How do I determine the maximum number of subnets of a classless address with the prefix /x? Example: Given the prefix /10, What is the the maximum number of subnets? How do I determine this?

cajalat

The whole idea behind classless is that you are no longer bound by the traditional A, B, C class networks. So if are asking how many subnets can I have for a traditional class A, B, or C networks using a slash notation then you basically subtract the number of bits normally reserved for the network from the number of bits that you designate for the hosts to get the max subnets. You subtract what you reserved for a mask from 32 to get the max hosts. e.g:

Class A: 120.0.0.0 Network
The natural network mask is 255.0.0.0 (i.e. not subnetted)
can be designated as 120.0.0.0/8

Now lets say you want 120.0.0.0/10

You subtract 10-8 = 2 bits for the subnets and 32-10 = 22 for the hosts.
2 bits give a maximum of 4 subnets and 22 bits give you maximum of 4104304 (of which two would be unusable as hosts).

Here is another example with a Class B:

Class B: 128.0.0.0
Natural mask: 255.255.0.0
Slash notation: 128.0.0.0/16

If we choose 128.0.0.0/20 as an example that gives us:

20-16 = 4 bits (used for subnets)
32-20 = 10 bits (used for hosts)

4 bits = 16 subnets
10 bits = 4096 hosts (of which 2 are not valid host addresses which gives 4094 usable hosts)

Hope that helps.