An introduction to Binary

Binary is the language used by computers. It uses 0 and 1 to represent different numbers.

In the everyday number system we use 0 – 9 to show numbers.

H T U 5 6 9

If a number has two whole numbers to its right we know that it has a ‘hundreds’ value. In this example the ‘5’ actually represents 500.

This number system is known as ‘Base 10’. Each position to the left is worth 10x more than the place to the right: H T U 100 10 1 x10 x10

Binary uses ‘Base 2’. Each position to the left is worth 2x more than the place to the right: 16 8 4 2 1 x2 x2 x2 x2

Of course you don’t have to write in 1,2,4 etc. You just remember them like you remember HTU.

How do I write numbers in binary, Binary-Bot?

To write numbers in Binary you only have to be able to add.

For example:

If I wanted to write 9 as a Binary number I have to see which columns I can use to get to 9 16 8 4 2 1 1 0 0 1

I would put a 1 in the place that has the value of ‘8’, zeroes in the ‘4’ and ‘2’ columns and a 1 in the ‘1’ column. (1 x 8) and (1 x 1) gives me 9

But couldn’t I get to 9 like this, Binary-Bot? 16 8 4 2 1 4 1

Or like this? 16 8 4 2 1 1 2 1

(1 x 4) and (2x2) and (1x1) will give me a 9!

No! Binary only uses 1s and 0s.

Here are some more examples: 32 16 8 4 2 1 1 0 1 0 = 10 1 0 0 1 0 = 18 1 0 0 0 0 1 = 33

Ah! I see now!

1 0 1 11 0 0 0 1

1 0 1 1 01 0

1 1 1 1 1 11 0 1 0 1 0

1 0 1 1 1

Can you tell straight away which numbers will be odd?

Try working out these numbersHere are the answers

11

17

22 2

6342

23

You can easily count from 1 – 10 using the base 10 system – but could you do this in Binary?

Here are the first three numbers to get you started:

0 0 0 0 1 1

Yes! I just need to ‘add’ another column to the left. 64 32 16 8 4 2 1 1 1 1 1 1 0 1

This would give me 125!

Consider this:

In the everyday way of writing numbers 125 is equal to one 100, two 10s and five 1s.

In the Binary system 1111101 is equal to one 64, one 32, one 16, one 8, one 4 and one 1.

Can you make numbers over 100 in

Binary?

That was

An introduction to Binary