Ip Address From Router?

I'm connecting 2 computers to the router, which connects to the internet. My question is, does each computer have its own unique IP address when connecting to a site, or does each computer use the IP address of the router?

Thanks

the router uses NAT routing which decides what computer the information has coem from and going to etc,

the router will have a wan i.p which is our internet i.p and will asign to local i.ps to the computers, usually something like 192.168.1.xxx

and only the router can actually be seen form the internet everything behind the router is "hidden" basically from the internet.

nope as far as the outside internet is concerned it only see,s the router ip addy, although why are you using a router with only 2 comps, all you need is a crossover cable between the 2 comps.

usualy, but not always one comp connects directly to the internet, and the other comp just piggybacks, eg the first comp would have 2 nic cards in it , 1 for adsl, and one for lan

i thinks thats right lol

http://computer.howstuffworks.com/router.htm this may yeild some info for you.

Thanks guys. I had a feeling that it would only show the Routers IP. Reason being, I'm trying to order some tickets online, and I don't want the same IP address to show up twice (its an online waiting room, i was hoping one computer will be accepted into buying tickets faster).

Thanks for the help and quick replies!