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Can a layer 2 broadcast work alone or should be accompanied by a layer 3 broadcast? If layer 3 broadcast cannot cross the router why do we even need a layer 3 broadcast within a subnet?

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Short answer, an L2 broadcast is only used for L2 operations, and often does not carry L3 or higher protocol data. L3 broadcasts carry data that is pertinent to L3 or higher protocols.

As you say, L2 broadcasts cannot cross routers, but that's not what they are for. L2 broadcasts are used for tasks pertinent only to L2 operations like DHCP, ARP, STP (and other automatic topology control schemes), etc. in short, a L2 broadcast is used only by layer 2 protocols. None of these protocols should cross routers to perform their job.

A L3 broadcast comes from an L3 function or higher layer application protocol, and does not relay on any particular L2 implementation. It doesn't care if you use MAC addresses or some other identifier, or what topology it must cross.

Think about this: what would happen if you had a LAN with some clients on an IP network, and some using IPX/SPX (or NCP, or decnet or SNA)? if you sent an IP broadcast to the LAN, and the L2 frame was broadcast, the IPX/SPX hosts would receive the frame as well, which is not desirable. If the IP broadcast uses unicast frames however, only the IP clients would receive the broadcast.

So, to sum up, L2 and L3 broadcasts are directly not related to each other, and are not generally used together. They support different kinds of protocols designed for different tasks.

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