Data Representation in Computer - ProLearner

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     Data Representation in Computer

INTRODUCTION

Digital techniques have found their way into innumerable areas of tech- nology, but the area of automatic digital computers is by far the most notable and most extensive. As you know, a computer is a system of hardware that performs arithmetic operations, manipulates data, and makes decisions.
In science, technology, business, and, in fact, most other fields of endeavor, we are constantly dealing with quantities; so are computers. Quantities are measured, monitored, recorded, manipulated arithmetically, observed, or in some other way utilized in most physical systems. In digital systems like computers, the quantities are represented by symbols called digits. Many number systems are in use in digital technology that represent the digits in various forms. The most common are the decimal, binary, octal, and hexadecimal systems. This chapter discusses these number systems and the physical representation of digits in computers.

DIGITAL NUMBER SYSTEMS

In digital representation, various number systems are used. The most common number systems used are decimal, binary, octal, and hexadecimal systems. Let us discuss these number systems briefly.

Decimal Number System

The decimal system is composed of 10 numerals or symbols (Deca means 10, that is why this system is called decimal system). These 10 symbols are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9; using these symbols as digits of a number, we can express any quantity. The decimal system, also called the base-10 system because it has 10 digits, has evolved naturally as a result of the fact that man has 10 fingers.
The decimal system is a positional value system in which the value of a digit depends on its position. For example, consider the decimal number 729 We know that the digit 7 actually represents 7 bred, the 2 represents 2 tes, and the 9 represents In essence, the 7 carries the most weight of three digits: it is referred to as the most significant digit (MSD). The 9 carries the least weight and is called the least significant digit (LSD).
Consider another example, 25.12 This number is actually equal to 2 tens plus 5 units plus 1 tenths plus 2 hundredths ie, 2x10+5x1+ 1x1+2x1 The decimal point is used to separate the integer and fractional parts of the number. 10 100 More rigorously, the various positions relative to the decimal point carry weights that can be expressed as powers of 10. This is illustrated in Fig. 3.1 where the number 2512.1971 is represented. The decimal point separates the positive powers

of 10 from the negative powers. The number 2512.1971 is thus equal to 210+5 10+1x10 +2x10"-1-10-9-10-7-10-1-10-4
In general, any number is simply the sum of the products of each digit value and its positional value

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The sequence of decimal numbers goes as 0, 1,2,3,4,5,6,7,8,9, 10, 11 12, 13, 14, 15, 16, 17, 18, 19, 20, 21 See after 9, each successive number is a combination of two (or more) (unique) symbols of this system.

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