数字电子技术(Floyd 第十版)课件Chapter 3PPT文件格式下载.pptx

数字电子技术(Floyd 第十版)课件Chapter 3PPT文件格式下载.pptx

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,DigitalFundamentalsTenthEditionFloyd,Chapter2,2008PearsonEducation,Thepositionofeachdigitinaweightednumbersystemisassignedaweightbasedonthebaseorradixofthesystem.Theradixofdecimalnumbersisten,becauseonlytensymbols（0through9）areusedtorepresentanynumber.,Summary,Thecolumnweightsofdecimalnumbersarepowersoftenthatincreasefromrighttoleftbeginningwith100=1:

@#@,DecimalNumbers,105104103102101100.,Forfractionaldecimalnumbers,thecolumnweightsarenegativepowersoftenthatdecreasefromlefttoright:

@#@,102101100.10-110-210-310-4,Summary,DecimalNumbers,Expressthenumber480.52asthesumofvaluesofeachdigit.,Example,Solution,（9x103）+（2x102）+（4x101）+（0x100）or9x1,000+2x100+4x10+0x1,Decimalnumberscanbeexpressedasthesumoftheproductsofeachdigittimesthecolumnvalueforthatdigit.Thus,thenumber9240canbeexpressedas,480.52=（4x102）+（8x101）+（0x100）+（5x10-1）+（2x10-2）,Summary,BinaryNumbers,Fordigitalsystems,thebinarynumbersystemisused.Binaryhasaradixoftwoandusesthedigits0and1torepresentquantities.,Thecolumnweightsofbinarynumbersarepowersoftwothatincreasefromrighttoleftbeginningwith20=1:

@#@,252423222120.,Forfractionalbinarynumbers,thecolumnweightsarenegativepowersoftwothatdecreasefromlefttoright:

@#@,222120.2-12-22-32-4,Summary,BinaryNumbers,Abinarycountingsequencefornumbersfromzerotofifteenisshown.,00000100012001030011401005010160110701118100091001101010111011121100131101141110151111,DecimalNumber,BinaryNumber,Noticethepatternofzerosandonesineachcolumn.,Digitalcountersfrequentlyhavethissamepatternofdigits:

@#@,Summary,BinaryConversions,Thedecimalequivalentofabinarynumbercanbedeterminedbyaddingthecolumnvaluesofallofthebitsthatare1anddiscardingallofthebitsthatare0.,Convertthebinarynumber100101.01todecimal.,Example,Solution,Startbywritingthecolumnweights;@#@thenaddtheweightsthatcorrespondtoeach1inthenumber.,252423222120.2-12-2,32168421.,100101.01,32+4+1+=,37,Summary,BinaryConversions,Youcanconvertadecimalwholenumbertobinarybyreversingtheprocedure.Writethedecimalweightofeachcolumnandplace1sinthecolumnsthatsumtothedecimalnumber.,Convertthedecimalnumber49tobinary.,Example,Solution,Thecolumnweightsdoubleineachpositiontotheright.Writedowncolumnweightsuntilthelastnumberislargerthantheoneyouwanttoconvert.,26252423222120.,6432168421.,0110001.,Summary,Youcanconvertadecimalfractiontobinarybyrepeatedlymultiplyingthefractionalresultsofsuccessivemultiplicationsby2.Thecarriesformthebinarynumber.,Convertthedecimalfraction0.188tobinarybyrepeatedlymultiplyingthefractionalresultsby2.,Example,Solution,0.188x2=0.376carry=0,0.376x2=0.752carry=0,0.752x2=1.504carry=1,0.504x2=1.008carry=1,0.008x2=0.016carry=0,Answer=.00110（forfivesignificantdigits）,MSB,BinaryConversions,1,0,0,1,1,0,Summary,Youcanconvertdecimaltoanyotherbasebyrepeatedlydividingbythebase.Forbinary,repeatedlydivideby2:

@#@,Convertthedecimalnumber49tobinarybyrepeatedlydividingby2.,Example,Solution,Youcandothisby“reversedivision”andtheanswerwillreadfromlefttoright.Putquotientstotheleftandremaindersontop.,24,12,6,3,1,0,Continueuntilthelastquotientis0,Answer:

@#@,BinaryConversions,Summary,BinaryAddition,Therulesforbinaryadditionare,0+0=0Sum=0,carry=0,0+1=0Sum=1,carry=0,1+0=0Sum=1,carry=0,1+1=10Sum=0,carry=1,Whenaninputcarry=1duetoapreviousresult,therulesare,1+0+0=01Sum=1,carry=0,1+0+1=10Sum=0,carry=1,1+1+0=10Sum=0,carry=1,1+1+1=10Sum=1,carry=1,Summary,BinaryAddition,Addthebinarynumbers00111and10101andshowtheequivalentdecimaladdition.,Example,Solution,001117,1010121,0,1,0,1,1,1,1,0,1,28,=,Summary,BinarySubtraction,Therulesforbinarysubtractionare,0-0=0,1-1=0,1-0=1,10-1=1withaborrowof1,Subtractthebinarynumber00111from10101andshowtheequivalentdecimalsubtraction.,Example,Solution,001117,1010121,0,/1,1,1,1,0,14,/1,/1,=,Summary,1sComplement,The1scomplementofabinarynumberisjusttheinverseofthedigits.Toformthe1scomplement,changeall0sto1sandall1sto0s.,Forexample,the1scomplementof11001010is,00110101,Indigitalcircuits,the1scomplementisformedbyusinginverters:

@#@,11001010,00110101,Summary,2sComplement,The2scomplementofabinarynumberisfoundbyadding1totheLSBofthe1scomplement.,Recallthatthe1scomplementof11001010is,00110101（1scomplement）,Toformthe2scomplement,add1:

@#@,+1,00110110（2scomplement）,11001010,00110101,1,00110110,Summary,SignedBinaryNumbers,Thereareseveralwaystorepresentsignedbinarynumbers.Inallcases,