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Suppose two systems are there in two different LANs, LAN-1 and LAN-2 respectively.System-1 (present in LAN-1) wants to communicate to system-2(present in LAN-2), for which sys-1 needs the MAC ddress of that system in adition to its IP address.So, it sends an ARP request messgae which contains the destination IP address which is broadcasted by the switch present at the interface of LAN-2.
My doubt is, how does the system-2 will come to know, that the request messgae belongs to it..? I think dest. IP which is present inside the ARP request message belongs to the public IP(of the LAN).[correct me, if i am wrong].Then,how the system-2 is going to reslove that request packet belongs to it..? Please explain.
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First of all router never broadcast between two lan. Machine which are on the lan2 never see the broadcast produce by the lan1.machine. Study about proxcy arp and  arp spoofing you can clear your concept.
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basically u don't even need to know the mac address of the final host. always the mac address which will be used will be the next hope. which in this case will be default gateway. and arp request outside the network are not entertained .

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