1.1a Decimal System

Decimal System

The decimal system is a base-10 numbering system that uses digits from 0 to 9.

To convert a number $x_{10}$ from decimal to another number system base-$n$:

1. Find $x_{10}(\mathrm{mod}n)$ and write it down at the rightmost digit.
2. Floor divide $x_{10}$ by n such that $\lfloor \frac{x}{n}\rfloor$ and repeat.

Then, to reverse the conversion,
$x_{10}={\sum }_{i=0}^{k-1}{b}_i\cdot n^i,$
where $k$ is the length of the string in base-$n$, and $b_i$ is its $i$-th digit.