CHAPTER 4 The Components of the System 3. Data Representation 课件

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1、CHAPTER4TheComponentsoftheSystemUnitDataRepresentation2BinarynumbersBinarynumberissimplyanumbercomprisedofonly0'sand1's.Computersusebinarynumbersbecauseit'seasyforthemtocommunicateusingelectricalcurrent--0isoff,1ison.Youcanexpressanybase10(ournumbersystem--wh

2、ereeachdigitisbetween0and9)withbinarynumbers.Theneedtotranslatedecimalnumbertobinaryandbinarytodecimal.Therearemanywaysinrepresentingdecimalnumberinbinarynumbers.(later)3Howdoesthebinarysystemwork?ItisjustlikeanyothersystemIndecimalsystemthebaseis10Wehave10po

3、ssiblevalues0-9Inbinarysystemthebaseis2Wehaveonlytwopossiblevalues0or1.Thesameasinanybase,0digithasnoncontribution,where1’shascontributionwhichdependsatthereposition.4Example3040510=30000+400+5=3*104+4*102+5*100101012=10000+100+1=1*24+1*22+1*205UnsignedRepres

4、entationRepresentspositiveintegers.Unsignedrepresentationof157:Additionissimple:1001+0101=1110.position76543210Bitpattern10011101contribution27242322206FractionRepresentationTorepresentfractionweneedotherrepresentations:FixedpointrepresentationFloatingpointre

5、presentation.7RepresentationofnegativenumbersIsarepresentationofnegativenumberspossible?Unfortunately:youcannotjuststickanegativesigninfrontofabinarynumber.(itdoesnotworklikethat)Therearethreemethodsusedtorepresentnegativenumbers.SignedmagnitudenotationExcess

6、notationnotationTwo’scomplementnotation8Unicode-representationASCIIcodecanrepresentonly128=27characters.ItonlyrepresentstheEnglishAlphabetplussomecontrolcharacters.Unicodeisdesignedtorepresenttheworldwideinterchange.Ituses16bitsandcanrepresents32,768character

7、s.Forcompatibility,thefirst128UnicodearethesameastheoneoftheASCII.9ColourrepresentationColourscanrepresentedusingasequenceofbits.256colours–howmanybits?HintforcalculatingTofigureouthowmanybitsareneededtorepresentarangeofvalues,figureoutthesmallestpowerof2that

8、isequaltoorbiggerthanthesizeoftherange.Thatis,findxfor2x=>25624-bitcolour–howmanypossiblecolorscanberepresented?Hints16millionpossiblecolours(why16millions?)1024-bits--theTruecolour24-bit