The Internet is a public network, and therefore a device connected directly to the Internet has a public IP address. Those IP addresses must be administered by someone in such way that two devices connected to the public network don't use the same IP address or that two networks don't have the same network address. This job was done by InterNIC (Internet Network Information Center), which has been succeeded by IANA (Internet Assigned Numbers Authority). IANA makes sure to provide unique IP network addresses to Internet Service Providers (ISPs) and keeps track of their usage. Both IPv4 and IPv6 addresses are assigned in a delegated manner. Users are assigned IP addresses by ISPs. ISPs obtain allocations of IP addresses from a local Internet registry (LIR) or national Internet registry (NIR), or from their appropriate regional Internet Registry (RIR):

• AfriNIC (African Network Information Centre): Africa Region, http://www.afrinic.net

• APNIC (Asia Pacific Network Information Centre): Asia/Pacific Region, http://www.apnic.net

• ARIN (American Registry for Internet Numbers): North America Region, http://www.arin.net

• LACNIC (Regional Latin-American and Caribbean IP Address Registry): Latin America and some Caribbean Islands, http://www.lacnic.net

• RIPE NCC (Réseaux IP Européens): Europe, the Middle East, and Central Asia, http://www.ripe.net

A local area network connected to the Internet through a router doesn't always need public IP addresses for all the devices in that network. The devices will use local IP addresses, and when going outside the network, the router can do Network Address Translation (NAT), a process that translates the local IP address of the device into one IP address that is actually routed on the Internet to that router. NAT will be explained in greater detail later in this article.
NAT must be done by using private IP addresses that are not routed anywhere on the Internet. If we didn't have private IP addresses when using NAT, devices behind NAT could access any public IP address, except those within the same subnet as the ones used for the network behind NAT.

C IP address 217.207.125.0, which the router will translate into its own IP address whenever a device will access the Internet. This way, everything works fine, except one thing: no devices in the local network will be able to access, for example, www.packtpub.com, which has the IP address 217.207.125.58, because they will search for that IP address in the local network. In fact, no device in the local network will be able to access any devices in the Internet that have public addresses assigned by IANA within the class C network 217.207.125.0.
To address this problem, IANA has reserved several IP classes that can't be used in the public network, meaning that they will not be routed in the Internet. These IP classes are described by RFC 1918 as private IP addresses that should be used in private networks. They are:

By using these private IP addresses for local networks (intranets) connected to the Internet, the number of public IP addresses needed for devices accessing the public network decreases a lot. If a company has two local networks connected to the Internet in geographically distanced locations without a separate connection between those two networks, it doesn't have to use public IP addresses for the devices in each network. Instead, both networks can communicate by creating a virtual connection over the Internet, thus creating a VPN (Virtual Private Network), which will be discussed later in this article.

IP Subnetting

Subnetting is the process in which you break a network into smaller pieces. This can be done for a variety of reasons. For example, a company having department LANs use the same network part and the same mask for devices in all departments because they would not communicate with each other.
Using different IP network addresses for devices in different LANs within the same company is not recommended because of the large number of IP addresses that might be wasted in the process.
Subnetting is done by choosing an appropriate mask, called a subnet mask or NetMask to define the number of hosts in that network. The network address of a subnet can be a valid IP address from the subnetted network that devices will no longer be able to use. By subnetting, you lose some usable IP addresses (two for each subnet).

