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L02 - Number Systems Computer Architecture Computer...

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Number Systems & Computer Architecture Outline Number Systems and Representa- tions Bases Representations Machine Architecture Computer Architecture Margot Gerritsen Shela Aboud Emmet Caulfield School of Earth Sciences Stanford University January 5, 2010
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Number Systems & Computer Architecture Outline Number Systems and Representa- tions Bases Representations Machine Architecture Outline Computers represent everything in binary , so we’ll review number systems before we talk about computer architecture. 1 Number Systems and Representations Bases Representations 2 Machine Architecture
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Number Systems & Computer Architecture Outline Number Systems and Representa- tions Bases Representations Machine Architecture Number Systems & Representations Number systems — base- n , binary, octal, hexadecimal Representation of integer, negative, and fractional numbers Motivate the notion of type
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Number Systems & Computer Architecture Outline Number Systems and Representa- tions Bases Representations Machine Architecture Bases In a base- n (or radix- n ) system: Symbols representing values from 0 to n - 1 are used in weighted columns Every column’s weight is n times the weight of the column on its right Units are immediately left of the radix point Name n Digits Ex. Column Weights Decimal 10 0-9 13.25 . . . 10 1 10 0 . 10 - 1 . . . Binary 2 0-1 1101.01 . . . 2 1 2 0 . 2 - 1 . . . Octal 8 0-7 15.20 . . . 8 1 8 0 . 8 - 1 . . .
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