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1、1NumberSystems0,10,1,2,3,4,5,6,70,1,2,3,4,5,6,7,8,90,1,2,3,4,5,6,7,8,9,A,B,C,D,E,FbinaryoctaldecimalhexdecimalAppendixF2NumberSystemsComputersusebinarynumbersinternallybecausestoragedeviceslikememoryanddiskaremadetostore0sand1s.Anumberoratextinsideacomputerisstoredasasequenceof0sand1s.Each0and1isca
2、lledabit,shortforbinarydigit.Thebinarynumbersystemhastwodigits,0and1.Binarynumbersarenotintuitive,sinceweusedecimalnumbersinourdailylife.Whenyouwriteanumberlike20inaprogram,itisassumedtobeadecimalnumber.Internally,computersoftwareisusedtoconvertdecimalnumbersintobinarynumbers,andviceversa.3NumberSy
3、stems,cont.Thedigitsinthedecimalnumbersystemare0,1,2,3,4,5,6,7,8,and9.Adecimalnumberisrepresentedusingasequenceofoneormoreofthesedigits.Thevaluethateachdigitinthesequencerepresentsdependsonitsposition.Apositioninasequencehasavaluethatisanintegralpowerof10.Forexample,thedigits7,4,2,and3indecimalnumb
4、er7423represent7000,400,20,and3,respectively,asshownbelow:Thedecimalnumbersystemhastendigitsandthepositionvaluesareintegralpowersof10.Wesaythat10isthebaseorradixofthedecimalnumbersystem.Similarly,thebaseofthebinarynumbersystemis2sincethebinarynumbersystemhastwodigitsandthebaseofthehexnumbersystemis
5、16sincethehexnumbersystemhassixteendigits.4NumberSystems,cont.Binarynumberstendtobeverylongandcumbersome.Hexadecimalnumbersareoftenusedtoabbreviatebinarynumbers.Thehexadecimalnumbersystemhas16digits:0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,andF.ThelettersA,B,C,D,E,andFcorrespondtothedecimalnumbers10,11,12,13,
6、14,and15.5BinaryNumbers=>DecimalsGivenabinarynumbertheequivalentdecimalvalueis10inbinary=2indecimal1000inbinary=8indecimal10101011inbinary=171indecimal6Decimals=>BinaryToconvertadecimalnumberdtoabinarynumberistofindthebinarydigits..suchthatThesenumberscanbefoundbysuccessivelydividingdby2untilthequo
7、tientis0.TheremaindersareForexample,thedecimalnumber123is1111011inbinary.Theconversionisconductedasfollows:7WindowsCalculatorTheWindowsCalculatorisausefultoolforperformingnumberconversions.Torunit,choosePro
