I wrote this in PHP but you can use the same concept in other languages, I also assume an understanding of bits, bytes, binary to decimal conversion and vice-versa and bitwise operations on numbers like ‘or’, ‘and’ and ‘xor’ etc. if you have no idea, search and read about these first. You don’t have to be a guru but you should have an idea. Here are some pages to get you started:
http://en.wikipedia.org/wiki/Byte
http://en.wikipedia.org/wiki/Bitwise_operation
http://us.php.net/manual/en/language.operators.bitwise.php
Some binary to decimal calculators to make it easier
We will use simple numbers to represent different permissions and as you might know a number is a collection of bytes. For example: an integer is usually 4 bytes. Although you don’t have to worry about the size of a number in a high level language like PHP but a little understanding of representation of numbers will help you better understand this technique.
So let’s assume when I say:
<?php $user_perms = 7; ?>
Internally the variable $user_perms looks like this:
|0|0|0|0|0|0|0|0|0|0|0|0|0|1|1|1|
This is a 2 byte representation of number 7, although, it might not look like this internally – it looks similar. Just assume this for now.
Let’s say that your application supports 4 functions that a user can use:
1 – Post a blog post
2 – Comment on blog posts
3 – Edit posts
4 – Delete posts
Normally, you could have 4 fields in your database table (structure or whatever) for a user titled:
1 – can_post
2 – can_comment
3 – can_edit
4 – can_delete
This is not good, 4 additional fields for your user table and who knows, what if your application has 100 functions? Do you want to add 100 fields to your user table?
With bits, you can have only 1 column and track all the permissions.
1 – perms
To do this, we will have to assign numbers for each of the functions: (Tip: use one of the calculators in the above list 
)
1 – Post a blog post |0|0|0|0|0|0|0|1| is 1 in decimal
2 – Comment on blog posts |0|0|0|0|0|0|1|0| is 2 in decimal
3 – Edit posts |0|0|0|0|0|1|0|0| is 4 in decimal
4 – Delete posts |0|0|0|0|1|0|0|0| is 8 in decimal
So you could have an array like this:
<?php $perms = array( 'can_post' => 1, 'can_comment' => 2, 'can_edit' => 4, 'can_delete' => 8 ); ?>
Almost there, let’s look at user’s perms field now.
I hope you know about bitwise ‘or’, when you ‘or’ 1 and 1 you get 1; 0 ‘or’ 1 is 1; 1 ‘or’ 0, is 1 and finally 0 ‘or’ 0 is 0, it’s just like the meaning of ‘or’ in the English language.
Similarly, bitwise ‘and’; when you ‘and’ 1 and 1 you get 1; 0 ‘and’ 1 is 0; 1 ‘and’ 0, is 0 and finally 0 ‘and’ 0 is 0, again it’s just like the meaning of ‘or’ in the English language.
Bitwise ‘xor’; when you ‘xor’ 1 and 1 you get 0; 0 ‘xor’ 1 is 1; 1 ‘xor’ 0, is 1 and finally 0 ‘xor’ 0 is 0.
So suppose you want to give a user permissions to post a blog post, post a comment and edit posts but not delete posts, you do it like this:
<?php $user_perms = $perms['can_post'] | $perms['can_comment'] | $perms['can_edit']; ?>
Note that, in PHP ‘|’ means ‘or’, so what just happened is something like this:
|0|0|0|0|0|0|0|1| ‘or’
|0|0|0|0|0|0|1|0| ‘or’
|0|0|0|0|0|1|0|0|
_______________________
|0|0|0|0|0|1|1|1|
Now $user_perms has the value 7 and |0|0|0|0|0|1|1|1| in it internally.
Suppose that this is on top of your post_blog.php or where ever you want to handle permissions for posting a blog, the only thing you need to do is:
<?php if ($user_perms & $perms['can_post']) { /* He/She has permissios to do this */ } else { /* He/She doesn't */ } ?>
In PHP ‘&’ is for bitwise ‘and’, please also note that ‘&&’ is logical ‘and’ and doesn’t operate on individual bits.
This is exactly what just happened:
|0|0|0|0|0|1|1|1| ‘and’
|0|0|0|0|0|0|0|1|
_______________________
|0|0|0|0|0|0|0|1|
So that’s ‘one’ not ’0′, which means ‘if’ passes and the user has permissions to do this. But when it comes to deleting posts:
<?php if ($user_perms & $perms['can_delete']) { /* He/She does permissios to do this */ } else { /* He/She doesn't */ } ?>
Thus:
|0|0|0|0|0|1|1|1| ‘and’
|0|0|0|0|1|0|0|0|
_______________________
|0|0|0|0|0|0|0|0|
It’s ‘zero’ so ‘if’ fails and you show an error message or whatever it is you do.
To add ‘delete’ permissions, you use ‘or’ again:
<?php $user_perms |= $perms['can_delete']; ?>
So this happens:
|0|0|0|0|0|1|1|1| ‘or’
|0|0|0|0|1|0|0|0|
_______________________
|0|0|0|0|1|1|1|1|
To take away permissions you use ‘xor’:
<?php $user_perms ^= $perms['can_delete']; ?>
And this will happen:
|0|0|0|0|1|1|1|1| ‘xor’
|0|0|0|0|1|0|0|0|
_______________________
|0|0|0|0|0|1|1|1|
And delete permissions are gone!
Now let’s take away post permissions:
<?php $user_perms ^= $perms['can_post']; ?>
Thus:
|0|0|0|0|0|1|1|1| ‘xor’
|0|0|0|0|0|0|0|1|
_______________________
|0|0|0|0|0|1|1|0|
So this was just the basics, you can build on this and do more once you understand.
I hope this post will help someone 
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