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1-2 BACKGROUND AND HISTORY Man’s earliest number or counting system was probably developed to help determine how many possessions a person had. As daily activities became more complex, numbers became more important in trade, time, distance, and all other phases of human life. As you have seen already, numbers are extremely important in your military and personal life. You realize 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 easier ways to count them. The abacus, developed by the Chinese, is one of the earliest known calculators. It is still 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. About 1672, Gottfried Wilhelm von Leibniz (German) perfected a machine that could perform all the basic operations (add, subtract, multiply, divide), as well as extract the square root. Modern electronic digital computers still use von Liebniz's principles. MODERN USE Computers are now employed wherever repeated calculations or the processing of huge amounts of data is needed. The greatest applications are found in the military, scientific, and commercial fields. They have applications that range from mail sorting, through engineering design, to the identification and destruction 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 more important workwork that cannot be handled by a computer. People and computers do not normally speak the same language. Methods of translating information into forms that are understandable and usable to both are necessary. Humans generally speak in words and numbers expressed in the decimal number system, while computers only understand coded electronic pulses that represent digital information. In this chapter you will learn about number systems in general and about binary, octal, and hexadecimal (which we will refer to as hex) number systems specifically. Methods for converting numbers in the binary, octal, and hex systems to equivalent numbers in the decimal system (and vice versa) will also be described. You will see that these number systems can be easily converted to the electronic signals necessary for digital equipment. TYPES OF NUMBER SYSTEMS Until now, you have probably used only one number system, the decimal system. You may also be familiar with the Roman numeral system, even though you seldom use it. THE DECIMAL NUMBER SYSTEM In this module you will be studying modern number systems. You should realize that these systems have certain things in common. These common terms will be defined using the decimal system as our base. Each term will be related to each number system as that number system is introduced.

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