As an alternative to giving a symbolic mode, you can give an octal (base 8) number that represents the 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’. (However, modes of five digits or more, such as ‘00055’, are sometimes special. See Directory Setuid and Setgid.)
A numeric mode is usually shorter than the corresponding symbolic mode, but it is limited in that normally it cannot take into account the previous file mode bits; it can only set them absolutely. The set-user-ID and set-group-ID bits of directories are an exception to this general limitation. See Directory Setuid and Setgid. Also, operator numeric modes can take previous file mode bits into account. See Operator Numeric Modes.
The permissions granted to the user, to other users in the file’s group, and to other users not in the file’s group each require three bits, which are represented as one octal digit. The three special mode bits also require one bit each, and they are as a group represented as another octal digit. Here is how the bits are arranged, starting with the lowest valued bit:
Value in Corresponding Mode Mode Bit Other users not in the file's group: 1 Execute/search 2 Write 4 Read Other users in the file's group: 10 Execute/search 20 Write 40 Read The file's owner: 100 Execute/search 200 Write 400 Read Special mode bits: 1000 Restricted deletion flag or sticky bit 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 ‘a=’.