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Data Representation: Understanding Quantitative and Qualitative Data in Computer Systems, Study notes of School management&administration

Colorado State University (CSU)School management&administration

An overview of data representation in computer systems, focusing on both quantitative and qualitative data. Topics covered include terminology, measuring data, bit and byte, metrics used to measure quantities of data, data representation in computers, unsigned and signed integers, binary addition, character representation, and ascii and unicode. Students will gain a solid understanding of the fundamental concepts of data representation in computer systems.

Typology: Study notes

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Uploaded on 11/08/2009

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Data Representation

CS101-Computer Systems

By:

Dilum Bandara

Dept. of Computer Science & Engineering

University of Moratuwa ©CSE 2

Outline

pTerminology

pMeasuring data

pData representation

nQuantitative

nQualitative

©CSE 3

Terminology

pComputers store & process data

pWhat is data?

pThe processed data is called information

pPhysical devices used to store & process

data in computers are 2-state devices

pState is represented using;

n0 –OFF

n1 -ON

©CSE 4

Bit & Byte

pAn abbreviation for BInary digiT

pBit is the smallest unit of data

representation

pWhen 8 bits are combined together it is

called a byte

p1024 (210) bytes are called a Kilobyte

©CSE 5

Metrics used to measure quantities

of data

-

125,0001000 Kilobits

MbMegabit

-

1251000 bits

KbKilobit

2401,099,511,627,7761024 Gigabyte

TBTerabyte

2301,073,741,8241024 Megabytes

GBGigabyte

2201,048,5761024 Kilobytes

MBMegabyte

21010241024 Bytes

KBKilobyte

2018 bits

ByteByte

-

BitBit

Power of 2BytesSymbolAbbreviation

©CSE 6

Data representation

Data

Representation

•Represents quality or

characteristics

•Not proportional to a value

•Name, NIC no, index no,

Address

•Quantifiable

•Proportional to value a

•Number of students, marks

for CS101, GPA

Qualitative

Quantitative

Discover Study notes of School management&administration Colorado State University (CSU)

Partial preview of the text

Download Data Representation: Understanding Quantitative and Qualitative Data in Computer Systems and more Study notes School management&administration in PDF only on Docsity!

1

Data Representation

CS101 - Computer Systems

By: Dilum Bandara Dept. of Computer Science & Engineering University of Moratuwa © CSE 2

Outline

p Terminology

p Measuring data

p Data representation

n Quantitative

n Qualitative

Terminology

p Computers store & process data

p What is data?

p The processed data is called information

p Physical devices used to store & process

data in computers are 2-state devices

p State is represented using;

n 0 – OFF

n 1 - O N

Bit & Byte

p An abbreviation for BInary digiT

p Bit is the smallest unit of data

representation

p When 8 bits are combined together it is

called a byte

p 1024 (

) bytes are called a Kilobyte

Metrics used to measure quantities

of data

Megabit Mb 1000 Kilobits 125,000 -

Kilobit Kb 1000 bits^125

Terabyte TB 1024 Gigabyte 1,099,511,627,776 240

Gigabyte GB 1024 Megabytes 1,073,741,824^30

Megabyte MB 1024 Kilobytes 1,048,576 220

Kilobyte KB 1024 Bytes 1024 210

Byte Byte 8 bits^120

Bit Bit - -

Abbreviation Symbol Bytes Power of 2

Data representation

Data

Representation

Represents quality or

characteristics

Not proportional to a value
Name, NIC no, index no,

Address

•Quantifiable

•Proportional to value a

•Number of students, marks

for CS101, GPA

Qualitative

Quantitative

Quantitative data

Data representation in computers

p Data is stored as Registers

p Register is a series of switches

p Registers are limited in size

n So number of bits are limited

n-1 n-2 … ... ... 2 1 0

n-bits

ß Min value - 0

ß Max value - 2n-

Unsigned Integers

p Only the positive numbers

p With a single byte (8-bits)

n We can denote 2^8 (256) numbers

n 0 (00000000 2 ) is the minimum

n 255 (11111111 2 ) is the maximum

Binary addition

p In order to perform arithmetic operations

all operands should be in the same

number base

p Example:

n Add 01010 2 and 10001 2

n Answer = 11011 2

Example

p Add 111110 2 and 11000111 2

n You are given only 8-bit registers

111110 ‡ 00111110

11000111 + ‡ 11000111 +

100000101 ‡ 00000101

Carry bit

Overflow

Signed Integers

p Denote whole numbers with are both

positive & negative

p Representing sign integers

n Sign & Magnitude method (S&M)

