The Number System

Introduction

The computer that we know of is digital device, which means that digital signals are used for the functioning of the computer. One property of digital signals is that it has discrete level of voltages. This Property of digital signals proves to be very useful to represent data in the computer. Why is it so? The answer to this question lies to the fact that there are many electrical and electronic devices which can be in any one of their two possible sates. For example, a simple switch can be either ON or OFF, a bulb or a Ligth Emitting Diode can be glowing or not glowing et. Therefore, representation of data becomes necessary to understand how the computer represents data. As we will see shortly, the com0uter use two values to represent data. These two values are called bits, switch stand for Binary Digits. They take the values 0 and 1. John von Neumann suggested this convention. Since there are only two values with which data can be represented in computer, at the lowest level, two discrete voltage values are used to represent the bits. Thus, digital signals, with their property mentioned above, proved to be ideal for computer systems.

Nearly all of our arithmetic operations are carried out with decimal numbers. The computer on the other hand does not use this numbering system. As mentioned earlier, the computer does its computational jobs with binary numbers, which is based on the number 2, for a number of reasons. The most important of them are the facts that operations with binary numbers are more precise and also the operations are faster because of the fact that for certain binary operations, there is hardware circuitry available.

For common numbering systems are generally used. They are the decimal numbering system, binary system, octal numbering system and finally, the hexadecimal numbering system. Decimal numbering system use base 10 (thus the prefix deci). Binary number system use base 2, octal numbering system use base 8 and hexadecimal numbering system use base 16. Thus, they have the prefix bi, octal and hexa respectively. We said that the numbering system use a base value. What do we understand by a base value? We can say that the base of a number refers to how many digits are required to represent a numerical value in that numbering refers to how many digits are required to represent a numerical value in that numb erring system. Thus, decimal been base 10, system requires two digits, 0 and 1, to represent any numerical value. The following sections will describe three common numbering systems.