Notational Systems | CompTIA IT Fundamentals FC0-U61 | 1.1

In this video you will learn about various notational systems such as binary, hexadecimal, decimal in addition to learning about how data representation such as ASCII & Unicode.


In mathematics and digital electronics, a binary number is a number expressed in the base-2 numeral system or simply referred to as the binary numeral system.  This system uses only two symbols: typically 0 & 1. This number system is the basis for all binary code, which is used to write data such as the computer processor instructions used every data.

Decimal Values from 0 to 15 & Their Binary Equivalents

How Does Binary Work?

The 0s and 1s in binary represent OFF or ON respectively, meaning either there is no flow of electricity moving (0) or there is a flow of electricity moving (1).  The flow or restriction of flow of this electricity moves through a component known as a transistor, which is the primary building block of all microchips. Depending upon the arrangement of transistors, logic gates are created which essentially tell a computer to either pass a current of electricity (1) or restrict a current of electricity (2) in order to process basic computing instructions.

What is Base 10?

To truly understand how binary numbers work, we must first discuss a numbering system known as Base 10.  If you’ve ever used your fingers to add numbers or count items, then you are already familiar with the concept of the base 10 numbering system.  Basically numbers 0-9 is the base 10 numbering system, too include the use of decimal numbers.

Powers of Two

By definition, in mathematics, a power of two is a number of the form 2n where n is an integer, the result of exponentiation with number two as the base and integer n as the exponent. In layman’s terms, powers of two is simply the mathematical doubling of numbers starting with the base number 2.

Decimal 2 to 1024 in Binary & Power of Two


By definition, in mathematics & computing, hexadecimal (also known as base 16 or hex) is a positional system that represents numbers using a base of 16.  Base 16 notation uses the following digits: 0-9 (which are equivalent to values 0-9 in decimal notation) and A-F (which are equivalent to values 10-15 in decimal notation), for a total of 16 digits. Every hex digit is the equivalent of four bits (also known as a nibble) in binary notation. Hexadecimal is used quite commonly in the computing world such as expressing color values in Hypertext Markup Language (HTML) to how internet addresses using IPv6 protocol to Media Access Control addresses, also known as MAC addresses that are used for devices that connect to a network, like your smartphone and laptop.

Decimal Values from 0 to 15 & Their Hexadecimal Equivalents
Decimal 2 to 1024 in Binary & Hexadecimal

Hexadecimal Color Values

When you are looking at your computer monitor, television screen or smartphone screen, you are looking at a spectrum of colors being represented by the mix of what is called RGB (red, green, blue)…primary colors.  For example, the hexadecimal color code for red is #FF0000, which means, a maximum of the color red is displayed, while no green and no blue is displayed. For the color blue, the color code is #0000FF. White is #FFFFFF, which means when all of the colors of light are mixed together, the result is white.  Black is #000000 which means the values representing red, green and blue are turned off. If you want a secondary color like orange (a mix of red and green), the color code would be #FFA500.

IPv4 & IPv6 Addresses

If you are trying to get access to a certain website, most of you are familiar with just typing in the name of the website like  What most of you are probably unfamiliar with is that the name is directly tied to numbering system used to help locate that website.  The numbering system is called an IP address or an internet protocol address. IP addresses come in two different protocols. The first protocol is called IPv4 which looks something like  That IP address is then compared with a name in what is called a DNS server which essentially simplifies the process for the end user of having to memorize a bunch of numbers as opposed to simply remembering a name like The reason we have two different IP protocols is because we have essentially ran out of IPv4 addresses.  There are about 4.3 billion IPv4 addresses in the entire world, but there are more than 4.3 billion networked devices and websites in the entire world that need an IP address to take part in the greater concept called the world wide web. So that’s where IPv6 comes into play.

IPv6 is the most recent version of the Internet Protocol (IP) that provides an identification and location system for computers on networks and routes traffic across the internet. Compared to the 4.3 billion IPv4 addresses in the world, IPv6 can offer up approximately 340 undecillion addresses, or 340 billion billion billion billion addresses, or 3.4×1038 addresses.  Now some of you may be wondering was there and IPv5 and if so, why did we skip it.  Well, there was an IPv5 which was essentially the precursor to wonderful world of streaming that we all enjoy so much.  The problem with IPv5 is that is used IPv4 addressing, which I discussed earlier that there simply was not enough IP addresses to go around to cover all of the devices we use to enjoy the connectivity of the internet.  So IPv6 became the new standard.

An IPv6 address is 128 bits long, comprising of eight 16-bit sections.

IPv6 Address (Binary)
Hexadecimal (Default) Representation of the IPv6 Address


As mentioned earlier, the most common numbering system used in everyday life is that of base 10.  Base 10 also encompasses the the decimal system as well. We use the decimal system every time we count money or spare change in our pocket, every time we discuss the percentage of some concept and even when we view the size of a storage device such as a hard drive.  If want to see the capacity of a hard drive, normally the capacity will be displayed in the measurements of bytes (decimal notation), such as:

Capacities for Hard Drive Given in Bytes (Decimal) & Binary GB in Window’s Drive Property Sheet

Data Representation

When it comes to data, data can be stored, transmitted and also displayed.  The text that you are currently looking at on your screen is numeric codes that are mapped to characters to make them understandable.  There are two broad categories of character sets that have been used in computer storage: ASCII & Unicode.


ASCII stands for American Standard Code for Information Interchange.  ASCII is a 7-bit character set that includes 128 characters, of which 97 are printable.  These characters include the upper & lowercase English alphabet, numbers 0-9, and punctuation marks.


In order to display copyright, trademark, currency and mathematical symbols, in addition to foreign-language accents, the ASCII was extended to 255 characters.  The extension is known as ANSI (American National Standards Institute).

Sample of Extended ASCII Characters

Code Pages

An issue that standard & extended ASCII characters present is that they cannot display characters used by languages that do not use the Latin alphabet (A-Z).  To solve this problem for operating systems to work with non-Latin alphabets or Latin alphabets that use accents, vendors produced code pages which are language-specific collections of characters mapped to codes.  To explain in another way, when you are loading up an operating system on your computer and it asks you to select a region and language, based on the response you enter, the operating system will select the correct code page for your region and language.


ASCII & ASCII extended have been replaced with a print and display language known as unicode.  Unicode supports ASCII, extended ASCII, both Latin & non-Latin alphabets and special characters.  Unicode supports up to 576 printable and displayable font characters.

Sample Unicode