Difference between revisions of "Number Systems/Formal Representation"

Revision as of 09:48, 24 November 2021

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Formal Representation[edit]

Let x be a string of digits, such that: $x=x_{n}x_{n-1}x_{n-2}\cdots x_{0}$

Then, the value of $x$ in any particular base, $b$ , is calculated as: $\sum _{i=0}^{n}x_{i}\cdot b^{i}$

The rightmost digit, $x_{0}$ is referred to as the least significant digit, or LSD. It is least significant because in terms of the overall value of the entire number, this digit will always have the least impact. Conversely, the leftmost digit, $x_{n}$ is referred to as the most significant digit, or MSD. It is most significant because in terms of the overall value of the entire number, this digit will always have the most impact.

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Revision as of 09:44, 24 November 2021 (view source) Dinas-emrys (talk \| contribs) (Created page with "== Formal Representation == Let x be a string of digits, such that: <math>x = x_{n}x_{n-1}x_{n-2} \cdots x_{0}</math> Then, the value of <math>x</math> in any particular bas...")		Revision as of 09:48, 24 November 2021 (view source) Dinas-emrys (talk \| contribs) (→‎Formal Representation) Newer edit →
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	The rightmost digit, <math>x_{0}</math> is referred to as the '''least significant digit''', or '''LSD'''. It is ''least significant'' because in terms of the overall value of the entire number, this digit will always have the least impact. Conversely, the leftmost digit, <math>x_{n}</math> is referred to as the '''most significant digit''', or '''MSD'''. It is ''most significant'' because in terms of the overall value of the entire number, this digit will always have the most impact.		The rightmost digit, <math>x_{0}</math> is referred to as the '''least significant digit''', or '''LSD'''. It is ''least significant'' because in terms of the overall value of the entire number, this digit will always have the least impact. Conversely, the leftmost digit, <math>x_{n}</math> is referred to as the '''most significant digit''', or '''MSD'''. It is ''most significant'' because in terms of the overall value of the entire number, this digit will always have the most impact.


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