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 ${\sum}_{i\=\mathrm{\∞}}^{n}\phantom{\rule[0.0ex]{5.0px}{0.0ex}}{x}_{i}\mathbf{}{b}^{i}$, where $0\le {x}_{i}b$.
The corresponding base $b$ representation of this number is:
${x}_{n}\mathbf{}{x}_{n1}\cdot \cdot \cdot {x}_{1}\mathbf{}{x}_{0\mathbf{\xb7}}{x}_{1}{x}_{2}\mathbf{}\cdot \cdot \cdot$
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 $\mathit{x}$ is called normal in base $\mathit{b}$ 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 ${x}_{i\+1}\cdot \cdot \cdot {x}_{i\+k}$ in the representation of $x$ is ${b}^{k}$. The number $x$ is normal if it is normal in every base $b\>1$.
