Binary

As computers don’t have fingers to count on they must use another method. Their method is to use the presence or absence of electricity as the numbers 1 and 0. These are known as binary digits, or bits. Eight bits make up a byte.

Think of binary as being like a light switch. If the switch is off the light is off. That is a 0. If the switch is on the light is on. That is a 1.

A binary number  looks different from the decimal numbers we are used to. Where we would write 13 a computer would represent this as ON ON OFF ON, or 1101. We can represent this visually by putting the digits into columns, numbered from right to left:

What does each column represent?

We can express the values of the columns of the numbers we use as exponents. You will already be familiar with this concept from decimal number, where we often refer to the columns as tens, hundreds and thousands.

Exponents use powers to represent numbers.  For example 102 means 10 raised to the second power or 10 multiplied by itself 2 times. This gives us (10 x 10) or 100.

105 is (10 x 10 x 10 x 10 x 10) or 100000.

How, then, do we use exponents to represent the columns in numbers? From right to left the columns are 1s, 10s, 100s, etc. We have seen that 102 is 100. 101 is simply 10. What about the 1s column?

To work this out we can use an example. What is 103 x 102? If we expand this we get (10 x 10 x 10) x (10 x 10). This is simply (10 x 10 x 10 x 10 x 10) or 105.

So 103 x 102 is the same as 103+2 or 105.

What then is 103 x 100? It is 103+0 or simply 103.

What number can we use to multiply 103 and get 103? The answer is 1. Therefore 100 is 1.

Next: Exponents