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1、外文资料原文ComputerArithmeticIncomputerarithmetictwofundamentaldesignprinciplesareofgreatimportance:numberrepresentationandtheimplementationofalgebraicoperations[25,26,27,28,29].Wewillfirstdiscusspossiblenumberrepresentations,(e.g.,fixed-pointorfloating-point),thenbasicoperationslikeadderandmultiplier,an
2、dfinallyefficientimplementationofmoredifficultoperationssuchassquareroots,andthecomputationoftrigonometricfunctionsusingtheCORDICalgorithmorMACcalls.FPGAsallowawidevarietyofcomputerarithmeticimplementationsforthedesireddigitalsignalprocessingalgorithms,becauseofthephysicalbitlevelprogrammingarchitec
3、ture.Thiscontrastswiththeprogrammabledigitalsignalprocessors(PDSPs),withthefixedmultiplyaccumulatorcore.CarefulchoiceofthebitwidthinFPGAdesigncanresultinsubstantialsavings.2.2NumberRepresentationDecidingwhetherfixed-orfloating-pointismoreappropriatefortheproblemmustbedonecarefully,preferablyatanearl
4、yphaseintheproject.Ingeneral,itcanbeassumedthatfixed-pointimplementationshavehigherspeedandlowercost,whilefloating-pointhashigherdynamicrangeandnoneedforscaling,whichmaybeattractiveformorecomplicatedalgorithms.Figure2.1isasurveyofconventionalandlessconventionalfixed-andfloating-pointnumberrepresenta
5、tions.Bothsystemsarecoveredbyanumberofstandardsbutmay,ifdesired,beimplementedinaproprietaryform.2.2.1Fixed-PointNumbersWewillfirstreviewthefixed-pointnumbersystemsshowninFig.2.1.Table2.1showsthe3-bitcodingforthe5differentintegerrepresentations.UnsignedIntegerLetXbeanN-bitunsignedbinarynumber.Thenthe
6、rangeis[0,2n-1]andtherepresentationisgivenby:wherexnisthenthbinarydigitofX(i.e.,x∈[0，1]).Thedigitx0iscalledtheleastsignificantbit(LSB)andhasarelativeweightofunity.ThedigitXn-1isthemostsignificantbit(MSB)andhasarelativeweightof2n-1。Signed-Magnitude(SM)Insigned-magnitudesystemsthemagnitudeandthesignar
7、erepresentedseparately.Thefirstbitxn-1(i.e.,theMSB)representsthesignandtheremainingN−1bitsthemagnitude.Therepresentationbecomes:.Therangeofthisrepresentationis[-(2n-1-1),2n-1-1].Theadvantageofthesigne
