### Analysis of a commercial DSL Order - subnetting

network/netmask summary: 64.52.25.224/27 or equivalently 64.52.25.224/255.255.255.224

"Range  .226-.254" suggests that (with adjustments) the size of this network is 32 addresses. That corresponds to a netmask with 5 rightmost 0 digits from which to compose host addresses (since from 5 digits 32 distinct values can be composed). The netmask is therefore:

11111111 11111111 11111111 11100000, or 255.255.255.224

One of the addresses will be reserved for the ISP-supplied gateway. Since the Gateway address given is 64.52.25.225, we know that the first 3 dot-quad values for all our network's addresses must be 64.52.25.

The address of the network (here called "subnet") must be aligned on an address boundary that is a multiple of the network's extent, or size, which is 32. So the possible 4th dot-quad elements of the network addresses would be 0, 32, 64, 96, 128, 160, 192, 224. Among these, "Subnet:  .224" is our clue that our network (i.e., the first of its addresses) lies at 224, or more precisely at 64.52.25.224. (It is coincidence that the measure of the network's extent, 255.255.255.224, also happens to contain "224")

64.52.25.224
64.52.25.225
64.52.25.226
64.52.25.227
64.52.25.228
64.52.25.229
64.52.25.230
64.52.25.231
64.52.25.232
64.52.25.233
64.52.25.234
64.52.25.235
64.52.25.236
64.52.25.237
64.52.25.238
64.52.25.239
64.52.25.240
64.52.25.241
64.52.25.242
64.52.25.243
64.52.25.244
64.52.25.245
64.52.25.246
64.52.25.247
64.52.25.248
64.52.25.249
64.52.25.250
64.52.25.251
64.52.25.252
64.52.25.253
64.52.25.254
64.52.25.255

Of these, 2 are reserved and 30 are available for assignment to hosts (computers). And of the 30, one is taken by the "Gateway." That one happens to be 64.52.25.225 (but could be any of the other 29).

64.52.25.224 - reserved, functions as the address of this network itself
64.52.25.225 - assigned to the ISP-supplied Gateway
64.52.25.226
64.52.25.227
64.52.25.228
64.52.25.229
64.52.25.230
64.52.25.231
64.52.25.232
64.52.25.233
64.52.25.234
64.52.25.235
64.52.25.236
64.52.25.237
64.52.25.238
64.52.25.239
64.52.25.240
64.52.25.241
64.52.25.242
64.52.25.243
64.52.25.244
64.52.25.245
64.52.25.246
64.52.25.247
64.52.25.248
64.52.25.249
64.52.25.250
64.52.25.251
64.52.25.252
64.52.25.253
64.52.25.254
64.52.25.255 - reserved, functions as the "broadcast" address to which all hosts in this network will respond in addition to their own address