Adding and Removing Permissions Shorthand

Shorthand yes, but long brain!
To understand how this shorthand method works we first need a little background in number systems. Our typical number system is decimal. It is a base 10 number system and as such has 10 symbols (0 - 9) used. Another number system is octal which is base 8 (0-7). Now it just so happens that with 3 permissions and each being on or off, we have 8 possible combinations (2^3). Now we can also represent our numbers using binary which only has 2 symbols (0 and 1). The mapping of octal to binary is in the table below.

Octal Binary
0 000
1 001
2 010
3 011
4 100
5 101
6 110
7 111