatimeInputsOutputs111000kswkswBeltWarnSeatbelt5253Moreexamples:SeatbeltwarninglightextensionsOnlyilluminate（照亮）warninglightifpersonisintheseat(p=1),andseatbeltnotfastenedandkeyinsertedw=pANDNOT(s)ANDkkpswBeltWarna5354Moreexamples:SeatbeltwarninglightextensionsaGivent=1for5secondsafterkeyinserted.Turnonwarninglightwhent=1(tocheckthatwarninglightsareworking)w=(pANDNOT(s)ANDk)ORtakwpstBeltWarn546、Fan－In（扇入）TheNumberofInputsthataGatehave

(门电路所具有的输入端的数目)TheAdditive“on”ResistanceofseriestransistorslimitstheFan–InofCMOSgates.