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Understanding Binary: The Basics of the Binary Number System

Binary is a base-2 number system (also called the binary numeral system), which means it has two digits. The digits in a binary number are 0 and 1, represented by the absence or presence of voltage on electric circuits. 

Binary can be used to represent any integer value from 0 to 255, which is enough for most computer applications.

As you might expect, binary numbers are really simple: they're made up of only 1s and 0s (0 volts = OFF; 5 volts = ON). This may seem limited at first—how many things can you think of that have only two possible states? 

But if you look around at all the "off" switches in your life—things like light switches, alarm clocks and radios—you'll realize that there's actually quite a lot going on here!

Binary numbers have been around since long before computers were invented: they were originally developed by mathematicians in India during the 9th century CE who wanted an efficient way to count money (that's right; even back then our ancestors knew how important it was).

The Octal Number System

The octal number system is a base-8 number system that uses the first 7 letters of the alphabet (0 to 7), as opposed to decimal 10 or binary 2. Unlike decimal and binary, which are positional number systems, octal numbers represent digits using place-value: ones, twos, threes, fours, fives and sixes. 

Because it only has eight digits and there are no negative values in an octal system — unlike decimal or binary — it is not suitable for representing fractional values or negative numbers.

Octal numbering was developed by Carl Friedrich Gauss around 1796 for his calculations with complex numbers (complex numbers are made up of real and imaginary components). 

Today octal is used primarily in programming languages such as Perl and Java; alternatively it can be useful when working with hexadecimal data since they have many similarities.

Other 2 Popular Number Systems

There are other popular number systems that you should know about as well.

The hexadecimal (or base-16) system uses the digits 0 through 9 and the letters A through F to represent numbers. This is used in computer programming because it allows for easy representation of letters, which are easier to understand than binary values!

The duodecimal (or base-12) system uses the digits 0 through 9 and the letters A and B to represent numbers. 

In this case, 12 is used instead of 10 for two reasons: 

1) because it's easier to divide by 2 than 10; 

2) because it was more common historically - before decimal became dominant worldwide during the 19th century. 

Most modern calculators can only do up to 10 digits at once so they'll round up any extra amount after hitting 8 or 9 digits! 

This can cause problems when calculating taxes or checking your account balance online if you're not careful with how many decimal places are needed in order for each calculation...

Plus: Why Math is the Most Fascinating and Coolest Subject Ever?

Math is the language of science. It helps us make sense of the world and helps us solve problems in everyday life. 

If you're not good at math, then it can seem boring or difficult—but there are lots of reasons why math should be thought of as cool.

Why Math Is Cool:

  • Math will always be relevant. In today's society, where everything revolves around technology and computers, knowing how to do basic calculations will help you understand what a computer is doing when it comes to things like saving money on your phone bill or filling out an online application for college courses. 
  • Plus: having access to calculators means that most people don't have to know how to do complex equations anymore (or at least until they're in their thirties).
  • People who are good at math earn more than people who aren't. Statistically speaking, people with higher education levels also tend to earn higher salaries; having mathematical skills can therefore help anyone get ahead financially through work experience alone!

Last Words

Before we close this article, let’s take a moment to remember what we learned: the binary number system is extremely useful in computing and other fields. It is also very easy to understand once you get some basic knowledge of it. 

And finally, there are many other ways besides octal to represent numbers in base 8. 

Hopefully after reading this article, you have a better understanding of how all these number systems work!

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