The way that CIDR conserves IP address space is by eliminating the need for classful networks for every subnet. What used to be a class A network (i.e. 32.0.0.0/8) can be broken up and assigned to various entities (i.e. 32.0.1.0/24 to one company and 32.0.2.0/24 to another). Also, subnets which require less than the number of hosts given by a classful boundary can be assigned a subnet in line with the number of hosts required. For example, company A has an address space of 32.0.1.0/24 assigned to them. If they have multiple serial links, they can assign 32.0.1.0/30 to one, 32.0.1.4/30 to another, and still use 32.0.1.128/25 for a LAN segment which requires up to 126 hosts. Previous to CIDR, this would have required 3 classful networks. If using class A address space, this would have used up 16,777,216 addresses, instead of the 136 used in this example, with the possibility to use the rest of the /24 for other subnets.
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