Number systems

A number system is a method for expressing numbers using a consistent set of digits and a base. The base (or radix) determines how many unique digits are used and how place values increase. For example, in base $b$, each digit represents a multiple of a power of $b$.

Important properties

• A number in base $b$ is written as $d_n d_{n-1} \\ldots d_1 d_0$, where each $d_i$ is a digit from $0$ to $b-1$.

• The value is $d_n b^n + d_{n-1} b^{n-1} + \\ldots + d_1 b^1 + d_0 b^0$.

• Common bases: decimal (10), binary (2), ternary (3), hexadecimal (16).

• Changing bases involves converting numbers by expressing them in terms of another base.