With respect to your logical operation, the next step is to implement it in the BigNum repository we checked out and have started playing with.
This means understanding where to put it, and what files need to be edited.
The include/bignum_logic.h file will be an important one to edit, as you'll want to put your function prototype there.
Also, you'll want to add your file in logic/, which will organize all the various logical operations.
Copy, modify, and be sure to hg add; hg commit; hg push a testing/ program to demonstrate the functionality of your logical operation.
Remember, the implementation for Logical OR is there for you to reference. Please do reference it!
You'll likely want to do an hg pull; hg update more frequently within bignum, as some people have already started making their changes, and you'll want to receive them.
All these things, working, and successfully pushed to the upstream repository will be considered as deliverables for this project.
Having questions is a good thing, but unasked questions are not. So please ask questions.