Hi Rico,
calculating 2's complement of negative number requires it to be inverted and adding 1, right? 2's complement of positive number is same number, right? You have unsigned 16-bit numbers, so inverting and adding is not required, I believe.
So, 1) if your unsigned 16-bit data has MSB 16th bit as 1, then you need to shift the data to right by 1 to make the MSB bit, which is sign bit, as 0. But you should keep that in mind, if you will be doing further processing on it.
2) If you any of your data do not have 16th bit as 1, then you already have proper signed data, so shifting may not required in this case.
Let me know if you still have any confusion.
Thanks,
Prashant