About using a new product activation code...

Hello. I want to ask a question about using a new product activation code. I have already norton internet security and norton 360 in my computers. They are remaining to finish 111 days. I want to buy a new norton internet security and norton 360 from online shopping with discount. If i use a new (different from old one) product activation code, old subscription will be deleted or a new subcsription will be added to old one? Thanks.