[GTALUG] how many addresses possible

Greetings (My head is swimming with all the explanations on IP routing - - - have spent about 3 hours now looking at various documents - - - - I just can't find a clear answer. The first statement is my present network - - - I'm trying to figure out how to move beyond the access of only 254 devices at one time. Please - - - this is not my business - - - - I'm just using a highly connected system design idea in the planning and trying to figure out how to get what I would like - - - done. ) If I set up a router using the 192.168.1.1 I can access some 254 distinct IP addresses from my router. If I set up a router using the 176.10.1.1 how many distinct IP addresses can I access? (I'm thinking some 64k worth but dunno!) TIA