data representation class11 notes

Chapter-13
data representation class11 notes

Introduction :

Digital techniques have found their way into innumerable areas of technology, 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 perform arithmetic operations, manipulates data, and make decisions.

DIGITAL NUMBER SYSTEMS

In digital representation, various number systems are used. The most common number used are decimal, binary, octal, and hexadecimal systems.

Decimal Number System

Base — 10

Minimum — 0 { digits }

Maximum — 9 { digits }

Ex — — -> (125)10

Binary Number System

Base — 2

Minimum — 0 { digits }

Maximum — 1 { digits }

Ex — — -> (100)2

Octal Number System

Base — 8

Minimum — 0 { digits }

Maximum — 7 { digits }

Ex — — -> (200)8

Hexadecimal Number System

Base — 16

Minimum — 0 { digits }

Maximum — 15(F) { digits }

Number Conversions

The binary number system is the most important one in digital systems as it is very easy to implement in circuitry. The decimal system is important because it is universally used to represent quantities outside a digital system.

In a digital system, tree or four of these number system may be in use at the same time, so that understanding of the system operation requires the ability to convert from one number system to another. This section discusses how to perform these conversions. So , let us discuss them one by one.

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