Numbering Systems
All numbering systems work the same way.

Using the decimal system (Base-10), all numbers are represented by powers of 10, using 0 – 9. To obtain the value 1024, you take 1000 + 20 + 4, which may also be expressed as:  (1*10^3) + (0*10^2) + (2*10^1) + (4*10^0).
 

The binary system (Base-2), allows the use of only two numbers, 0 and 1. A single 0 or 1 in binary is called a bit (binary digit), and groups of bits create binary numbers. The binary number 1101 is expressed as (1*2^3) + (1*2^2) + (0*2^1) + (1*2^0). 

Since computers use binary (often groups of 8-bits, called a byte), it’s often necessary to convert between binary and decimal. To determine the decimal equivalent of the former expression, one must merely add the placeholders together: 8 + 4 + 0 + 1 = 13.

Networks and Subnets
Most networks today are based upon TCP/IP. Such networks, of which the Internet is a prime example, identify individual devices on the network (hosts) using an IP address. This address consists of four numbers, separated by periods. The format is x.x.x.x, where x can be any number between 0 and 255. A typical IP address might appear as 192.168.1.1.

But we said computers use binary! 

The decimal numbers of the IP address must be converted. Knowing that 255 is the highest possible value for any particular number in the address, it is possible to determine that these numbers can be represented with 8 bits. Each 8-bit representation is called an octet. For example, the decimal number 255 equals the binary number 11111111.

Easy conversions can be made using the following table:
 

Base-2	2^7	2^6	2^5	2^4	2^3	2^2	2^1	2^0
Base-10	128	64	32	16	8	4	2	1
Binary	1	1	1	1	1	1	1	1

Using 8-bits, one can determine that the binary number 11111111 equals 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 or the decimal number 255.

Thus, the IP address 192.168.1.1 equals 11000000.10101000.00000001.00000001.

In TCP/IP, addresses consist of two parts: the first portion represents the network, and the second portion defines the actual host. Think of IP addresses as street addresses—with the network portion identifying which street you live on and the host portion identifying which specific house you live in on that street. To determine the network and host portions of the address, a subnet mask is employed. Subnet masks allow the computer to “mask” portions of the IP address based upon bit usage.

Many are accustomed to defining networks based upon class, as defined in the TCP/IP standards. The following chart illustrates some of the defined classes, and their default subnet masks.
 

Class A networks are identified by the first octet, Class B networks by the second octet, and Class C by the third. Following our example, one can determine that 192.168.1.1 is Class C, with the default subnet mask of 255.255.255.0. This mask is represented in binary as 11111111.11111111.11111111.00000000. The network portion thus becomes 192.168.1, with the host being represented by the final octet.
 

In TCP/IP networking, the first IP address of a network is required to represent that particular network (or street) and the final IP address is required to represent a broadcast (or a message sent to every house on the street). This means that 192.168.1.0 is our sample network address and 192.168.1.255 is our sample broadcast address. That leaves us with 192.168.1.1 – 254 to assign to hosts on the network, for a total of 253 possible nodes. These are the defining numbers for individual devices on the network that can interact with each other locally.

One can easily see situations where assigning networks by class can cause problems. There are only a finite number of IP addresses available. If a network is assigned more hosts than it needs, the unused IP addresses are wasted. And what can you do if you’re assigned a single Class C range of addresses, but need to create separated networks? This is when you need subnets.

Creating subnets requires you to alter the default subnet mask by masking additional bits. To do this, one must determine the required number of networks, the number of hosts, and which IP address ranges belong to a particular network. These answers are obtained using some simple formulas. To determine the number of possible networks: take 2^x, where x is the number of 1-bits in the subnet mask. To determine the number of possible hosts: take 2^x – 2, where x is the number of 0-bits in the subnet mask. You must subtract 2 when figuring the possible number of hosts, since the first possible address is reserved for the network and the last address is reserved for the broadcast. Your IP address range is thus defined by the remaining possible host numbers.

Let’s say that a network designer decided that she needed to create 8 separate networks (subnets) using a single Class C network of 192.168.1.0. To increase the number of networks available, she must borrow additional bits from the last octet in the subnet mask. Using the formulas above, 2^3 = 8. She needs 3 more 1’s. Enter those three 1’s into the table:
 

128	64	32	16	8	4	2	1
1	1	1	0	0	0	0	0

The decimal value of the binary created here is 128 + 64 + 32 or 224. The appropriate subnet mask to create these 8 networks is 255.255.255.224. This can also be represented as 192.168.1.0/27.

She can now use the table above to determine the maximum number of hosts that will be available to her: 2^5 – 2 = 32 – 2 = 30 hosts.

So, how can you use this information?

Common scenarios involve being confronted with an IP address and a subnet mask, and being asked to determine what other IP addresses exist on the same network. As many of my students so often hear when preparing for certification, “You may see this again!”
Using the table above, you can create another simple table to guide you in defining the starting and ending points of the subnets. Take the decimal value represented by the final 1 of the subnet mask, and use this as a step value—adding it all the way down the first column of the following table.
 

Using 192.168.1.0/27 as our example, the range of 192.168.1.1-30 comprises the usable host IP’s for that network, with 192.168.1.31 as the broadcast. It would then logically follow that you could answer the following question:

Given a host address of 192.168.1.165/27, are the following IP addresses on the same network:

Hopefully, this has made the art of creating and determining subnets a little more understandable. With the use of simple formulas and tables which can be created on the fly, it really doesn’t have to be that complicated. There is no need to fear the subnet. They are, after all, there for your safety!