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1、FoundationsofComputerScienceSecondEditionBEHROUZFOROUZANFIROUZMOSHARRAFChapter2NumberSystems1OutlinesòIntroductionòPositionalNumberSystems–Base10,2,8,16.òNonpositionalNumberSystems–RomanNumerals2CSIM@PUObjectivesAfterstudyingthischapter,thestudentshouldunderstand:òThecon
2、ceptofnumbersystems.òNon-positionalandpositionalnumbersystems.òDecimal,Binary,HexadecimalandOctalsystem.òConvertanumberamongbinary,octal,hexadecimal,anddecimalsystems.òFindthenumberofdigitsneededineachsystemtorepresentaparticularvalue.3CSIM@PU1-1Introduction4TheDefinitio
3、nofNumberSystem•Anumbercanberepresentedusingdistinctsymbolsanddifferentlyindifferentsystems.•Forexample,•Thetwonumbers(2A)and(52)bothreferto168thesamequantity,(42),buttheir10representationsaredifferent•Twogroups•positionalandnon-positionalsystems5CSIM@PU1-2PositionNumber
4、Systems6OverviewòInapositionalnumbersystem,anumberrepresentedas:hasthevalueof:inwhichSisthesetofsymbols,bisthebase(orradix).TheBaseincludesBase10(Decimal),Base2(Binary),Base16(Hexadecimal),orBase8(octal)。7CSIM@PUThedecimalsystem(base10)òTheworddecimalisderivedfromtheLati
5、nrootdecem(ten).–baseb=10,and–tensymbols:S={0,1,2,3,4,5,6,7,8,9}òThesymbolsinthissystemareoftenreferredtoasdecimaldigitsorjustdigits.–Integerexamples–Realexamples8Base10–Integers(1)Figure2.1Placevaluesforanintegerinthedecimalsystem9Base10–Integers(2)òExample2.1showsthepl
6、acevaluesfortheinteger+224inthedecimalsystemòExample2.2showstheplacevaluesforthedecimalnumber−7508()Values10Base10–RealsòAreal–anumberwithafractionalpartòExample2.3showstheplacevaluesfortherealnumber+24.13.11Thebinarysystem(base2)òThewordbinaryisderivedfromtheLatinrootbi
7、ni(ortwobytwo).–baseb=2,and–twosymbols,S={0,1}òThesymbolsinthissystemareoftenreferredtoasbinarydigitsorbits(binarydigit).–Integerexamples–Realexamples12Base2–Integers(1)òWecanrepresentanIntegeras:Figure2.2Placevaluesforanintegerinthebinarysystem13Base2–Integers(2)òExampl
8、e2.4showsthatthenumber(11001)2inbinaryisthesameas25indecimal.Thesubscript2showsthatthebaseis2.Theequiva
