1-2BACKGROUND AND HISTORYMan’s earliest number or counting system was probably developed to help determine how manypossessions a person had. As daily activities became more complex, numbers became more important intrade, time, distance, and all other phases of human life.As you have seen already, numbers are extremely important in your military and personal life. Yourealize that you need more than your fingers and toes to keep track of the numbers in your daily routine.Ever since people discovered that it was necessary to count objects, they have been looking for easierways to count them. The abacus, developed by the Chinese, is one of the earliest known calculators. It isstill in use in some parts of the world.Blaise Pascal (French) invented the first adding machine in 1642. Twenty years later, an Englishman,Sir Samuel Moreland, developed a more compact device that could multiply, add, and subtract. About1672, Gottfried Wilhelm von Leibniz (German) perfected a machine that could perform all the basicoperations (add, subtract, multiply, divide), as well as extract the square root. Modern electronic digitalcomputers still use von Liebniz's principles.MODERN USEComputers are now employed wherever repeated calculations or the processing of huge amounts ofdata is needed. The greatest applications are found in the military, scientific, and commercial fields. Theyhave applications that range from mail sorting, through engineering design, to the identification anddestruction of enemy targets. The advantages of digital computers include speed, accuracy, and man-power savings. Often computers are able to take over routine jobs and release personnel for moreimportant workwork that cannot be handled by a computer.People and computers do not normally speak the same language. Methods of translating informationinto forms that are understandable and usable to both are necessary. Humans generally speak in wordsand numbers expressed in the decimal number system, while computers only understand coded electronicpulses that represent digital information.In this chapter you will learn about number systems in general and about binary, octal, andhexadecimal (which we will refer to as hex) number systems specifically. Methods for convertingnumbers in the binary, octal, and hex systems to equivalent numbers in the decimal system (and viceversa) will also be described. You will see that these number systems can be easily converted to theelectronic signals necessary for digital equipment.TYPES OF NUMBER SYSTEMSUntil now, you have probably used only one number system, the decimal system. You may also befamiliar with the Roman numeral system, even though you seldom use it.THE DECIMAL NUMBER SYSTEMIn this module you will be studying modern number systems. You should realize that these systemshave certain things in common. These common terms will be defined using the decimal system as ourbase. Each term will be related to each number system as that number system is introduced.