Assuming we have a router connecting 4 different networks, with the prefixes 00, 01, 10 and 11, the router would need to have an IP address with such a prefix in each network, to be addressable as the standard gateway, is that correct?
Now, I was wondering, the Link-Layer address that is needed to reach the standard gateway is gotten with ARP, by broadcasting for someone to reveal themselves as that address. However, couldn't we just have a router have just one IP that is in one of those networks? What would be the problem? If a device in a different network will want to talk to the router, it will just send a packet to that address, and the router will recognize that it has that particular address. So where is the need for each router to have one IP per network it is in?