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:
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binary (base two), binary digits (bits) = {0,1}
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octal (base eight), octal digits = {0,1,2,3,4,5,6,7}
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hexadecimal (base sixteen), hexadecimal digits = {0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F}
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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 .
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