Hello! Do you recognise the kind of switch in the image on the right?

Have you ever wondered why there is a line and a circle on this switch?

How about that power symbol on the far right, do you recognise that?

When you think about it, that's another line and a circle, but this time the line is inside the circle. So why are we using these symbols for on and off?

That is where binary comes in.

Binary is a way of counting, only using the numbers Zero and One.

The number One is sometimes referred to as representing "On", and that is why it is used on power switches.

The number Zero is sometimes referred to as representing "Off", and that is why it is also used on power switches.

In binary, we only use Zeroes and Ones.

To fully appreciate how Binary works, we should first remind ourselves of the numbers we are used to - Denary. Denary is the "Official" word for our number system, where everything is based on the number 10. Once our "units" column gets to 9, we add one to the "tens" column and reset the units back to zero.

You can see in the example on the right, each column is 10 times larger than the previous one. (If you think of the units column as being the "ones" column, which it is)

In Denary, everything is based on the number 10. Our columns go up getting ten times bigger each time and we have 10 numbers to count with: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Using these 10 numbers and the column system shown on the right, we can create numbers that are very tiny or numbers that are massive.

Look at the example on the left. We have columns just like we do in Denary, however, these columns are only two times bigger than their previous column, rather than ten times like we had in Denary.

We also only have two numbers available to us: 0 and 1. The prefix "bi" means two, and so in Binary, we should expect everything to be based on the number two.

To work out what the number 10100 is (in the image on the left), we simply look at the columns that have a 1 in it. If it has a 1 in it, we add the value of that column to our total. Our total will start at zero obviously, and we will add to it.

Remember, it is not the 1s we are adding, but the value of the columns. The two columns that have 1s in them are the 32s column and the 8s column. And so we add together 32 and 8 to get our answer.

So 101000 in Binary is the same number as 40 in Denary.

Watch this video where I explain binary using Redstone lamps in Minecraft, and complete the accompanying document, pausing at each time stamp to answer each question.

You should have this Document posted to Google classroom if you are a student of mine. Otherwise, you can take your own copy of the document below.