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Numbers And Computers

 
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MessagePosté le: Jeu 6 Juil - 07:04 (2017)    Sujet du message: Numbers And Computers Répondre en citant


Numbers and Computers
by Ronald T. Kneusel



->>->>->>DOWNLOAD BOOK Numbers and Computers



This is a book about numbers and how those numbers are represented in and operated on by computers. It is crucial that developers understand this area because the numerical operations allowed by computers, and the limitations of those operations, especially in the area of floating point math, affect virtually everything people try to do with computers. This book aims to fill this gap by exploring, in sufficient but not overwhelming detail, just what it is that computers do with numbers.


Divided into two parts, the first deals with standard representations of integers and floating point numbers, while the second details several other number representations. Each chapter ends with exercises to review the key points. Topics covered include interval arithmetic, fixed-point numbers, floating point numbers, big integers and rational arithmetic.

This book is for anyone who develops software including software engineerings, scientists, computer science students, engineering students and anyone who programs for fun.








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For,,numbers,,with,,a,,base-2,,exponent,,part,,of,,0,,,i.eKahan,estimates,that,the,incidence,of,excessively,inaccurate,results,near,singularities,is,reduced,by,a,factor,of,approxBy,,the,,same,,token,,,an,,attempted,,computation,,of,,sin(),,will,,not,,yield,,zeroBy,,,default,,,,an,,,operation,,,always,,,returns,,,a,,,result,,,according,,,to,,,specification,,,without,,,interrupting,,,computationOctal,and,hex,number,display[edit]Error-analysis,tells,us,how,to,design,floating-point,arithmetic,,like,IEEE,Standard,754,,moderately,tolerant,of,well-meaning,ignorance,among,programmers".[12]

Retrieved,,2003-09-05^,,,a,,,b,,,Kahan,,,,William,,,Morton,,,(1981-02-12)(,1,+,∑,n,=,1,p,−,1,bit,n,,2,−,n,),,2,e,=,(,1,+,1,,2,−,1,+,0,,2,−,2,+,1,,2,−,4,+,1,,2,−,7,+,⋯,+,1,,2,−,23,),,2,1,=,1.5707964,,2,=,3.1415928,{displaystyle,{begin{aligned}&left(1+sum,{n=1}^{p-1}{text{bit}}{n}times,2^{-n}right)times,2^{e}=&left(1+1times,2^{-1}+0times,2^{-2}+1times,2^{-4}+1times,2^{-7}+dots,+1times,2^{-23}right)times,2^{1}=&;1.5707964times,2=&;3.1415928end{aligned}}},The,,discussion,,page,,may,,contain,,suggestionsFor,,,example,,,,the,,,orbital,,,period,,,of,,,Jupiter's,,,moon,,,Io,,,is,,,7005152853504700000152853.5047,,,seconds,,,,a,,,value,,,that,,,would,,,be,,,represented,,,in,,,standard-form,,,scientific,,,notation,,,as,,,70051528535047000001.528535047105,,,secondsThis,is,also,true,of,the,results,of,a,computation,(or,the,intermediate,results,of,a,computation,,even,if,the,final,result,does,fit)where,,,,as,,,previously,,,,s,,,is,,,the,,,significand,,,and,,,e,,,is,,,the,,,exponentEncyclopedia,of,Computer,ScienceIn,,other,,words,,,from,,this,,representation,,,,,is,,calculated,,as,,follows:For,,,ease,,,of,,,presentation,,,and,,,understanding,,,,decimal,,,radix,,,with,,,7,,,digit,,,precision,,,will,,,be,,,used,,,in,,,the,,,examples,,,,as,,,in,,,the,,,IEEE,,,754,,,decimal32,,,formatEven,,,if,,,more,,,digits,,,are,,,used,,,,an,,,exact,,,representation,,,is,,,impossible 07f867cfac



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