2019姜书艳-数字逻辑设计及应用-2.ppt

1数字逻辑设计及应用Chapter2NumberSystemsandcodes(数系与编码)介绍在数字逻辑体系中信号的表达方式、类型，不同表达方式之间的转换，运算的规则等。DigitalLogicDesignandApplication(数字逻辑设计及应用)2ReviewofChapter1(第一章内容回顾)AnalogversusDigital(模拟与数字)DigitalDevices(数字器件)：Gates（门电路）、Flip-flops（触发器）ElectronicandSoftwareAspectsofDigitalDesign(数字设计的电子技术和软件技术)DigitalLogicDesignandApplication(数字逻辑设计及应用)3ReviewofChapter1(第一章内容回顾)IntegratedCircuit（IC，集成电路）ProgrammableLogicDevices（PLA、PLD、CPLD、FPGA,可编程逻辑器件）Application-SpecificICs（ASIC,专用集成电路）Printed-CircuitBoards(PCB,印制电路板)DigitalLogicDesignandApplication(数字逻辑设计及应用)4Chapter2NumberSystemsandcodes(数系与编码)TwokindsofInformation(信息主要有两类)：NumericData(数值信息)NonnumericData(非数值信息)DigitalLogicDesignandApplication(数字逻辑设计及应用)—NumberSystemsandtheirConversions(数制及其转换)--NonnumericDataRepresentation–Codes(非数值信息的表征--编码)5Chapter2NumberSystemsandcodes(数系与编码)数字系统只处理数字信号0,1；需要将任意信息用(0,1)表达；用（0，1）表达数量：数制二进制用（0，1）表达不同对象：符号编码DigitalLogicDesignandApplication(数字逻辑设计及应用)66HowtoEncodeText:ASCII,UnicodeASCII:7-(or8-)bitencodingofeachletter,number,orsymbolSampleASCIIencodingsSymbolEncoding0100000space␠0100001!01000100100011#0100100$0100101%0100110&0100111'0101000(0101001)0101010*0101011+0101100,0101101-0101110.0101111/SymbolEncoding1001110N1001111O1010000P1010001Q1010010R1010011S1010100T1010101U1010110V1010111W1011000X1011001Y1011010Z1000001A1000010B1000011C1000100D1000101E1000110F1000111G1001000H1001001I1001010J1001011K1001100L1001101MSymbolEncodingSymbolEncoding011000000110001101100102011001130110100401101015011011060110111701110008011100191100001a1100010b...1111001y1111010z……77HowtoEncodeText:ASCII,UnicodeUnicode:Increasinglypopular16-bitencodingEncodescharactersfromvariousworldlanguages……88HowtoEncodeNumbers:BinaryNumbersBaseten(decimal)Tensymbols:0,1,2,...,8,and9Morethan9--nextpositionSoeachpositionpower（幂）of10Nothingspecialaboutbase10--usedbecausewehave10fingers104103102523101100•Eachpositionrepresentsabasequantity;symbolinpositionmeanshowmanyofthatquantity99HowtoEncodeNumbers:BinaryNumbersBasetwo(binary)Twosymbols:0and1Morethan1--nextpositionSoeachpositionpower（幂）of22423221012120Q:Howmuch?+=415+=a•Eachpositionrepresentsabasequantity;symbolinpositionmeanshowmanyofthatquantityThereareonly10typesofpeopleintheworld:thosewhounderstandbinary,andthosewhodon't.1010Usefultoknowpowersof2:2423222120292827262516842151225612864321684215122561286432Practicecountingupbypowersof2:112.1PositionalNumberSystem(按位计数制)AnyDecimalNumberDCanBeRepresentedastheFollowing(任意十进制数D可表示如下):D=dp-1dp-2...d1d0.d-1d-2...d-n推广：D2=∑di×2iD16=∑di×16i1pniiirdWeightofibit;BaseorRadixofrNumberSystem(第i位的权；r计数制的基数)DigitalLogicDesignandApplication(数字逻辑设计及应用)122.1PositionalNumberSystem(按位计数制)按位计数制的特点1)采用基数（BaseorRadix），R进制的基数是R2)基数确定数符的个数如十进制的数符为：0、1、2、3、4、5、6、7、8、9，个数为10二进制的数符为：0、1，个数为23）逢基数进一DigitalLogicDesignandApplication(数字逻辑设计及应用)132.1PositionalNumberSystem(按位计数制)DigitalLogicDesignandApplication(数字逻辑设计及应用)DecimalandBinaryDecimalsystem:baseis10,thedigitmaybe0to91012101011011001011.101Binarysystem:baseis2,thedigitmaybe0or110122212120211.101bit:onedigitinbinarysystem;1414UsingDigitalDatainaDigitalSystemtemperaturesensor0011000033AtemperaturesensoroutputstemperatureinbinaryThesystemreadsthetemperature,outputsASCIIcode:“F”forfreezing(0-32)“B”forboiling(212ormore)“N”fornormal1515UsingDigitalDatainaDigitalSystemtemperaturesensor0011000033DigitalSystemdisplayNN1000111if(input=00100000)//32output=1000110//Felseif(input=11010100)//212output=1000010//Belseoutput=1001110//NAdisplayconvertsitsASCIIinputtothecorrespondingletter162.2OctalandHexadecimalNumbers(八进制和十六进制)基数数码特性OctalNumber(八进制)80~7逢八进一BinaryNumber(二进制)20,1逢二进一HexadecimalNumber(十六进制)160~9,A~F逢十六进一DigitalLogicDesignandApplication(数字逻辑设计及应用)17说明DigitalLogicDesignandApplication(数字逻辑设计及应用)选择什么数制来表示信息，对数字系统的成本和性能影响很大，在数字电路中多使用二进制.MostSignificantBit（MSB,最高有效位）LeastSignificantBit（LSB,最低有效位）1011100010112MSBLSB18DigitalLogicDesignandApplication(数字逻辑设计及应用)表2.1十进制、二进制、八进制与十六进制数十进制二进制八进制十六进制00000001000111200102230011334010044501015560110667011177810001089100111910101012A11101113B12110014C13110115D14111016E15111117F1919BaseSixteen:AnotherBaseUsedbyDesignersNicebecauseeachpositionrepresentsfourbase-twopositionsCompactwaytowritebinarynumbersKnownashexadecimal,orjusthexQ:Write11110000inhexF0Q:ConverthexA01tobinary101000000001A:A:20二进制与八进制和十六进制之间的转换位数替换法：保持小数点不变，每位八进制数对应3位二进制数;每位十六进制数对应4位二进制数;二进制转换时，从小数点开始向左右分组，在MSB前面和LSB后面可以加0；转换为二进制时，MSB前面和LSB后面的0不写；例：1011100010112=56138=B8B1610111000.10112=207.548=B8.B161000110010012=()8=()16DigitalLogicDesignandApplication(数字逻辑设计及应用)2121HexExample:RFIDTagBatteryless（无电池）tagpowered（功率）byradiofieldTransmits（发送）uniqueidentification（鉴定）numberExample:32bitid（身份证明）8-bitprovincenumber,8-bitcitynumber,16-bitanimalnumberTagcontentsareinbinaryButprogrammersusehexwhenwriting/readingRFIDtagProvince#City#Animal#Province:7City:160Animal:51310100000000001110000001000000001A0070201TagIDinhex:07A00201(a)(b)(c)(d)(f)(e)222.3GeneralPositional-Number-SystemConversion(常用按