Binary system and more

Interested to know a little about the origin of numbers? Click here.
There are various numbering systems (or notational systems) that can be used to represent numbers. Nowadays everybody is familiar with the decimal system, but it is merely an historical convention, not necessarily the best possible choice. The base_10 system appears to be “natural” to human beings because we have 10 fingers, and supposedly we learn how to count using our fingers. However, this is not very convincing if we consider that other peoples used quite different methods: the Mayans and the Babylonians, for example. Despite the fact that the decimal system is now the standard notation throughout the world, computers commonly use the binary system, and the reason why is very simple: it is the system that most resembles the way an electronic machine uses to understand messages from the outside. In fact, the machine can sense a difference in the states of the electrical circuit (ON or OFF), and thanks to these two elements only, a whole code can be worked out (think of the Code morse: only two "letters" to write any kind of message). Theoretically, computers could be designed to operate on a decimal system code as well. In this case, instead of relying simply on ON (yes current) and OFF (no current), the circuitry could be set on 9 different voltages of current (plus the "zero" voltage), so that each one can be recognized by the machine. But this solution is not very practical, and besides the binary system is a perfectly manageable solution. From a mathematical standpoint, there is no difference at all between base_10 and base_2 systems, except numbers are longer in the latter case. In fact, the larger the base, the more symbols are required, but fewer digits are needed to express a given number. For example the decimal 413 (3 digits) needs fewer digits than the equivalent binary 111011001 (9 digits). It is clear, however, that large quantities of digits take time to be processed. And time is a crucial factor in computing. It is time that makes all the difference and, finally, makes computers what they are. The processing speed of data is extraordinarily fast, so fast that we can hardly conceive it in terms of human calculating capabilities. What really matters, then, is not the method of computing but the speed of the processing, which is measured in megahertz (millions of cycles per second), so if your computer has a “speed clock” of 350MHz, it can execute 350.000.000 operations per second. In the same amount of time, an average person can hardly manage to figure out 1 or 2 very simple operations. A basic notion of the binary system applied to computing is the byte, a cluster of 8 digits, each one being represented by either 0 or 1. One byte ranges from 00000000 to 11111111, therefore 1 byte can represent up to 256 values, in fact 256 = 2⁸ (eight digits in a row, each having two values: 0 or 1). The 256 data of a byte can be used to indicate a letter of the alphabet, a digit, or a special character or symbol like @ # , ? £ ; ψ and so on.	Read more about numbers and their origin Click on image to see how to transform a decimal number into a binary number. And now click below to see how to transform a binary number into a decimal one. A table on bytes that might help.