The short answer to the question is to simply apply a bitwise NOT to the number that you want to convert and add 1 to the result. I wrote about bitwise logic in The Arcane Science of Bitwise Logic and SQL Server but didn’t mention the bitwise NOT.
If you want to apply a bitwise NOT to a value, simply use the ~
Give it a go, try converting 10 to a negative,SELECT ~ 10 + 1
The result, -10.
One of my rules of thumb (given how many I have, I need more thumbs) is that if you’re using bitwise logic in SQL Server, something has likely gone wrong somewhere along the way. But read David’s explanation, which is quite clear.