Now you got me worried that you
don't understand...
All you need to do is get the two's complement:
1. complement the number
2. add 1
If you start out with a negative number, you will get its positive and vice versa.
The way you showed it would be way too long unless you've memorized all the powers of 2 and can add really fast. I'm not even sure it'll give you the right result for all, if any, numbers.