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Fixed-Point Arithmetic: An Introduction

STechnical ReferenceFixed-Point Arithmetic: An Introduction1 (13) YatesAugust 23, 2007 11:05PA5 Arithmetic: An IntroductionRandy YatesAugust 23, 2007ss i g n a lp r o c e s s i n gs y s t e m using LATEX2 Digital Signal LabsPublic InformationsTechnical ReferenceFixed-Point Arithmetic: An Introduction2 (13) YatesAugust 23, 2007 11:05PA5 Introduction32 Fixed-Point Binary Unsigned Fixed-Point Rationals .. 43 The Operations of One s Complement and Two s Complement54 Signed Two s Complement Fixed-Point Rationals55 Fundamental Rules of Fixed-Point Unsigned Wordlength .. Signed Wordlength .. Unsigned Range .. Signed Range .. Addition Operands .. Addition Result .. Unsigned Multiplication .. Signed Multiplication .. Unsigned Division .. Signed Division .. Wordlength Reduction .. Shifting .. Literal Shift.

representation has a integer bits and b fractional bits. The value of a particular N-bit binary number x in a U(a,b)representation is given by the expression x =(1/2b) NX−1 n=0 2nx n where xnrepresents bit n of x. The range of a U(a,b)representation is from 0 to (2N− 1)/2b=2a−2−b.

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