OCT2BIN

Converts a octal number to binary.

Syntax:

OCT2BIN(octalnumber, numdigits)

returns text representing a binary number, given octalnumber, which may be text, or a number (taken to be octal although it is not).

The binary number returned may have up to ten bits in two's complement representation; positive numbers are 0 to 111111111 (nine bits representing 0 to 511 decimal) and negative numbers 1111111111 to 1000000000 (ten bits representing -1 to -512 decimal).

octalnumber must therefore also lie in this range, and is given in twos complement form with up to ten digits.

numdigits is an optional number specifying the number of digits to return.

Example:

OCT2BIN("14")

returns 1100 as text.

OCT2BIN(14)

returns 1100 as text. The number 10 is read as octal.

OCT2BIN("2", 4)

returns 0010 as text. OCT2BIN adds leading zeroes to make 4 digits.

OCT2BIN("7777777776")

returns 1111111110 as text (twos complement representation of decimal -2).

Application:

An application of the OCT2BIN function is in computer science and digital electronics, particularly when working with file permissions in Unix-like operating systems (such as Linux or macOS).

In these systems, file permissions are often represented using a three-digit octal number. Each digit in the octal number corresponds to the permissions for a specific user group: the owner, the group, and all other users.

The permissions themselves are based on a binary system, where:

Read permission is represented by the binary value 100 (which is 4 in decimal).
Write permission is 010 (which is 2 in decimal).
Execute permission is 001 (which is 1 in decimal).

By using the OCT2BIN function, a developer or system administrator can easily see the binary breakdown of a file's permissions, which tells them exactly who can read, write, or execute a file.

Example Table:

Let's say a file has the octal permission code 754. Here's how the OCT2BIN function helps to interpret it:

	Octal Permission Code	Group	OCT2BIN Function	Binary Result	Binary Breakdown
	A	B	C	D	E
1	7	Owner	OCT2BIN(7)	111	100 (Read) + 010 (Write) + 001 (Execute)
2	5	Group	OCT2BIN(5)	101	100 (Read) + 001 (Execute)
3	4	Others	OCT2BIN(4)	100	100 (Read)

This table clearly shows that:

The owner has all three permissions (read, write, and execute) because 7 in octal is 111 in binary.
The group has read and execute permissions because 5 in octal is 101 in binary.
Other users only have read permission because 4 in octal is 100 in binary.

This simplifies the process of understanding and setting file permissions, as it provides a clear, bit-level view of the access rights associated with an octal number.