File permissions are stored internally as 16 bit integers. As an alternative to giving a symbolic mode, you can give an octal (base 8) number that corresponds to the internal representation of the new mode. This number is always interpreted in octal; you do not have to add a leading 0, as you do in C. Mode 0055 is the same as mode 55.
A numeric mode is usually shorter than the corresponding symbolic mode, but it is limited in that it can not take into account a file's previous permissions; it can only set them absolutely.
The permissions granted to the user, to other users in the file's group, and to other users not in the file's group are each stored as three bits, which are represented as one octal digit. The three special permissions are also each stored as one bit, and they are as a group represented as another octal digit. Here is how the bits are arranged in the 16 bit integer, starting with the lowest valued bit:
Value in Corresponding
Mode Permission
Other users not in the file's group:
1 Execute
2 Write
4 Read
Other users in the file's group:
10 Execute
20 Write
40 Read
The file's owner:
100 Execute
200 Write
400 Read
Special permissions:
1000 Save text image on swap device
2000 Set group ID on execution
4000 Set user ID on execution
For example, numeric mode 4755 corresponds to symbolic mode u=rwxs,go=rx, and numeric mode 664 corresponds to symbolic mode ug=rw,o=r. Numeric mode 0 corresponds to symbolic mode ugo=.