Binary, Decimal and Hexadecimal Numbers

Decimals

To understand Binary and Hexadecimal numbers, it is best to know how Decimal Numbers work.

Every digit in a decimal number has a "position", and the decimal point helps us to know which position is which.

The position just to the left of the point is the "Units" position. Every position further to the left is 10 times bigger, and every position further to the right is 10 times smaller:

Now, this is just a way of writing down a value. Other ways include Roman Numerals, Binary, Hexadecimal, and more. You could even just draw dots on a sheet of paper!

Counting with Different Number Systems

The Decimal Number System is also called "Base 10". Because it is based on the number 10.

In decimal there are ten symbols (0 to 9), but notice something interesting: there is no symbol for "ten". "10" is actually two symbols put together, a "1" and a "0":

In decimal you count like this: 0,1,2,3,4,5,6,7,8,9, but then you say "I have run out of symbols here, so I will start again at 0, but first I will add 1 to the number on the left".

But you don't have to use 10 as a "Base". You could use 2 ("Binary"), 16 ("Hexadecimal"), or any number you want to! But you follow the same rule:

Count up until just before the "Base", then start at 0 again, but first you add 1 to the number on your left.

Why not try it yourself? See how you would count dots using Bases from 2 to 16 in this little demonstration:

Try this: after selecting a Base and watching it count for a while, use the "Pause" button and see if it has tallied the right number of dots, as in this example using base 2:
Example:	1×16 + 1×8 + 1×1 = 16+8+1 = 25

Binary Numbers

Binary Numbers are just "Base 2" instead of "Base 10". So you start counting at 0, then 1, then you run out of digits! So you start back at 0 again, but increase the number on the left by 1.

Like this:

Hexadecimal Numbers

The Hexadecimal number are interesting. There are 16 of them! They look the same as the decimal numbers up to 9, but then there are the letters ("A',"B","C","D","E","F") in place of the decimal numbers 10 to 15.

So a single Hexadecimal digit can show 16 different values instead of the normal 10 like this: