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My networks professor said "Routers cannot connect networks of different classes". For example, it is impossible to connect Class-A network with a Class-B network, using a router. Is this true? If so, then how's the internet connected. I mean, those routers(of different classes) must be connected with each other at some point in the hierarchy. So, what's that point (or device) called?

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I believe you are taking the conversation out of context. Perhaps the "class" he was talking about is not the Class-# network divisions (which by the way are no-longer used, its all CIDR now). Can you give more information about the broader context of what you where discussing? – Scott Chamberlain Aug 1 '13 at 21:58
@ScottChamberlain Currently he's teaching the basics of networking. I'm confident that he was talking about Class-# networks. i.e. Class-C for Institutions, Class-B for Corporates, etc. But I didn't know that that method was replaced by CIDR. Thanks for the info! – Vishnu Vivek Aug 1 '13 at 22:07
I really wish they would stop teaching it, it has not been used seance the 90's. – Scott Chamberlain Aug 1 '13 at 22:09

From Wikipedia

A router is a device that forwards data packets between computer networks, creating an overlay internetwork. A router is connected to two or more data lines from different networks.

A router is the thing that connects networks, either your professor was wrong or he was not talking about the networks you are talking about in this question.

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I've laid emphasis on "networks of different classes". – Vishnu Vivek Aug 1 '13 at 22:15
All the "class" is is whether you set the subnet on the network adapter to (class A), (class B), or (class C). You can use different subnet sizes with routers without a problem, so as I said before "either your professor was wrong or he was not talking about the networks you are talking about in this question." – Scott Chamberlain Aug 1 '13 at 22:19

No, you either misunderstood your professor or he was wrong.

It is entirely practical for a router to connect networks of different classes, and indeed this is BY FAR the most common setup for a router. (Even your home adsl/ethernet router will connect a CLASS C to a /30). It is not uncommon in larger organisations for a single organisation to use routers to connect (for example a Class A address with ( a Class B address, while offering a.b.c.x - a Class C address through a DMZ for servers.

Moreover, the whole design of IP addresses is to allow breakdown and aggregation of addresses to reduce load on routing tables - and routing tables are typically large lists of directories stored in routers showing how to reach Class A,B,C and subsets of these through the router.

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