Number Bases

Computers move numbers around. That’s all they do. Everything they do – playing music, drawing, going on the Internet – is done by moving numbers around. It’s important for us as computing professionals to understand how this is done.

For example, how do we count? You probably haven’t thought about it since you were five. It’s important, however, to think about how we count ‘normally’ before we attempt to figure out how computers do it.

Look down. Chances are that you have ten digits, and that provides a clue about how counting works.

When humans started counting we kept it simple. We used our digits to keep a note of how many things we had. To begin with it was unlikely that anyone had more than ten of anything.

As people gathered more things they needed to count them and used something like the rock method. This worked like counting with fingers except that when you ran out of fingers you grabbed a rock and threw it onto a pile. Each rock represented ten things so that when you finished counting you could tell that you had used 3 rocks and 6 fingers.

Some quick arithmetic tells us that this is (3 x 10 fingers) + (6) or 36.

Rocks and Fingers: If you had used 6 rocks and 2 fingers how many things would you have counted? Show

This way of counting, using 10 as a base  for counting, is called decimal or denary.

Counting in different bases can seem frightening but we use it all the time. Many people are comfortable with weights expressed in pounds and ounces. As there are 14 ounces to the pound this is an example of counting in base 14.

Base 60: Can you think of any time you might use base 60? Show

Most people have no problem with counting using these bases – it is simply a matter of practise.

Next: Binary