Order #1
network/netmask summary: 206.111.240.104/29 or equivalently 206.111.240.104/255.255.255.248
"Allocation: 206.111.240.104/29" tells us that this represents the following set of 8 IP addresses:
206.111.240.104
206.111.240.105
206.111.240.106
206.111.240.107
206.111.240.108
206.111.240.109
206.111.240.110
206.111.240.111
Of these, 2 are reserved and 6 are available for assignment to hosts (computers):
206.111.240.104 - reserved, functions as the address of the network itself
206.111.240.105
206.111.240.106
206.111.240.107
206.111.240.108
206.111.240.109
206.111.240.110
206.111.240.111 - reserved, functions as the "broadcast" address to
which all hosts in this network will respond in addition to their own address
Of the 6 host addresses, one is immediately consumed to be given to the ISP-supplied router as its address within our network. (This router has another "external" interface that connects it to the ISP premises, and it's through the router that our network becomes "internet connected." The address on the router's external interface is 209.220.201.74) Any of the 6 could be given to the router, in this case it happens to be 206.111.240.105. The router is a small device that, though it has no monitor nor keyboard, is a computer. It has built-in a CPU, memory, an operating system, some interfaces, a routing table, some (limited) software such as a telnet server and an ftp server. It is sometimes called a "DSL modem" but this is a misnomer since a modem has no CPU, memory, operating system, etc. Here is one example of a commercial router, and here is another.
206.111.240.104 - reserved, functions as the address of the network itself
206.111.240.105 - assigned to the ISP-supplied router
206.111.240.106
206.111.240.107
206.111.240.108
206.111.240.109
206.111.240.110
206.111.240.111 - reserved, functions as the "broadcast" address to
which all hosts in this network will respond in addition to their own address
"Allocation: 206.111.240.104/29" expresses a position and an extent, on an address number line. The position is represented by "104" and the extent by "29." The 29 defines the netmask. A netmask is a 32-bit binary number consisting of some number of 1s in the leftmost digit positions, followed by solid 0s thereafter in all rightward digits. "29" says that this netmask is
11111111 11111111 11111111 11111000
or 29 1s, followed by 3 0s. Alternatively this netmask can be converted to dot-quad notation and written:
255.255.255.248
Since with 3 digits 8 distinct values can be composed, the extent of this network is 8 addresses. The address of the network must be aligned on an address boundary that is a multiple of the network's extent, or size, which is 8. So the possible network addresses would be 0, 8, 16, 24, 32, 40, ..., 96, 100, 104, 108, ... , 240, 244, 248, 252. Because 104 is a multiple of 8, 206.111.240.104 is a valid address for our network.
Order #2
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 with 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 (for which order #1's ISP above used the term "router"). 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 64.52.25.226 (but could be any of the other 29).
64.52.25.224 - reserved, functions as the address of the 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
It's useful to think of these networks or subnets as being defined by a position, and an extent measured from that position, on the continuum of IP addresses represented as a number line. Of the parameters supplied by ISPs, it is the so-called network address that establishes the position or starting point of the address range or block. And it is the netmask that establishes its extent or size. In this case the network address is 64.52.25.224 and the netmask is 255.255.255.224 (coincidence that they both end with 224). The number line below is a microscopic segment of the number line for the whole internet. That number line is 4 billion addresses in length (because with 32 bits 4 billion is the number of distinct address values that can be composed). Here, with the first 24 bits of our address (64.52.25) we are narrowing in on a particular little 256-address segment within that number line. Within the segment, the network address further positions us with final precision. This idea of sectioning off the 4 billion addresses into separately addressable subordinate pieces is called subnetting, and the resulting pieces or address groups are called subnets.
