INTRODUCTION

India developed the method of expressing all numbers using 10 symbols, each symbol receiving a

value of position as well as an absolute value. Since hands are the most convenient tools nature has

provided, man has always tended to use them in his counting. It is both natural and fortunate that our

number system is based on 10 digits. The decimal system has been so widely adopted throughout the

world that we rarely consider that other number systems exist. A seldom used but very simple system,

the binary number system has proved to be the most natural and efficient system for computer use. The

decimal system is positional, each numbers position indicating its relative value. Not all systems are

positional. The Roman Numeral System is an example of a nonpositional system. Since only positional

number systems are used in computers, they are the only ones discussed in this subcourse.

Personnel who work with computers must understand numbering systems because the computer

operates only with numbers. Therefore, this subcourse describes several numbering systems and explains

how to work with them. By definition, a numbering system is a way of expressing quantity with symbols.

The same symbols might express different quantities in any one of several numbering systems, and how

to express any given quantity in any given numbering system. Numbers are not expressed as decimal

numbers within the computer because other systems are more suitable for machine processes. To

understand fully how the computer calculates, you must be able to calculate in the same manner with

pencil and paper.

Digital computers use a simple numbering system; it is so simple that it only has two digits: 1 and 0.

Digital computers are designed to operate on a YES/NO basis. A digital number is either 1 or 0; a

function is there, or it is not there; a diode is conducting or it is not conducting; a voltage pulse is present

or not present or it is high state or low state. The numbering systems you will learn to use in this

subcourse -binary, octal, and hexadecimal - can all be easily expressed with just 1's and 0's.