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It sound like you're confusing Private IP Addresses with Public IP Addresses. If you are connecting to the Internet via a MODEM/Router, then the outside interface connected to the Internet is assigned a Public IP Address which is routable on the Internet. The MODEM/Router then assigns Private IP Addresses to all internal network computers and other systems which are not routable on the Internet. Usually a conversion algorithm, NAT, is used to translate a Public IP Address to the originating Private IP Address on the internal network computer. All computers and other systems must have a unique IP Address to support TCP/IP.
Like the fellow above said you are not specifying much. But from what I got reading your post: If 2 computers are connected to the same modem simultaneously, with no other devices in between such as routers, hubs etc... then yes, they both have different public IPs. This is because most modems (at least the ones I've seen) have one Ethernet output and one USB output that work simultaneously. Where I live all modems are like that and I think that this applies to pretty much any other place, so you can at least connect 2 computers at home.
In fact many people switch from Ethernet to USB whenever they need to avoid IP restrictions since each output gives you a different address. Now, usually your ISP changes your IP every now a then, usually a day or two. This is because ISP uses dynamic IPs, which mean they change.
As to "can you change that address".. I don't know if you can do it yourself. In fact I'm trying to myself to avoid an Ip restriction I got, and I've already used both IPs. Since it's a public IP and not private it's your ISP who decides when to change it. A method usually used to get your IP renewed is to unplug your modem and router over night and hopefully you will have a different IP by the morning, this isn't a very desirable method though. And if anyone knows an effective one or a way to hide or mask my IP, please tell me !
I hope this help, you should add more context to your post. Cheers.
Ip address are two type one is Private and another one is Public Ip-address.Private Ip-address are assigned by modem/routers to every device connected through it.It's not routable on internet...But Public ip-address is provide by ISP ..This routable on internet ..Every computers connected in a LAN have different ip-address ,the ip-address will not be same.You can assign ip-address to each device ..You can change LAN Ip-address for every device.But you cannot change the Public ip address.You can check the internet ip address of yours at Ip-Details.com
Of course its possible, but we must have more details about your question. There is modems-routers with Multi-NAT service inside. Multiple public IP addresses can be used (static or dynamic) on Internet. You didnt specify do you mean on Public or intranet side. Public addresses range must be given by ISP, and intranet or private is based on sysadmin management. Sysadmin can manage router and make policy about usage of IP address resources. Often companies dont have only one public IP address, in some cases company leases pool of 5-15 public addresses, for various purposes, as dedicated mail server, web, VPN,... Modem/router can use several of them, not just one IP address, of course this depends also from modem/router capabilities, he must have that capability to support that.
Also sysadmin can reserve particular public or private IP address for some particular client based on MAC address.
All of this can have security and load balancing reasons for usage. For load balancing, round-robin, sends each connection to a different IP address in the group, looping back to the beginning once it has gone through every IP. The first incoming connection goes to the first address in the pool, the second to the second address, and so on. You may have problems if using round-robin load balancing for SSL web servers or certain web applications that track user information by IP address. Random load balancing sends each connection to a random IP address in the pool. This has all of the disadvantages of round-robin load balancing, with the additional restriction that the address pool must be a proper network block instead of just a list of IP addresses. Source-hash load balancing uses a hash of the IP address to assign connection requests to a pool address. This means that every machine that connects is always assigned to the same address, which will avoid many software problems of round-robin and random load balancing. Using a fixed hash value means that each client gets an identical IP address even across firewall reloads.
You should get some material and read about NAT and TCP/IP header and encapsulation.