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I've got a problem that I can't seem to understand.

192.168.255.0 /24 is a valid network address. The broadcast address for this network is 192.168.255.255.

192.168.0.0 /16 is a valid network address. The broadcast address for this network is 192.168.255.255.

In other words, would there not be a problem with broadcasting for the 192.168.255.0 network, as devices in the 192.168.x.0 network would think the broadcast was meant for them as well?

Would this make it a good practice to divide different subnets into different vlans?

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You simply cannot (reasonably) use the subnets 192.168.255.0/24 and 192.168.0.0/16 in the same network since they overlap.

Using them in separate L2 segments makes communication between them impossible (without trickery).

Using them in the same L2 segment enables normal communication inside the overlapped scope 192.168.255.0/24 but 192.168.255.0/24 nodes would require a gateway for the rest of 192.168.0.0/16, even if they are within direct L2 reach.

The broadcasts overlap as well, as you wrote. Note that directed broadcasts are translated into L2 broadcasts once they reach the destination subnet (they can be routed, depending on configuration). The L2 broadcast is transmitted to all nodes, 192.168.255.0/24 and 192.168.0.0/16 alike. Both subnets' nodes also match the destination address to their directed broadcast address, so they'd all process the packet.

This is all no good practice at all. Overlapping subnets generally cause routing conflicts and must be avoided.

192.168.0.0/16 can be used as an aggregated route where appropriate but don't overlap subnets of any size.

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If you use the 192.168.255.0/24, then you cannot use the 192.168.0.0/16 network as they would be overlapping networks. Trying to do something like that would be a misconfiguration on the hosts, or a configuration error on a router.

If you have hosts on the same LAN with those configurations, a host in the 192.168.255.0/24 network could not send something to a host addressed like 192.168.10.11 because the source host would think the destination is in a different network, so it would send traffic to the router.

If you had a router with two interfaces, one for each network, you could not configure those two networks because you would get an error about overlapping networks. Hosts on the 192.168.0.0/16 network could not send anything to hosts on the 192.168.255.0/24 network because they will assume that the destination is on the same network, not a different network.

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