Definition:Octal Notation

Definition

Octal is another word for base $8$.

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

$\ds x = \sum_{j \mathop \in \Z} r_j 8^j$

where:

$\forall j \in \Z: r_j \in \set {0, 1, 2, 3, 4, 5, 6, 7}$

Also known as

Octal notation is also known as octonary or octenary.

Examples

Example: $371 \cdotp 24$

The integer expressed in octal as $371 \cdotp 24$ is expressed in decimal to $2$ decimal places as $249 \cdotp 31$.

Also see

• Results about octal notation can be found here.

Historical Note

Octal notation was advocated by Emanuel Swedenborg.

Octal notation used to be important in the field of computer science, but is less so nowadays, as hexadecimal has proved itself more convenient in general.

Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $8$
• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): octal
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $8$
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): octal notation
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): octal system
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): octal notation
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): octal system
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): octal