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CHAPTER 2 - Integer Representation and Operations

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2.1 Representations of Integers

 

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An excellent discussion of binary and hexadecimal representations of integers together with issues related to working with them in computer programming can be found at http://web.uccs.edu/wbahn/ECE1021/STATIC/LESSONS/BinaryRepresentations_Integer.htm (Binary Representations - Integers)

 

You can find the base b expansion of an integer using the tool at http://www.numbertheory.org/php/base.html (Finding the base b expansion of a positive integer n)

 

 

You can use the applet at http://www.math.com/students/converters/source/base.htm (Number Base Converter) to convert the representation of an integer to its representation in another base

 

 

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Biographical information about D.R. Kaprekar can be found at http://www.geocities.com/bvijay/unsung/kaprekar.html

Information concerning Kaprekar's constant and related topics can be found at
http://mathworld.wolfram.com/KaprekarRoutine.html (Kaprekar's Routine)

 

 

Computer Operations with Integers

 

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An applet providing an on-line calculator that can be used to perform operations with integers in any base can be found at http://world.std.com/~reinhold/BigNumCalc.html (Big Number Calculator Applet)

 

 
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You can find a biography of Al-Khwârizmî at the MacTutor History of Mathematics Archive at http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Al-Khwarizmi.html (al'Khwarizmi)

 

 

Section 2.3 Complexity of Integer Operations

 
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Biographical information about Paul Bachmann can be found at the MacTutor History of Mathematics Archive at
http://www-groups.dcs.st-andrews.ac.uk/~history/Mathematicians/Bachmann.html (Bachmann)

Biographical information and a portrait of Edmund Landau can be found at the site of the Edmund Landau Center for Research in Mathematical Analsyis at the Hebrew University in Israel http://www.ma.huji.ac.il/~landau/landau.html (Landau)

Biographical information and a portrait of Edmund Landau can be found at the MacTutor History of Mathematics Archive at http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Landau.html (Landau)

Donald Knuth's home page, containing a wealth of information about his activities, books, and interests can be found at
http://www-cs-faculty.Stanford.EDU/~knuth/ (Donald Knuth's home page)