Definition:Octal Notation

Definition

Octal notation is the positional number system whose base is $8$.

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

An octal system is also known as octonary or octenary.

Hence we also have octonary notation or octenary notation.

Examples

Example: $141$

The integer expressed in octal as $215$ is expressed in decimal as $141$.

Example: $187$

The integer expressed in octal as $273$ is expressed in decimal as $187$.

Example: $371 \cdotp 24$

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

Also see

• Definition:Octal System of which octal notation is an instance

• 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): number system
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): octal notation
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): number system
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): octal notation