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How does a PC know which DHCP scope to use?

This was such a good explanation I had to copy it down so I can find it again. Source: http://forums.anandtech.com/showthread.php?t=1249649

"You can set up all the scopes for different subnets you want, but your DHCP server will only hand out an IP for a different subnet if the request comes through a router or a DHCP relay agent. This request will be a multi cast, the packet will contain the IP info from the subnet the request originated from and the DHCP server will hand out an address from the co-responding scope.

If the DHCP request arrives as a broadcast, this means the requesting host is on the same subnet. The DHCP server will hand out an IP from a scope that handles it's own subnet.

Certian Routers can forward DHCP requests, but as a general rule broadcasts don't pass through routers. So if a DHCP server recieves a request in the form of a broadcast it knows to dishout an IP on it's own subnet. 

If a DHCP request comes in by way of a DHCP relay agent or a compliant router, the packet will contain info about its originating subnet. THat's how the DHCP server knows what scope to hand out an IP from.

This is all handled automagically by the DHCP server."