What are Binary and Hexadecimal Number Systems?

What Are Binary Numbers?

A binary number is part of a numeral system expressed only with 0s and 1s. Importantly, this is the basis for all binary code — the language in which computer hardware communicates with another piece of hardware.

Basics of Binary Numbers

Firstly, before I start talking about a good old computer networking conversation, let’s start by introducing some of the basics of binary calculations. As kids, we all learn how to use the decimal system. My daughter is 3 years old and already learning to count to 10. This is easy because most of us have 10 fingers so we don’t have to count off the top of our head.

Computers, networking devices, and machines use the binary system because of its simplicity of using only 1s and 0s. For a machine using electrical signals, it’s easier to communicate using only two states: 1 for On and 0 for Off.

All calculations in a computer are based on millions of transistors that are either in an ON or OFF position. In binary, the numbers 0s and 1s do not simply mean that the computer is on or off. To clarify, these ON and OFF signals can be interpreted by devices to achieve a broad range of results.

To understand how a computer network works, you need to learn how to convert numbers between decimal, binary, and hexadecimal. This is useful when learning about IP addresses and subnetting.

How to convert decimal numbers to binary?

Firstly, let’s do a recap. To clarify, binary is a numerical notation system that uses 0s and 1s. Most often, numbers are represented by the Decimal system, which is base 10.

• Decimal: (deci)mal → (deci) meaning 10. → 10
• Binary: (bi)nary → (bi) meaning 2. → 12

In the decimal system, there are ten unique numbers from 0 to 9. In the binary system, there are only two unique numbers: 0 and 1. Each number is commonly known as a bit.

If you are preparing for a CCNA or Network+ exam you will need to learn how to convert an IP Address into a binary number. Let’s look at the following example. Use the table below to convert from a decimal to a binary number or vice versa.

Basic Decimal to Binary Conversion Table

Ex. If we want to convert the binary number 10100110 into a decimal form.

Plug the numbers from right to left and add the decimal number shown in the same column. Each column represents the number two raised to an exponent, and that exponent’s value increases by one as you move through each of the eight positions.

To clarify, read the table from right to left. In addition, add each column’s value from the decimal row to the value on the previous column: (128+32+4+2) = 166. As you can see, we do not count the bits with a 0 because they’re “turned off.”

In the real world, you can use a calculator to do this conversion.

How to Convert an IPv4 Address into Binary

Let’s start by understanding what an IPv4 address is. IPv4 is a 32-bit number that uniquely identifies a network interface on a machine. That is to say, an IPv4 address is typically written in decimal digits, formatted as four 8-bit long octets or segments separated by periods. In addition, every octet must be a decimal value between 0 and 255.

For example, I will be using the Decimal to Binary Conversion Table to convert the following IPv4 addresses into their binary form.

Ex.1
192.168.0.12
11000000.10101000.00000000.00001100

Ex.2
172.16.0.5
10101100.00010000.00000000.00000101

Ex.3
10.0.1.11
00001010.00000000.00000001.00001011

Introduction to IPv6 Address

Now that you understand the binary system let’s move into the hexadecimal system. This numerical system has become a very important element of the computer world as a result of the rapid increase of network-connected devices. Therefore, the necessity to maintain unique identifiers forced the industry to include hexadecimal numbers. This new address system is called IPv6.

First, let’s begin by introducing the hexadecimal number system. This numerical system is also known as hex or the base-16 number system. It consists of 16 alphanumeric characters that include a range of numbers from 0 to 9 and a set of letters from A to F.

An IPv6 address format consists of eight groups or segments of hexadecimal values separated by colons. In addition, the first 64 bits of the IPv6 address are used for routing purposes. It consists of the routing prefix and subnet ID.

The last 64 bits identify the address of the interface or interface ID. In other words, it is derived from the physical or MAC address using IEEE’s Extended Unique Identifier (EUI-64) format.

Convert an IPv6 Address into Decimal or Binary

Similar to IPv4 addresses, you can convert an IPv6 address into the binary system. The following example will help you simplify the process.

For example, given below is a 128 bit IPv6 address represented in binary format and divided into eight 16-bit blocks:

0010000000000001 0000000000000000 0011001000111000 1101111111100001 0000000001100011 0000000000000000 0000000000000000 1111111011111011

Each block is then converted into hexadecimal and separated by a : symbol:

2001:0000:3238:DFE1:0063:0000:0000:FEFB

Even after converting into hexadecimal format, the IPv6 address remains long. IPv6 provides some rules to shorten the address.

How to Simplify or Compress an IPv6 Address

In addition to an increase in the supply of IP addresses, IPv6 also addressed some of IPv4’s weaknesses. However, this longer type of IP address increases the difficulty for the network engineer to remember addresses.

Consequently, a simplifying trick called IPv6 address compression is applied to help network engineers remember these types of IP addresses, making it easier to read by the human eye.

IPv6 Address Compression Rules

The Bottom Line

In conclusion, the conversion between binary, decimal, and hexadecimal numbers is the backbone of computer networking. This is the main reason IT professional certifications include these types of questions in their exams.