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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.Anumberoratextinsideacomputerisstoredasa
2、sequenceof0sand1s.Each0and1iscalledabit,shortforbinarydigit.Thebinarynumbersystemhastwodigits,0and1.Binarynumbersarenotintuitive,sinceweusedecimalnumbersinourdailylife.Whenyouwriteanumberlike20inaprogram,itisassumedtobeadecimalnumber.Internally,computersoftwareisusedt
3、oconvertdecimalnumbersintobinarynumbers,andviceversa.3NumberSystems,cont.Thedigitsinthedecimalnumbersystemare0,1,2,3,4,5,6,7,8,and9.Adecimalnumberisrepresentedusingasequenceofoneormoreofthesedigits.Thevaluethateachdigitinthesequencerepresentsdependsonitsposition.Aposi
4、tioninasequencehasavaluethatisanintegralpowerof10.Forexample,thedigits7,4,2,and3indecimalnumber7423represent7000,400,20,and3,respectively,asshownbelow:Thedecimalnumbersystemhastendigitsandthepositionvaluesareintegralpowersof10.Wesaythat10isthebaseorradixofthedecimalnu
5、mbersystem.Similarly,thebaseofthebinarynumbersystemis2sincethebinarynumbersystemhastwodigitsandthebaseofthehexnumbersystemis16sincethehexnumbersystemhassixteendigits.4NumberSystems,cont.Binarynumberstendtobeverylongandcumbersome.Hexadecimalnumbersareoftenusedtoabbrevi
6、atebinarynumbers.Thehexadecimalnumbersystemhas16digits:0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,andF.ThelettersA,B,C,D,E,andFcorrespondtothedecimalnumbers10,11,12,13,14,and15.5BinaryNumbers=>DecimalsGivenabinarynumbertheequivalentdecimalvalueis10inbinary=2indecimal1000inbinary=8
7、indecimal10101011inbinary=171indecimal6Decimals=>BinaryToconvertadecimalnumberdtoabinarynumberistofindthebinarydigits..suchthatThesenumberscanbefoundbysuccessivelydividingdby2untilthequotientis0.TheremaindersareForexample,thedecimalnumber123is1111011inbinary.Theconver
8、sionisconductedasfollows:7WindowsCalculatorTheWindowsCalculatorisausefultoolforperformingnumberconversions.Torunit,choosePro
