coreutils: Numeric Modes
26.3 Numeric Modes
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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. 
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. Directory Setuid and Setgid. Also,
operator numeric modes can take previous file mode bits into account.
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=’.
Info Catalog
coreutils: Symbolic Modes
coreutils: File permissions
coreutils: Operator Numeric Modes