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If the subnet mask is 255.255.252.0, then would 10.10.12.1 be on the same network as 10.10.14.1? Or would they require a NAT to communicate?

NMaestro
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Yes they are because when you do and operation of both IPs with the subnet mask you will get the same result 10.10.12.0 so they belongs to same network 10.10.12.0.

storm
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I find that an easy way to calculate this is if you recall your mask combinations against their powers of 2 within the binary 8 bits of an octet:

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In your example where you have 4 aligned to 252 (/22 mask = 255.255.252.0), then you have a range of 4 networks counting up from the network number. The octet where your mask changes from .255 will correspond to the octet of your host address. In this instance it is in the 3rd octet so you will have a range from 10.10.12.1 - 10.10.15.255/22, so yes they are within the same subnet.

MattE
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