Editing Chmod (section)

=== Octal notation ===
Given a numeric permissions argument, the {{code|chmod}} command treats it as an [[octal]] number, and replaces ''all''  the mode bits for each file. (Although 4 digits are specified, leading {{code|0}} digits can be elided.)<ref>This differs from the “C” language, where the {{code|0}} prefix for octal numbers is a remnant of its early period.</ref>

Why octal rather than decimal? <ref>Although rarely used today, during the early development of UNIX, octal was very useful because repeating groups of 3 bits were common in the physical structure of computers at the time, and these bits were easier to read & understand when encoded as octal digits, just as groups of 4 bits are easier when grouped into hexadecimal digits. The numeric expression of filesystem permissions in octal is one of the few of the few remnants of this time.</ref>

There are twelve standard mode bits, comprising 3 special bits ({{Mono|[[setuid]]}}, {{Mono|[[setgid]]}}, and {{Mono|[[Sticky bit|sticky]]}}), and 3 permission groups (controlling access by ''user'', ''group'', and ''other'') of 3 bits each (''read'', ''write'', and ''exec/scan''); each permission bit grants access if set (1) or denies access if clear (0).

As an octal digit represents a 3-bit value, the twelve mode bits can be represented as four octal digits. {{code|chmod}} accepts up to four digits and uses 0 for left digits not specified (as is normal for numeric representation). In practice, 3 digits are commonly specified since the special modes are rarely used and the user class is usually specified. 

In the context of an octal digit, each operation bit represents a numeric value: read: 4, write: 2 and execute: 1. The following table relates octal digit values to a class operations value.

{| class="wikitable"
|+ Octal digit permission
|-
! # !! bits 
! rwx
! granted operations 
|-
| 7
| {{Mono|4 + 2 + 1}} 
| {{code|rwx}}
| read, write and execute 
|-
| 6
| {{Mono|4 + 2   }}  
| {{code|rw-}}        
| read and write 
|-
| 5
| {{Mono|4 &nbsp;&nbsp;&nbsp; + 1}} 
| {{code|r-x}}
| read and execute 
|-
| 4
| {{Mono|4}} 
| {{code|r--}}                             
| read only 
|-
| 3
| {{Mono|&nbsp;&nbsp;&nbsp; 2 + 1}} 
| {{code|-wx}}
| write and execute 
|-
| 2
| {{Mono|&nbsp;&nbsp;&nbsp; 2}} 
| {{code|-w-}}
| write only 
|-
| 1
| {{Mono|&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 1}} 
| {{code|--x}}
| execute only 
|-
| 0
| {{Mono|}} 
| {{code|---}}       
| none 
|}

The command [[stat (Unix)|{{code|stat}}]] can report a file's permissions as octal. For example:

<syntaxhighlight lang="console">
$ stat -c %a findPhoneNumbers.sh
754
</syntaxhighlight>

The reported value, {{code|754}} indicates the following permissions:
* user class: read, write, and execute; 7 => (4 + 2 + 1)
* group class: read and execute; 5 => (4 + 1)
* others class: read only; (4)

A code permits execution if and only if it is [[Odd number|odd]] (i.e. 1, 3, 5, or 7). A code permits read if and only if it is greater than or equal to 4 (i.e. 4, 5, 6, or 7). A code permits write if and only if it is 2, 3, 6, or 7.