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It is said that, in the process of building a frame, the host checks if the destination IP address exists in the same network. My question is concerning how the host performs this check. Does the host need to access the routing table to know if the destination IP address exists in the same network or does it merely iterate over the multiple pairs of (IP address, subnetmask) associated to each of its interfaces and checks whether the destination IP address falls within one of the corresponding networks? I know that access to the routing table is needed to know which interface to send the frame through, but I'm unsure if the same access is required for checking if a particular IP address falls within one of the networks that the host belongs to.

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No. A hosts masks the destination address with its configured mask to see if the destination is on the same network.

There is a section in this two-part answer that explains that. See the IPv4 Network Address section.

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