chmod with octal modes

Three bits make one digit

Each triplet is three yes/no bits, and three bits are exactly one octal digit, 0 to 7. Give the bits their binary weights, r=4, w=2, x=1, and add up whatever is present: rwx is 4+2+1=7, r-x is 5, rw- is 6, r-- is 4, --- is 0. Do that for user, group and others and you get the whole mode as a three-digit number: -rwxr-xr-x is 755, -rw-r--r-- is 644. Going back is just as mechanical: 6 can only be 4+2, so rw-.

~% cd /root/lab/l47
l47% chmod 755 script.sh
l47% chmod 600 id_key
l47% chmod 640 report.txt
l47% ls -l
-rw-------    1 root     root             0 Oct  4 19:15 id_key
-rw-r-----    1 root     root             0 Oct  4 19:15 report.txt
-rwxr-xr-x    1 root     root             0 Oct  4 19:15 script.sh
l47% chmod -c 644 report.txt
mode of 'report.txt' changed to 0644 (rw-r--r--)

The modes you will actually use

Octal is absolute: chmod 644 f sets all nine bits regardless of what they were. That is its strength, you know the final state without looking, and its risk, because chmod -R 644 dir also strips x from every directory inside and locks you out of them. Use octal when you want to *state* a mode, symbolic when you want to *adjust* one. The two forms are interchangeable: 755 is u=rwx,go=rx.

A fourth digit

You will sometimes see four digits, 0644 or 4755. The leading digit holds the three special bits, setuid (4), setgid (2) and sticky (1), which lesson 50 explains; chmod -c prints modes that way. A leading 0 just means none of them is set, and chmod 644 is the same as chmod 0644.