n Bias notation

n Complement method

Character representation cont …

p With a single byte (8-bits) 256 characters

can be represented

p Standards

n ASCII - American Standard Code for

Information Interchange

n EBCDIC - Extended Binary-Coded Decimal

Interchange Code

n Unicode

ASCII

p De facto world-wide standard for the code

numbers used by computers to represent:

n upper & lower-case Latin letters

n Numbers

n Punctuations

p There are 128 standard ASCII codes

n Can be represented by a 7 digit binary

number: 000 0000 through 111 1111

ASCII table

NUL

SOH

STX

ETX

EOT

ENQ

ACK

BEL

BS

TAB

LF

VT

FF

CR

SO

SI

A

B

C

D

E

F

Hex Symbol

ASCII

(space) ! "

$ % & ' ( ) * + , -.

2A

2B

2C

2D

2E

2F

ASCII Hex Symbol 0 1 2 3 4 5 6 7 8 9 : ; < = >

3A

3B

3C

3D

3E

3F

ASCII Hex Symbol

ASCII table cont…

A

B

C

D

E

F

G

H

I J K L M N

O

4A

4B

4C

4D

4E

4F

ASCII Hex Symbol P Q R S T U V W X Y Z [ \ ] ^

_

5A

5B

5C

5D

5E

5F

ASCII Hex Symbol ` a b c d e f g h i j k l m n

o

6A

6B

6C

6D

6E

6F

ASCII Hex Symbol

ASCII - things to note

p ASCII codes for digits are not equal to the

numeric value

p A simple code set & supported by almost

every computer

p But, most languages need more than 128

characters

Unicode www.unicode.org

p Is designed to overcome the limitation of number

of characters

p Assigns unique character codes to characters in a

wide range of languages.

p A 16-bit character set

p 65,536 (

) distinct Unicode characters

p Unicode provides a unique number for every character,

no matter what the platform,

no matter what the program,

no matter what the language.

Unicode cont…

p Even

supports

Sinhala &

Tamil

Courtesy by Unicode.org

Summary

p Measuring data

p Data representation

n Quantitative

p Integers

ß Unsigned

ß Signed

p Non integers

n Qualitative

Data Representation: Understanding Quantitative and Qualitative Data in Computer Systems, Study notes of School management&administration

Related documents

Partial preview of the text

Download Data Representation: Understanding Quantitative and Qualitative Data in Computer Systems and more Study notes School management&administration in PDF only on Docsity!

Data Representation

CS101 - Computer Systems

Outline

p Terminology

p Measuring data

p Data representation

n Quantitative

n Qualitative

Terminology

p Computers store & process data

p What is data?

p The processed data is called information

p Physical devices used to store & process

data in computers are 2-state devices

p State is represented using;

n 0 – OFF

n 1 - O N

Bit & Byte

p An abbreviation for BInary digiT

p Bit is the smallest unit of data

representation

p When 8 bits are combined together it is

called a byte

p 1024 (

) bytes are called a Kilobyte

Metrics used to measure quantities

of data

Megabit Mb 1000 Kilobits 125,000 -

Kilobit Kb 1000 bits^125

Terabyte TB 1024 Gigabyte 1,099,511,627,776 240

Gigabyte GB 1024 Megabytes 1,073,741,824^30

Megabyte MB 1024 Kilobytes 1,048,576 220

Kilobyte KB 1024 Bytes 1024 210

Byte Byte 8 bits^120

Bit Bit - -

Data representation

Data

Representation

characteristics

Address

•Quantifiable

•Proportional to value a

•Number of students, marks

for CS101, GPA

Qualitative

Quantitative

p Data is stored as Registers

p Register is a series of switches

p Registers are limited in size

n So number of bits are limited

ß Min value - 0

ß Max value - 2n-

p Only the positive numbers

p With a single byte (8-bits)

n We can denote 2^8 (256) numbers

n 0 (00000000 2 ) is the minimum

n 255 (11111111 2 ) is the maximum

p In order to perform arithmetic operations

all operands should be in the same

number base

p Example:

n Add 01010 2 and 10001 2

n Answer = 11011 2

p Add 111110 2 and 11000111 2

n You are given only 8-bit registers

Carry bit

Overflow

p Denote whole numbers with are both

positive & negative

p Representing sign integers

n Sign & Magnitude method (S&M)

n Bias notation

n Complement method

p With a single byte (8-bits) 256 characters

can be represented

p Standards