### There Are Only 10 People In The World –

Those Who Understand Binary And Those Who Don’t …

Did you get the joke? …. No? Don’t worry, you will by the end of this article. You’ll also be on your way to mastering the concept, and being in a position to explain binary numbers to kids in a way that makes sense to them. They will be astounded at your knowledge and very proud of their super cool mum and dad. You’ll be ready to *jump* into action when they bring home their binary homework for coding classes in the future. Go you!

## Covering the Bases

Binary numbers, or Base 2, is an alternate way of expressing numbers which has many applications in today’s technological society. For instance, the device upon which you are currently reading this post speaks, at its very core, a language in binary code. It’s true. And understanding binary can lift a lot of the mystery about computers because at a fundamental level they are really just machines for switching binary digits on an off.

### Decimal System

So before we can look at binary code, let’s first take a look at the counting system us mere mortals use, known as the decimal system or Base 10. In Base 10 we have ten different symbols at our disposal to represent numbers.

As you know, in different combinations the symbols can represent any number we can think of using something called “place value”. This gives us many uses for a mere ten symbols. Each column of numbers represents multiplication times the power of ten.

So for example, if we take a trip back to grade school and look at the number 876, we can see quickly that it’s made up of 8 sets of 100, 7 sets of 10s and 6 sets of 1s. Pretty simple right?

PLACES | 100’s place (10^{2}) |
10’s place (10^{1}) |
1’s place (10^{0}) |

DIGIT | 8 | 7 | 6 |

VALUE | 800 | 70 | 6 |

Adding up these value: 800 + 70 + 6 = 876 …. Yay!

Most of the world has been using the decimal system for a long long time. Why? There actually is not definitive reason but maybe it’s because we have ten fingers?

### Binary Numbers for Kids – The System Explained

So, getting back on track – the point of all that was to provide a context for how binary works. In binary, instead of using ten symbols and powers of 10 we use just two symbols and powers of 2. And we can still express big numbers using just two symbols!

Now, before we move on, I want you to think of the symbols for “one” and “zero”. Picture them in your mind. Got that? Now I want you to think of 1 as representing “on” and the 0 as representing “off”. This will assist you as we move on. I’m so excited! And a nerd…. But mostly excited!

Binary numbers use only the digits 1 and 0. Each “place” in the system represents a power of 2. The furthest digit to the right will be in the ones place, followed by the twos place to the right of it, then the fours place, eights place, and so on. Finally, if the digit is a 1 then we can say that this place is “on” and if the digit is a 0 then the place is “off”.

Let’s try this with some examples:

Binary Number: **101**

PLACES | 4’s place (2^{2}) |
2’s place (2^{1}) |
1’s place (2^{0}) |

DIGIT | 1 | 0 | 1 |

ON / OFF | on | off | on |

VALUE | 4 | 0 | 1 |

4 + 0 + 1 = 5

So, the binary number **101** is equal to **5**.

Binary Number: **1010**

PLACES | 8’s place (2^{3}) |
4’s place (2^{2}) |
2’s place (2^{1}) |
1’s place (2^{0}) |

DIGIT | 1 | 0 | 1 | 0 |

ON / OFF | on | off | on | off |

VALUE | 8 | 0 | 2 | 0 |

8 + 0 + 2 + 0 = 10

So, the binary number **1010** is equal to **10**

## Why use binary numbers?

It may strike you that these numbers can get very long very quickly. If it’s that inefficient then why do computers use it? Well, it’s how computers store and use information. The core of computers is just electronics after all. For any given pathway on a circuit board, you’ve got to admit, either a current is flowing or it’s not. Yes, no, on, off, one, zero – binary. So remember, binary numbers are the language of all electronics. Do you get the joke now? How many types of people are there again? …. 🙂

Do you know I’ve heard that joke so many times. I work in IT and hear it all the time. I always laugh along. It’s been on a few TV shows too and I’ve chuckled at how my Wife doesn’t get it but my being in It I do!

Being honest though …. I never really got it lol

I do now. Thanks for explaining.

Wait until we do an article on Octal, Steve. The jokes get worse!

So when you say 10, you really mean 2!?

Great article Dan. Loved the simplicity too. Makes perfect sense to me, now that you explained it properly.

You got it Francis! There’s another joke about numbers in Octal (another number system) but we won’t go there. That’s for another article. Thanks for the comment. So glad you found it useful.

Dan

So if Binary is 1 & 0, could I assume that Octal is based on 8’s or something like that.

I have heard that Basic isn’t very basic, if they even use Basic anymore. I never did computing at school- far too old!

This has to be my most favourite article that I have read.

Hey Francis! Yep, Octal is Base 8. Hoping to do an article on that soon!

Thanks for the refresher course. It is because we entrenched in the decimal system, this is foreign language. Much like having to learn the metric system. Unless you use the binary system long enough you are going to have to be updated.

Hi Maurice. As they say: practice makes perfect! 🙂

I love how you broke it down and made it so simple for people to understand. I had to go through multiple classes about IP address schemes and Binary, Hexadecimal, and Octal number systems, so I learned those pretty well. My favorite thing about binary is that the number that the 1s and 0s represent go doubled as the made their way to the left. For example: 256, 128, 64, 32, 16, 8, 4, 2, 1. I also like how using binary is so much easier when converting to hexadecimal, octal, or decimal as opposed to converting directly from one of those to the others. I bet you’ll touch on those a bit more later on when you cover those number systems though. 🙂

Hey Garrett, thanks for your great comment. I would like to maybe cover Hexadecimal at some stage soon. An understanding of Hex fits very nicely with appreciating color values in CSS etc… So lots in the pipeline! Watch this space!