Maths index ## Binary Arithmetic

If I gave you a red ball and a blue ball and asked you to do arithmetic with them using one colour for one number and the other for another number (no other numbers allowed) I would be asking you to do binary arithmetic.Binary is from the Latin

binarius, which means doing it with two together (bini+ary)At first sight, it may seem that you cannot count higher than two. But this is not so. In our normal counting we have only ten digits (0 to 9), but, by putting them in different places, we can carry on counting until we stop with exhaustion. We can do the same with two balls.

The blue ball on its own is 0

The red ball on its own is 1

The red ball followed by the blue ball is 2

Two red balls is three

The red ball followed by two blue balls is four

The red ball, a blue ball, then a red ball is five

Two red balls then a blue ball is six

Three red balls is seven

The red ball followed by three blue balls is eight

The red ball, two blue balls, then a red ball is nine

A red ball, a blue ball, a red ball, then a blue ball is ten

A red ball, a blue ball, then two red balls is eleven

Two red balls and two blue balls is twelve

Two red balls, a blue ball, then a red ball is thirteen

Three red balls, then a blue ball is fourteen

Four red balls is fifteen

We can make

Binary numbersby writing 0 for the blue ball and 1 for the red balls.In binary numbers:

0 means 0

1 means 1

10 means two

11 means three

100 means four

101 means five

110 means six

111 means seven

1000 means eight

1001 means nine

1010 means ten

1011 means eleven

1100 means twelve

1101 means thirteen

1110 means fourteen

1111 means fifteenThere are 10 types of people in the world - Those who understand binary and

Those who do not

When you understand that joke you understand binary

Click here for an electronic calculator that converts our normal numbers to binary numbers

If all this driven you crazy, then pity the computer you are reading this on. Computers do all their counting in binary arithmetic. In fact, they do everything in binary. When you move the scroll bar the command is converted into binary patterns for the computer to understand it.

If you enjoy binary arithmetic and you can do it very very fast, perhaps you should apply for a job as a computer.

Click here for more about thinking like a computer.

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