Writing numbers in binary notation means expressing them as a sequence of binary digits (bits), either 0 or 1. Each number must be represented by powers of two. Counting from the left, the position represents the exponent of this power.

For example, in binary, we can write the number 155 into powers of two, as shown below:

$$\begin{gathered} 155 \\ \=128\+16\+8\+2\+1 \\ \= 2^7\+2^4\+2^3\+2^1\+2^0 \\ \= 1\cdot 2^7\+0\cdot 2^6\+0\cdot 2^5\+1\cdot 2^4\+1\cdot 2^3\+0\cdot 2^2\+1\cdot 2^1\+1\cdot 2^0 \\ \=10011011 \end{gathered}$$(in binary)

Digital electronics, such as digital computers, are made up of electronic circuits. These electronic circuits have only two states: on and off. How are computers then able to perform the complex operations they do? The underlying communications interface for computers is binary. The states on and off can be represented by the bits 1 and 0, respectively. These bits can be used in sequence to create a base two "binary" number system analogous to our base ten "decimal" number system. Various combinations of these binary bits are used in computing to represent various items, such as pictures and videos. Furthermore, computers are able to perform arithmetic operations on these binary numbers and can even employ Boolean algebra, which is a subsection of algebra dealing with only two states. Moreover, signals with binary representations can be generated and used by computers to communicate with other devices. Although there are many different types of computers, all of them use the same underlying binary language.