计算机中的二进制表达课件

计算机中的二进制表达ExampleRepresentationRealWorldTobe,ornottobe:thatisthequestion:Whether'tisnoblerinthemindtosufferTheslingsandarrowsofoutrageousfortune,Ortotakearmsagainstaseaoftroubles,Andbyopposingendthem?Todie:tosleep;Nomore;andbyasleeptosayweendTheheart-acheandthethousandnaturalshocksThatfleshisheirto,'tisaconsummationDevoutlytobewish'd.--WilliamShakespeare-(fromHamletAct3,Scene1)ComputerWorld101010001101111100000011000101010100011011001100110011000101110111011111100010101011010100010110111011000101010110001011011101001000100010101010111010101011011010010111101010001101111100000011000101010100011011001100110011000101110111011111100010101011010100010110111011000101010110001011011101001000100010101010111010101011011010010111101010001101111100000011000101010100011011001100110011000101110111011111100010101011010100010110111011000101010110001011011101001000100010101010111010101011011010010111…InternalandExternalRepresentationofDataRealWorldIntegers:34SignedIntegers:

-156DecimalNumbers:

-23.431Text:HelloMusic:HeyJudePictures:ComputerWorldZerosandOnes:

110101IntegerRepresentationWeuseabase10numbersystem(Decimal)

0,1,2,3,4,5,6,7,8,92,359

tenshundredsthousandsones100101102103Computersuseabase2numbersystem(Binary)

0,1

110101

202122232425ConversionfromBinarytoDecimal1x25+1x24+0x23+1x22+0x21+1x20=53YouTryit:Whatarethefollowingbinarynumbersindecimal?11011101100110111

110101

202122232425ConversionfromDecimaltoBinaryPerformrepeateddivisionsby2Keeptrackoftheremainders19/2 quotient=9 remainder=19/2 quotient=4 remainder=14/2 quotient=2 remainder=02/2 quotient=1 remainder=01/2 quotient=0 remainder=1Stopwhenthequotientis0Decimalnumber19inbinaryis10011YouTryitConvertthefollowingdecimalnumberstobinary123153AdditiononBinary0+0=01+0=10+1=11+1=10(carrythe1) 1101 11010

+1001

+10011FixedSizesforNumbersOncomputersafixednumberofdigitsaretypicallyusedtostoreanumber

(8,16,32,or64bitsarecommon)Thedecimalnumber3inbinaryis11,butusingafixedsizeof8bitsitwouldberepresentedas00000011Tryaddingthebinarynumbersusingafixedsizeof8bits: 11011001

+10001011InternalandExternalRepresentationofDataRealWorldIntegers:34SignedIntegers:

-156DecimalNumbers:

-23.431Text:HelloMusic:HeyJudePictures:√SignedIntegers-134Sign/MagnitudeNotation110000110magnitudeSign0=positive1=negativeNotfrequentlyusedoncomputers2numbersforzeroNoteasytoadd/subtractSignedIntegers-134Two’sComplementNotation(forfixedsizewindow16)Calculatethemagnitudeinbinary

0000000010000110Flipthebits

1111111101111001Addone

1111111101111010YouTryit -129 -151InternalandExternalRepresentationofDataRealWorldIntegers:34SignedIntegers:

-156DecimalNumbers:

-23.431Text:HelloMusic:HeyJudePictures:√√DecimalNumbers5.75Writethe5inbinaryandthe0.75inbinary5 –1010.75 –0.11Normalizethenumber,keepingtrackofMantissaandExponent: ±MxB±E

M–Mantissa B–Base(weusebase2) E–ExponentUsedfixedsizewindow(16bits) Firstbitissign Next9bitsareMantissa Nextbitissign Last5bitsareExponentYouTryIt:-8.25 11.5TextFixedSizeWindowrepresentsacharacterASCII(8bits) pg141intextUnicode(16bits) represents65,636 charactersBinaryRepresentationofSoundandImagesMultimediadataissampledtostoreadigitalformwithorwithoutdetectabledifferencesRepresentingsounddataSounddatamustbedigitizedforstorageinacomputerDigitizingmeansperiodicsamplingofamplitudevaluesBinaryRepresentationofSoundandImages(continued)Fromsamples,originalsoundcanbeapproximatedToimprovetheapproximationSamplemorefrequentlyUsemorebitsforeachsamplevalueFigure4.5DigitizationofanAnalogSignal(a)SamplingtheOriginalSignal(b)RecreatingtheSignalfromtheSampledValuesRepresentingimagedataImagesaresampledbyreadingcolorandintensityvaluesatevenintervalsacrosstheimageEachsampledpointisapixelImagequalitydependsonnumberofbitsateachpixelBinaryRepresentationofSoundandImages(continued)PicturesForeachpixelkeeptrackof:RGBvalues0-255(8-bit)WhyBinaryRepresentationElectronicdevicesaremostreliableinabistableenvironmentBistableenvironmentDistinguishingonlytwoelectronicstatesCurrentflowingornotDirectionofflowComputersarebistable:binaryrepresentationsMagneticcoreHistoricdeviceforcomputermemoryTinymagnetizedrings;flowofcurrentsetsthedirectionofmagneticfieldBinaryvalues0and1arerepresentedusingthedirectionofthemagneticfieldBinaryStorageDevicesFigure4.9U