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A '''number system''' is a mathematical notation for representing numbers of a given [[number set|set]]. They are the foundation for conveying, quantifying, and manipulating [[data]]. | A '''number system''' is a mathematical notation for representing numbers of a given [[number set|set]]. They are the foundation for conveying, quantifying, and manipulating [[data]]. | ||
− | Number systems are mainly classified according to [[number notation|notations]] ([[positional notation]] vs [[sign-value notation]]) and their [[base]]. Today, we largely use the [[Arabic numerals]] which is a [[base-10]] positional notation numbering system. Machines on the other hand may use a different number system - such as the [[ | + | Number systems are mainly classified according to [[number notation|notations]] ([[positional notation]] vs [[sign-value notation]]) and their [[base]]. Today, we largely use the [[Arabic numerals]] which is a [[base-10]] positional notation numbering system. Machines on the other hand may use a different number system - such as the [[base-2]]. |
== Notation == | == Notation == | ||
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− | === | + | === Decimal Number System === |
{{main|binary}} | {{main|binary}} | ||
In the binary number system, the [[radix]] is 2 - i.e. a number system capable of only representing two discrete values: <math>\{0,1\}</math>. Let's consider the following number <math>10101110.011_{2}</math>. Note that the subscript is ''2''. We can express this [[binary number]] in polynomial form as follows: | In the binary number system, the [[radix]] is 2 - i.e. a number system capable of only representing two discrete values: <math>\{0,1\}</math>. Let's consider the following number <math>10101110.011_{2}</math>. Note that the subscript is ''2''. We can express this [[binary number]] in polynomial form as follows: |