63Chapter3-Binary System and Boolean Algebra

科技英语中数学公式的读法数学公式的读法(Pronunciationofmathematicalexpressions)1逻辑(Logic)thereexistsforallpqpimpliesq/ifp,thenqpqpifandonlyifqpisequivalenttoqpandqareequivalent2集合(Sets)xAxbelongstoA/xisanelement(oramember)ofAxAxdoesnotbelongtoA/xisnotanelement(oramember)ofAABAiscontainedinB/AisasubsetofBABAcontainsB/BisasubsetofAABAcapB/AmeetB/AintersectionBABAcupB/AjoinB/AunionBB/AAminusB/thedifferencebetweenAandBA×BAcrossB/theCartesianproductofAandB(A与B的笛卡尔积)数学公式的读法(Pronunciationofmathematicalexpressions)数学公式的读法(Pronunciationofmathematicalexpressions)3实数(Realnumbers)x+1xplusonex-1xminusonex±1xplusorminusonexyxy/xmultipliedbyy(x-y)(x+y)xminusy,xplusyxovery=theequalssignx=5xequals5/xisequalto5x≠5x(is)notequalto5x≡yxisequivalentto(oridenticalwith)yyx3实数(Realnumbers)xyxisgreaterthanyx≥yxisgreaterthanorequaltoyxyxislessthanyxyxislessthanorequaltoy0x1zeroislessthanxislessthan10x1zeroislessthanorequaltoxislessthanorequalto1|x|modx/modulusxx2xsquared/x(raised)tothepower2x3xcubedx4xtothefourth/xtothepowerfourxnxtothenth/xtothepowernx-nxtothe(power)minusn数学公式的读法(Pronunciationofmathematicalexpressions)数学公式的读法(Pronunciationofmathematicalexpressions)3实数(Realnumbers)n!nfactorial(x+y)2xplusyallsquaredxixi/xsubscripti/xsuffixi/xsubithesumfromiequalsonetonai/thesumasirunsfrom1tonoftheaixoveryallsquaredxhatxbarxtildexˆxx~niia12yx数学公式的读法(Pronunciationofmathematicalexpressions)4线性代数(Linearalgebra)||A||thenorm(ormodulus)ofxOA/vectorOAOA/thelengthofthesegmentOAATAtranspose/thetransposeofAA-1Ainverse/theinverseofAOAOA数学公式的读法(Pronunciationofmathematicalexpressions)5函数(Functions)f(x)fx/fofx/thefunctionfofxf:S→TafunctionffromStoTxmapstoy/xissent(ormapped)toyf(x)fprimex/fdashx/the(rst)derivativeoffwithrespecttoxf(x)fdouble–primex/fdouble–dashx/thesecondderivativeoffwithrespecttoxf(x)ftriple–primex/ftriple–dashx/thethirdderivativeoffwithrespecttoxf(4)fourx/thefourthderivativeoffwithrespecttoxlnylogytothebasee/logtothebaseeofy/naturallog(of)yyx数学公式的读法(Pronunciationofmathematicalexpressions)5函数(Functions)thepartial(derivative)offwithrespecttox1thesecondpartial(derivative)offwithrespecttox1theintegralfromzerotoinfinitythelimitasxapproacheszerofromabove1xf212xf00limxComputerEnglishChapter3BinarySystemandBooleanAlgebraKeypoints:usefultermsanddefinitionsofBinarysystemandBooleanAlgebraDifficultpoints:ConversionoftheBinarySystemsandBooleanAlgebraRequirements:1.ConceptsofNumberSystemandtheirconversion2.BooleanAlgebra3.Moore’sLawNewWords&Expressions:decimalsystem十进制abacin.算盘verbalrepresentation口头表达式radixn.根,基数quinarysystem五进制duodecimalsystem十二进制stopat停在liein在于infact事实上inorderto为了Roman-numbern.罗马数字pencil-and-paper纸和笔的regardlessofa.不管,不顾contractionn.收缩，缩写式，紧缩grossn.罗，为一计数单位，1罗=12打positionalnotationn.位置记数法3.1TheDecimalSystemOurpresentsystemofnumbershas10separatesymbols0,1,2,3,…,9,wicharecalledArabicnumerals.Wewouldbeforcedtostopat9ortoinventmoresymbolsifitwerenotfortheuseofpositionalnotation.AnexampleofearliertypesofnotationcanbefoundinRomannumeral,whichareessentiallyadditive:III=I+I+I,XXV=X+X+V.Newsymbols(X,C,M,etc.)wereusedasthenumbersincreasedinvalue.ThusVratherthanIIIII=5.TheonlyimportanceofpositioninRomannumeralsliesinwhetherasymbolprecedesorfollowsanothersymbol(IV=4andVI=6).我们当前的数字系统有0、1、2、3….9十个单独的符号，称之为阿拉伯数字。如果不使用位置符号，我们数到9就被迫停下来，或发明更多的符号。在罗马数字里可以找到早期符号类型的例子，他们基本上是加法的：Ⅲ=Ⅰ+Ⅰ+Ⅰ，XXV=X+X+V。当数值增加时采用新符号（X、C、M等）。这样V就不是IIIII=５。罗马数字中位的唯一重要性在于这个符号处于另一个符号之前或之后（Ⅳ=4和Ⅵ=6）。3.1TheDecimalSystemTheclumsinessofthissystemcaneasilybeseenifwetrytomultiplyXIIbyXIV.CalculatingwithRomannumeralswassodifficultthatearlymathematicianswereforcedtoperformarithmeticoperationsalmostentirelyonabaci,orcountingboards,translatingtheirresultsbackintoRoman-numberform.Pencil-and-papercomputationsareunbelievablyintricateanddifficultinsuchsystems.Infact,theabilitytoperformsuchoperationsasadditionandmultiplicationwasconsideredagreataccomplishmentinearliercivilization.如果你要用XIV乘XII，很容易看出这个数字系统是笨拙的。用罗马数字计算太难了，以至于早期的数字家几乎完全被迫在算盘或演算板完成算术运算，然后再把结果翻译成罗马数字形式。在这样的数字系统中，纸和笔运算达到以难置信的复杂和困难程度。事实上，在早期文明中能进行这样的加法和乘法运算被看作是一项伟大的成就。3.1TheDecimalSystem3.1TheDecimalSystemThegreatbeautyandsimplicityofournumbersystemcannowbeseen.Itisnecessarytolearnonlythebasicnumeralsandthepositionalnotationsysteminordertocounttoanydesiredfigure.Aftermemorizingtheadditionandmultiplicationtablesandlearningafewsimplerules,itispossibletoperformallarithmeticoperations.Noticethesimplicityofmultiplying12×14usingthepresentsystem.现在可以看到我们的数字系统的巨大优势和简单明了，为了要数到任意想到的数字，只需要学会基本数字和进位符号，再记住加法和乘法表及学会一些简单规则，就可能完成所有的算术运算。看一下用现在数制计算12×14的简单性。3.1TheDecimalSystemTheactualmeaningofthenumber168canbeseenmoreclearlyifwenoticethatitisspokenas“onehundredandsixty-eight”.Basically,thenumberisacontractionof(1×100)+(6×10)+8.Theimportantpointisthatthevalueofeachdigitisdeterminedbyitsposition.Forexample,the2in2,000hasadifferentvaluethanthe2in20.Weshowthisverballybysaying“twothousand”and“twenty”.Differentverbalrepresentationshavebeeninventedfornumbersfrom10to20(eleven,twelve),butfrom20upwardwebreakonlyatpowersof10(hundreds,thousa