The Subnet Mask

The subnet mask is a 32 bit sequence of zeros and ones, just like the IP address. The subnet mask has all the bits in the network part of the IP address set to 1, and all the bits in the host part of the IP address set to 0. The subnet mask works like the network mask (it's basically the same thing), except that the subnet mask borrows some bits from the host part to identify the subnet.
Let's say the IP address 192.168.1.130 is in the class C network 192.168.1.0-255; so, it has the mask 255.255.255.0. The company has two different departments, and they are both in the same network, but it is required that they should be on different networks. When assigning IP addresses, the network administrator used to assign IP addresses ascending, starting with 192.168.1.1 to department A and descending starting from 192.168.1.254 to department B, and so decided to divide this class C network into two subnets, each containing 128 addresses. Those subnets will be 192.168.1.0-127 and 192.168.1.128-255.
Initially, we would have:

In order to break the class C network in two subnets, we need to borrow one bit from the host part of the IP address for the network part, so we will have the subnet mask:

The first bit in the last byte of the subnet mask is called a "borrowed bit". The logic is pretty simple and it's based on Boolean logic. A device with IP capabilities does a logical AND between the subnet mask and the IP address to find out the network this IP address belongs to.

the following operation:

This way it finds out that the IP address 192.168.1.130 having the subnet mask 255.255.255.128 is in the subnet 192.168.1.128.
For 192.168.1.1 having the subnet mask 255.255.255.128, the logical AND will be:

So the address is in the subnet 192.168.1.0.
By performing a logical AND of all IP addresses in the 192.168.1.0-255 class C with the subnet mask 255.255.255.128, the results can only be 192.168.1.0 or 192.168.1.128. This way, we divide the class C network in two.
Before dividing the class C network, we had the broadcast address 192.168.1.255. Now, the last IP address from every subnet becomes the broadcast address for that subnet. The first subnet will have 192.168.1.127 as a broadcast address, and the second will have 192.168.1.255 as a broadcast address. By dividing this class C in two, we lost two possible host IP addresses—192.168.1.127 (first subnet's broadcast) and 192.168.1.128 (second subnet's network).

Everything Divided in Two

If we need four subnets in that class C network, we do the same thing to the 255.255.255.128 subnet mask. This means we will borrow one bit from the host part of the IP address and add it to the subnet mask, and so we will be borrowing two bits from the class C mask:

By performing a logical AND with any IP address starting with 192.168.1, we will have four possible values for the last byte:

So we have created four subnets: 192.168.1.0, 192.168.1.64, 192.168.1.128, and 192.168.1.192.
We can divide those subnets in another two subnets, and so on.
The rule with the first and the last address of the subnet as being reserved still applies here; so, the first IP address in the subnet is the network address (to identify the subnet) and the last possible address in a subnet is used for broadcast. For the example we just saw, we have:

If the class C 192.168.1.0-255 network is subneted as in the example, the host having the IP address 192.168.1.71 and the subnet mask 255.255.255.192 will send the broadcasts to the IP address 192.168.1.127, and only the devices having IP addresses in the same subnet will receive those broadcasts.

For a class C network, the valid subnets are:

The smallest number of usable IP addresses in a subnet is two, given by the subnet mask 255.255.255.252, which has four IP addresses in that network (one for network, one for broadcast, and two usable IP addresses).

A Different Approach

Thinking in binary is not always that simple, but that is the process that devices using IP communication use to calculate things. A simple logic in decimal would be like this:
A class C network has 256 IP addresses (from 0 to 255). I need to create four subnets in that class C, and so, each subnet will have (256 / 4 =) 64 IP addresses (only 62 usable for devices). The last byte (in decimal) for the subnet mask will be (256 – 64 =) 192, and so, I get the subnet mask 255.255.255.192, and subnets 192.168.1.0, 192.168.1.64, 192.168.1.128, and 192.168.1.255.
The trick for subneting class C networks is to subtract the number of hosts that you want in that subnet from 256 and you get the subnet mask. Please remember that the number of hosts in that subnet must be a power of 2. For 16 addresses in a subnet, you will use the subnet mask 255.255.255.240 (256 – 16 = 240).
To subnet a class B network, if you don't want to use the binary logic, you can still use this procedure by working on the third byte of the subnet mask. For example, a full class B network has 256 * 256 IP addresses. If I want to use 16 * 256 IP addresses in a subnet, I will use for the third byte of the subnet mask the value 256 – 16 = 240, so I will have a subnet mask of 255.255.240.0.