Definition:Binary System

Definition

A binary system is a number system in which the base is $2$.

Binary Notation

Binary notation is the positional number system whose base is $2$.

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

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

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

Also see

• Results about binary systems can be found here.

Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $2$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $2$
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): binary system
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): number system
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): binary system
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): number system
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): binary system