13.1 Principles of digital electronics  (Page 5/7)

Using and storing binary numbers

In the previous section, we saw how the numbers 0 and 1 could represent `false' and `true' and could be used in decision making. Often we want to program a computer to count with numbers. To do this we need a way of writing any number using nothing other than 0 and 1. When written in this way, numbers are called binary numbers .

Binary Number System

A way of writing any number using only the digits 0 and 1.

Binary numbers

In normal (denary) numbers, we write 9+1 as 10. The fact that the `1' in 10 is the second digit from the right tells us that it actually means 10 and not 1. Similarly, the `3' in 365 represents 300 because it is the third digit from the right. You could write 365 as $3\times 100+6\times 10+5$ . You will notice the pattern that the $n$ th digit from the right represents ${10}^{n-1}$ . In binary, we use the $n$ th digit from the right to represent $2^{n-1}$ . Thus 2 is written as 10 in binary. Similarly $2^2=4$ is written as 100 in binary, and $2^3=8$ is written as 1000 in binary.

Once a number is written in binary, it can be represented using the low and high voltage levels of digital electronics. We demonstrate how this is done by showing you how an electronic counter works.

Counting circuits

To make a counter you need several `T flip flops', sometimes called `divide by two' circuits. A T flip flop is a digital circuit which swaps its output (from 0 to 1 or from 1 to 0) whenever the input changes from 1 to 0. When the input changes from 0 to 1 it doesn't change its output. It is called a flip flop because it changes (flips or flops) each time it receives a pulse.