姜书艳数字逻辑设计及应用4

1DigitalLogicDesignandApplication(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)2ReviewofChapter2(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)3ReviewofChapter2(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)4ReviewofChapter2(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)5ReviewofChapter2(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)6ReviewofChapter2(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)7DigitalLogicDesignandApplication(数字逻辑设计及应用)0101100111100110010010001000000001100110591410881610＋＋＋＋＋＋＋41＋611修正修正01000101100110011001001001101000459991810＋＋＋＋＋＋811修正8ReviewofChapter2(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)9ReviewofChapter2(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)102.11Graycode（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。)11ReviewofChapter2(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:110110110101001012ReviewofChapter2(第二章内容回顾)构造方法异或（XOR）运算：相异为1，相同为0Gn=BnBn=GnGn-1=Bn⊕Bn-1Bn-1=Gn⊕Gn-1……G0=B1⊕B0B0=Gn⊕Gn-1⊕…⊕G0DigitalLogicDesignandApplication(数字逻辑设计及应用)13Chapter3DigitalCircuits(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)14ConsidersomeQuestions（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)15DigitalLogicDesignandApplication(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)101616SwitchesElectronicswitchesarethebasisofbinarydigitalcircuitsAswitchhasthreepartsSourceinput,andoutputCurrenttriestoflowfromsourceinputtooutputControlinputVoltagecontrolswhetherthatcurrentcanflow“off”“on”outputsourceinputoutputsourceinputcontrolinputcontrolinput1717SwitchesTheamazing(令人惊奇的）shrinking（逐渐减小的）switch1930s:Relays1940s:Vacuumtubes1950s:Discretetransistor1960s:Integratedcircuits(ICs)InitiallyjustafewtransistorsonICThentens,hundreds,thousands...relayvacuumtubediscretetransistorICquarter(toseetherelativesize)1818TheCMOSTransistorCMOStransistorBasicswitchinmodernICsSilicon--notquiteaconductororinsulator:Semiconductor2.3gatesourcedrainoxideApositivevoltagehere...(a)ICpackageIC...attractselectronshere,turningthechannelbetweenthesourceanddrainintoaconductor1919TheCMOSTransistorCMOStransistorBasicswitchinmodernICsdoesnotconduct0conducts1gatenMOSdoesnotconduct1gatepMOSconducts02.32020Moore’sLawICcapacity（容量，集成度）doublingaboutevery18monthsforseveraldecadesKnownas“Moore’sLaw”afterGordonMoore,co-founderofIntelPredicted（预言）in1965predictedthatcomponentsperICwoulddoubleroughly（粗略地，大致上）everyyearorso21Moore’sLawForaparticular（特定的）numberoftransistors,theICareashrinksbyhalfevery18monthsConsiderhowmuchshrinkingoccursinjust10years(trydrawingit)Enablesincredibly（不能相信的，难以置信的）powerfulcomputationinincrediblytinydevices22Moore’sLawToday’sICsholdbillionsoftransistorsThefirstPentiumprocessor(early1990s)neededonly3millionAnIntelPentiumprocessorIChavingmillionsoftransistors233.1LogicSignalsandGates(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2424BooleanLogicGatesBuildingBlocksforDigitalCircuits(BecauseSwitchesareHardtoWorkWith)“Logicgates”arebetterdigitalcircuitbuildingblocksthanswitches(transistors)Why?...2.4Abstraction（提取）reducescomplexity!2525BooleanAlgebraanditsRelationtoDigitalCircuitsTounderstandthebenefitsof“logicgates”vs.switches,weshouldfirstunderstandBooleanalgebra“Traditional”algebraVariablesrepresentrealnumbers(x,y)Operators（运算器）operateonvariables,returnrealnumbers(2.5*x+y-3)a2626BooleanAlgebraanditsRelationtoDigitalCircuitsBooleanAlge