Binary Representation of Numbers

We commonly represent number is base $10$, there are $10$ elements in our base $10$ numbering system, $0,1,2,3,4,5,6,7,8,$ and $9$. In a base $n$ counting system there are $n$ distinct elements, $0$ through $n - 1$.

When a number which is greater than $n - 1$ needs to be displayed in base $n$ it is represented by a string composed of the $n - 1$ elements. The value of any given symbol in the string is found by multiplying that symbol by $n^{x}$, where $x$ is the number of symbols in the string that are to the right of the symbol in question.

For example; in base 10 the number 982 is equal to $9 * 10^{2} + 8*10^{1} + 2*10^{0}$.

In base two the number $10101001$ is equal to $1*2^{7}+0*2^{6}+1*2^{5}+0*2^{4}+1*2^{3}+0*2^{2}+0*2^{1}+1*2^{0} = 169$ in base $10$.