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Question: How many subnets and host per subnet can you get from the network 172.23.0.0 255.255.255.240?
We start with the idea of understanding that the base network is a class B network:
172.23.0.0 255.255.0.0 = 1 netowrk, 65534 possible hosts on this network.
If you now add an additional 12 bits to the network portion (the break down: 16 bits NetworkID,12 bits SubnetID, 4 bits HostID). You've taken ONE netowrk and created 2 to 12th power number of "subnets": 2^12 = 4096 networks. The remaining bits that are not associated with the network bits and subnet bits would be 4 bits for the Host bits. This gives you the 14 hosts per network. (For the host bits even if there are 16 possible combinations, we must subtract 2 -- 1 for the NetworkID, 1 for the BroadcastID).
Question: 172.16.0.0/18, how many subnets?
We start the same way: 172.16.0.0 255.255.0.0 is the base network (1 netowrk, 65534 hosts on this network). the new subnet mask= 255.255.192.0
If we add an additional 2 bits the network portion: (16 bits on base NetworkID, 2 bits as SubnetID, 14 bits as the hostID bits). So we would have 2^2 = 4 subnets we could create with each network having 2^14 = 16382 hosts per subnet.
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