Base and Normality - Maple Programming Help

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Base and Normality

Main Concept

A numeral system is a way of representing real numbers as an ordered sequence of symbols called digits from a finite ordered set. The number, b, of symbols in this set is called the base. The symbols themselves represent the number zero, followed by the first b1 positive integers.

For any base b, any real number can be written as a sum of the form i&equals;&infin;nxibi, where 0  xi<b.

The corresponding base b representation of this number is:



The standard numeral system around the world is the base ten decimal system, which uses the digits {0,1,2,3,4,5,6,7,8,9}. Systems using a base other than ten are used commonly in computing, including:



 binary (base two), binary digits (bits) = {0,1}


 octal (base eight), octal digits = {0,1,2,3,4,5,6,7}


 hexadecimal (base sixteen), hexadecimal digits = {0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F}


In number theory, a real number x is called normal in base b if the sequence of digits in its representation in base b appears random, in the following sense: The density of any length k digit subsequence xi&plus;1xi&plus;k  in the representation of x is bk. The number x is normal if it is normal in every base b&gt;1.


Input a Maple expression in the box below (or choose one from the drop-down box) that evaluates to a real number. Choose a base b > 1, and Maple will find the base b representation for your number. Use the slider to adjust the number of significant figures, and look at the graph to see if your number is normal in that base.



base =  

# of significant figures =  

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