Base and Normality - Maple 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, , of symbols in this set is called the base. The symbols themselves represent the number zero, followed by the first  positive integers.

For any base , any real number can be written as a sum of the form , where .

The corresponding base  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  is called normal in base  if the sequence of digits in its representation in base  appears random, in the following sense: The density of any length  digit subsequence   in the representation of  is . The number  is normal if it is normal in every base .

 

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 =  

More MathApps

MathApps/RealAndComplexNumbers


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