Hexadecimal

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Lesson Objectives

Hexadecimal numbers and their representation
How to convert binary and denary numbers to their hexadecimal equivalents and vice versa
What are the applications of the hexadecimal number system?

Introduction

Hexadecimal (or hex) is a system with base 16.
The 16 digits used in the hexadecimal system and their equivalent value in binary and in denary systems are shown in the table.
Hexadecimal (or hex) is a system with base 16.
The 16 digits used in the hexadecimal system and their equivalent value in binary and in denary systems are shown in the table.

Hexadecimal system

Each nibble (a group of 4 bits) can be represented with 1 digit in a hexadecimal system.
It is very convenient to write numbers in hex compared to a binary system.
It is helpful for programmers coding in low-level languages. Instead of 4 bits, it is enough if they type a single character.
The memory location in a computer is also stated in hexadecimal form. This makes the address more readable.
Consider a memory address A3F581. If represented in binary, it would be:
1010| 0011| 1111| 0101| 0100| 0001

Converting binary to hexadecimal: Step 1

Starting from right to left, the binary numbers are split into a group of 4 bits.

Converting binary to hexadecimal: Step 2

Converting binary to hexadecimal: Step 3

Converting hexadecimal to binary

Converting denary to hexadecimal: Step 1

To convert a denary number to hexadecimal, the number is first converted to binary.

Converting denary to hexadecimal: Steps 2 & 3

To convert a denary number to hexadecimal, the number is first converted to binary.
The binary number is converted to a hexadecimal system.
Ex: Converting the number 14 to hex. The binary form is 1110, which is E in the hexadecimal system.

Converting hexadecimal to denary

Hexadecimal numbers can be converted to the denary system by using place values.
The place value is in the powers of 16.
The value of each digit is multiplied by the place value, and the values are added to find the denary equivalent.

Applications of the hexadecimal system

Colors

Hexadecimal numbers are used to represent colors in various software tools.
A color is represented in #RRGGBB format. RR, GG, and BB represent the hex number of red, green, and blue colors.
A pure blue colour is #0000FF, white is #FFFFFFF and black is #0000000.
Using this method, 256 variants of each color can be made, hence making a total of 256 reds × 256 greens × 256 blues.
A shade of yellow is represented in hex format as #FEF65B.

RGB Colour Model

Colors can also be represented using the RGB color model.
This system is similar to hex system, but each color has a value between 0 to 255.
Hence, a shade of pink represented in hex format as #FEF65B has an R-value of 254, a G-value of 246, and a B-value of 91.

Errors

The error message contains a hex number that represents the memory location of the error.
This information is very useful to programmers.
The error can be easily rectified by verifying the code in that particular location.
The process in which the contents of memory are displayed or stored in a storage drive in case of a system crash is called a memory dump.
Using this information, a programmer can identify the exact location where the error lies.
Compared to binary, this is easier to understand. The binary form of DEF6B2C3 is: 11011110111101101011001011000011.
Even though using the hexadecimal system improves the readability of errors, the programmer must have knowledge about the computer architecture to interpret the results.

Mac Addresses

A media access control address refers to the number on the Internet that uniquely identifies a device on the Internet.
This is the address of the network interface card (NIC).
A MAC address is made up of 48 bits, which are shown as a six-group of hexadecimal digits.

NN-NN-NN-DD-DD-DD or NN: NN: NN: DD: DD: DD

The first half of the address represents the identification number of the manufacturer and the second half of the number represents the serial number of the device. For example: 00: 14: 22: 34: AC: 4F refers to a device made by Dell with a serial number of 34AC4F.

URL

Hexadecimal values are used to represent web addresses or URL (Uniform Resource Locator). The ASCII codes are used to represent the web address.
For example: www.google.com becomes: (using the ASCII codes)
% denotes that hexadecimal values are used.
Hexadecimal values are used to represent addresses of files and web pages to improve security.
A user is protected from accessing a fake website when he is asked to use a hexadecimal URL rather than a URL with letters that could be misleading.

Assembly code and machine code

Machine code and assembly code can be used to refer to the computer memory directly.
Use of hexadecimal numbers makes low-level language coding easier, faster and reduces errors when compared to the binary system.
For example: An assembly code instruction ADD is translated to machine code as 0100, which is equivalent to 4 in hexadecimal. It is enough for the programmer to type a single digit ‘4’ when compared to four digits ‘0100’.

Hypertext Markup language (HTML)

HTML is a markup language widely used in developing web pages.
It is used to define the attributes of a text, such as color. Tags are used to define objects on a web page.
For example: The tag <p> is used to define a paragraph. The tag </p> represents its end. The contents between the two are codes.
Color codes are also used in HTML to define objects.
For example:
<p style="color:#FF8000;">Welcome to my website.</p>
The color code FF8000 represents the orange color. The paragraph looks like this:
Welcome to my website.

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