# Number Systems/Formal Representation

## Formal Representation

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

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

The rightmost digit, ${\displaystyle x_{0}}$ 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, ${\displaystyle x_{n}}$ 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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