I've always been a little bit fuzzy on the topic.
I can type chmod a+w file fine, but I don't understand how to use numbers to represent it. If you are helping me, please don't just say "chmod 777" will give everyone rwx, I want to know how this representation system works.

Basically, you need to think of each number as a binary number. So a 7 in binary is actually 111. In this form, each position represents a permission with a 1 representing the permission as being granted and 0 as not allowed. The positions for the permissions are (in this order) read, write, execute.

So you can see that a 7 grants permissions for read, write and execute. A 6 (binary form 110) would grant permissions for reading and writing.

Now, back to the decimal form....these three positions are for the owner, members of the group, and lastly everyone else. This is why 777 translates into read, write and execute permissions for the owner, members of the group and all others. 700 would give all permissions, but only to the owner of the file.

Clear as mud?

This is all explained in 'man 1 chmod':
But I can try to rephrase it.
The numbers are interpreted as three bitfields (those 3 numbers; 7, 7 and 7 in your case) each containing three bits.

To figure out what those numbers mean, you have to convert them to bit representation.
For example the number 7 is '111' in binary (1*2^2+1*2^1+1) , (Equally similar to decimal representation of for example value 275 is 2*10^2+7*10^1+5 [Here the '^' means rising to power].
So, what does the bitfield '111' tells us? It means that reading, writing and executing flags are all on. So the original number serie 777 means that reading, writing and excuting are allowed for for owner, group and others.

Other example: What does mode 644 mean?
Interpreting the 6: '110' (that is 1*2^2+1*2^1+0)
Interpreting the 4: '100' (that is 1*2^2+0*2^1+0)
Now in '110' the reading and writing flags are on, but execution is not and in '100' reading is on, other flags off. So, the modeline 644 means that owner has read and write permissions and group and others have only reading permission.

And to the other way around; how to set for example permissions so that user can execute the file, group can read and execute it and others can do nothing with it?
Way 1:
Convert the idea to binary number and it to decimal
How? User: '001', group: '101', others: '000', so the mode is 150

Way 2:
Remember (or look from the manpage) that: read (4), write (2), and execute (1).
That is: set only execute:1, to set read and execute: 4+1, To set nothing: 0.
So we got the 150 again.

to complete ToniT's post, read this, which is very neat and quite understandable

http://www.linuxquestions.org/questi...ticle&artid=20

cheers