# Definition:Binary Notation

## Contents

## Definition

**Binary notation** is the technique of expressing numbers in base $2$.

That is, every number $x \in \R$ is expressed in the form:

- $\displaystyle x = \sum_{j \mathop \in \Z} r_j 2^j$

where $\forall j \in \Z: r_j \in \set {0, 1}$.

## Also see

**Binary notation**, like hexadecimal notation, has particular relevance in the field of computer science.

## Historical Note

The earliest known reference to binary notation appears to be in a Chinese book dating from approximately $3000$ B.C.E.

In Europe, binary notation was invented by Gottfried Wilhelm von Leibniz.

He associated God with $1$ and nothingness with $0$, and believed that it was mystically significant that all numbers could be built from $1$-ness and $0$-ness.

## Sources

- 1965: Seth Warner:
*Modern Algebra*... (previous) ... (next): $\S 24$ - 1986: David Wells:
*Curious and Interesting Numbers*... (previous) ... (next): $2$ - 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (previous) ... (next): $2$