Binary Number

numeric

Definition

Binary Number

A binary number is a number that is expressed in the base-2 system, which is the number system that uses only two digits, 0 and 1:

$$(a_k{a}_{k-1}\dots a_0{)}_2=\sum _{i=0}^k{a}_i\cdot 2^i$$

Example:

$$(1010{)}_2=1\cdot 2^3+0\cdot 2^2+1\cdot 2^1+0\cdot 2^0$$

The set of the binary digits 1 and 0 is often denoted as $\mathbb{B}=\{0,1\}$. The binary representation of $n\in \mathbb{N}$ is denoted as $[n{]}_2\in \mathbb{B}$.