1.3 Data Encoding · 2019. 5. 20. · Bits and binary •All computer data is represented using...

1.3

Data Encoding

Department of CSE,Coimbatore

Objectives

• To understand positional numeral systems.

• To describe how integer and real numbers can be encoded.

• To show that computers can be imprecise.

• To depict how complex information such as text, colors, pictures,

and sound can be encoded as bit strings.


Introduction

• A number system defines how a number can be represented using

distinct symbols.

• A number can be represented differently in different systems.

For example, the two numbers (2A)16 and (52)8 both refer to the

same quantity, (42)10, but their representations are different.


Common Number Systems


System Base Symbols

Used by

humans?

Used in

computers?

Decimal 10 0, 1, … 9 Yes No

Binary 2 0, 1 No Yes

Octal 8 0, 1, … 7 No No

Hexa-

decimal16

0, 1, … 9,

A, B, … FNo No

The decimal system (base 10)

• The word decimal is derived from the Latin root decem (ten). In this

system the base b = 10 and we use ten symbols.

• The symbols in this system are often referred to as decimal digits or

just digits.

S = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}


Integers

• Integers are generally represented in the form as …

Eg.

• The place values for the integer number +24 is …


Real Numbers

• Real Numbers are generally represented in the form as …

Eg.

• The place values for the real number +24.13 is …


S = {0, 1}

Department of CSE

The binary system (base 2)

• The word binary is derived from the Latin root bini(or two by two).

• In this system the base b = 2 and we use only two symbols.

• The symbols in this system are often referred to as binary digits or

bits(binary digit).


Bits and binary

• All computer data is represented using binary, a number system that

uses 0s and 1s.

• Binary digits can be grouped together into bytes.

• Computers use binary - the digits 0 and 1 - to store data.

• A binary digit, or bit, is the smallest unit of data in computing.

• It is represented by a 0 or a 1.

• Binary numbers are made up of binary digits (bits), eg the

binary number 1001.

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Bits and binary

• The circuits in a computer's processor are made up of billionsof transistors.

• A transistor is a tiny switch that is activated by the electronic signalsit receives.

• The digits 1 and 0 used in binary reflect the on and offstates of a transistor.

• Computer programs are sets of instructions.

• Each instruction is translated into machine code - simple binarycodes that activate the CPU.

• Programmers write computer code and this is converted bya translator into binary instructions that the processorcan execute.

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Byte to Terabyte

• Bits can be grouped together to make them easier to work with. Agroup of 8 bits is called a byte.

• Other groupings include:

• Nibble - 4 bits (half a byte)

• Byte - 8 bits

• Kilobyte (KB) - 1024 bytes (or 1024 x 8 bits)

• Megabyte (MB) - 1024 kilobytes (or 1048576 bytes)

• Gigabyte (GB) - 1024 megabytes

• Terabyte (TB) - 1024 gigabytes

• Most computers can process millions of bits every second. A harddrive's storage capacity is measured in gigabytes or terabytes. RAM isoften measured in megabytes or gigabytes.


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Big Data: Volume

Byte Kilobyte Megabyte Gigabyte Terabyte Petabyte Exabyte Zettabyte Yottabyte

KB MB GB TB PB EB ZB YB

1000 bytes 1000 KB 1000 MB 1000 GB 1000 TB 1000 PB 1000 ZB 1000YB

30KB

One page

of text

5 MB

One song

5 GB

One movie 6 million

books

1 TB

55 storeys

of DVD

1 PB

Data

up to

2003

5 EB

Data

in 2011

1.8

ZB

NSA

data center

1 YB

Decimal to Binary Conversion


• The number (156)10 in decimal is the same as (10011100)2 in binary.

• Let us see how the conversion is done!

Decimal to Binary Conversion Cntd..


• If the decimal number to be converted is (156.6875)10 , let us see

how the fractional part can be converted to binary!

Decimal to Binary Conversion Cntd..


• If the decimal number to be converted is (156.6875)10 , let us see

how the fractional part can be converted to binary!

• The binary of (156)10 is (10011100)2 and the binary of (0.6875)10 is

(0.1011)2

So the complete answer is (156.6875)10 = (10011100.1011)2

Binary to Decimal Conversion


• The number (11001)2 in binary is the same as 25 in decimal and is

represented as…

• The equivalent decimal number is N = 16 + 8 + 0 + 0 + 1 = 25.

• The number (101.11)2 in binary is equal to the number 5.75 in

decimal .

S = {0, 1}

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Can you perform the indicated conversion?


Decimal to Binary

a) 1310 = ?

b) 2210 = ?

c) 4310 = ?

d) 15810 = ?

Binary to Decimal

a) 0110 2 = ?

b) 11010 2 = ?

c) 0110101 2 = ?

d) 11010011 2 = ?

Decimal → Binary ………..Answers

a) 1310 = ?

b) 2210 = ?

c) 4310 = ?

d) 15810 = ?

1 1 0 1 2

1 0 1 1 0 2

1 0 1 0 1 1 2

1 0 0 1 1 1 1 0 2

Binary → Decimal ……….Answers

a) 0110 2 = ?

b) 11010 2 = ?

c) 0110101 2 = ?

d) 11010011 2 = ?

6 10

26 10

53 10

211 10

The hexadecimal system (base 16)

• The word hexadecimal is derived from the Greek root hex (six) and

the Latin root decem (ten). In this system the base b = 16 and we

use sixteen symbols to represent a number.

• The set of symbols are:

Note that the symbols A, B, C, D, E, F are equivalent to

10, 11, 12, 13, 14, and 15 respectively. The symbols in

this system are often referred to as hexadecimal digits.


S = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9,A, B, C, D, E, F}

The hexadecimal system (base 16) contd---

• The number (2AE)16 in hexadecimal is equivalent to 686 in

decimal is represented as…

• The equivalent decimal number is N = 512 + 160 + 14 = 686.


Using hexadecimal

• Hex codes are used in many areas of computing to simplify

binary codes.

• It is important to note that computers do not use hexadecimal - it is

used by humans to shorten binary to a more easily understandable

form.

• Hexadecimal is translated into binary for computer use. Some

examples of where hex is used include:

• colour references

• assembly language programs

• error messages


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Hex colour model

• Hex can be used to represent colours on web pages and image-

editing programs

• using the format #RRGGBB (RR = reds, GG = greens, BB =

blues).

• The # symbol indicates that the number has been written in hex

format.

• eg #FF6600.


The Hex color model uses two hex digits for each colour

Eg: #FF 66 00


As one hex digit represents

4 bits

Two hex digits together

make 8 bits (1 byte).

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• The values for each colour run between 00 and FF.

• In binary,

• 00 is 0000 0000

• FF is 1111 1111

• That provides 2^8 = 256 possible values for each of the three

colours.

• That gives a total spectrum of 256 reds x 256 greens x 256 blues -

which is over 16 million colours in total.


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• #FF0000 will be the purest red - red only, no green or blue.

• Black is #000000 - no red, no green and no blue.

• White is #FFFFFF.

• An orange colour can be represented by the code #FF6600.

• The hex code is much easier to read than the binary equivalent

1111 1111 0110 0110 0000 0000


• The figure on the left shows the additive mixing of red, green and blue primaries to form the three secondary colors yellow (red + green), cyan (blue + green) and magenta (red + blue), and white ((red + green + blue).

• RGB model – Computer display

• The figure on the right shows the three subtractive primaries, and their pairwise combinations to form red, green and blue, and finally black by subtracting all three primaries from white.

• CMYK model - Used in Printing


Colour model

• If you are making a web page with HTML or CSS you can use hex codes to choose the colours.

• The RGB model ( Additive ) is used for color monitors and most video cameras.

• Hex values have equivalents in the RGB colour model.

• The RGB model is very similar to the hex colour model,

you use a value between 0 and 255 for each colour.

• So an orange colour that is #FF 66 00 in hex would be

255, 102, 0 in RGB.

• Cyan color is 0,255,255

•Teal color is 0,128,128


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Hex and RGB colour codes

• Red #FF0000 (255,0,0)

• Tomato #FF6347 (255,99,71)

• Coral #FF7F50 (255,127,80)

• indian red #CD5C5C (205,92,92)



Color HTML / CSS Name Hex Code#RRGGBBDecimal

Code(R,G,B)

Black #000000 (0,0,0)

White #FFFFFF (255,255,255)

Red #FF0000 (255,0,0)

Lime #00FF00 (0,255,0)

Blue #0000FF (0,0,255)

Yellow #FFFF00 (255,255,0)

Cyan / Aqua #00FFFF (0,255,255)

Magenta / Fuchsia #FF00FF (255,0,255)

Silver #C0C0C0 (192,192,192)

Gray #808080 (128,128,128)

Maroon #800000 (128,0,0)

Olive #808000 (128,128,0)

Green #008000 (0,128,0)

Purple #800080 (128,0,128)

Teal #008080 (0,128,128)

Navy #000080 (0,0,128)

• Errors

• Hex is often used in error messages on your computer.

• The hex number refers to the memory location of the error.

• This helps programmers to find and then fix problems.



So far….


Table : summary of four positional number systems


Table : Four positional number systems

Figure : Converting decimal to other bases (integral part)

Decimal to any base



Figure : decimal to other bases (fractional part )


Converting FROM the base 10 To base 3

3 4 10 = __________3

Figure : Base 3

33 32 3 1

3 3 4

1 1 - 13

3 - 23

1 - 0

1 0 2 1

Binary-octal (base 8) conversion


• The binary bits are grouped into 3 and converted….

• Binary to octal and octal to binary conversion eg.

Binary-hexadecimal conversion


• The binary bits are grouped into 4 and converted…

• Binary to hexadecimal and hexadecimal to binary conversion eg.

Octal (base 8)-hexadecimal conversion


• Convert into binary first and then perform the required

conversion.

• Octal to hexadecimal and hexadecimal to octal conversion eg.

Try it yourself


Convert these binary numbers into octal numbers...

(a) 001011112 (8 bits) (b) 111101002 (8 bits)

Convert the following octal numbers into hexadecimal (16 bits)

(a) 658 (b) 1238Can you find out .........

What is the biggest binary number one can write with n bits?

How many unique patterns does a sequence of 5 bits generate?

Write all the patterns of a sequence of 5 bits.

Binary Octal ........ Answers

Refer to the binary-octal

conversion table

000 101 111

= 578

0 5 7

Refer to the binary-octal

conversion table

011 110 100

= 3648

3 6 4

Refer to the binary-octal conversion table

68 58

110 101

0000 0000 0011 01012

0 0 3 5

= 3516

Refer to the binary-octal conversion table

18 28 38

001 010 011

0000 0000 0101 00112

0 0 5 3

= 5316

Octal Hexadecimal Answers

Can we find out .........Answers

What is the biggest binary number one can write with n

bits?

N 1’s

How many unique patterns does a sequence of 5 bits generate?

2^5

Write all the patterns of a sequence of 5 bits.

00000,00001,00010…..11111

Conversion from Hexadecimal to Binary

Replace each hex digit by the 4 equivalent bits, for examples,

• A3C5H = 1010 0011 1100 0101B

• 102AH = 0001 0000 0010 1010B


Conversion from Binary to Hexadecimal

Starting from the right-most bit (least-significant bit), replace each

group of 4 bits by the equivalent hex digit (pad the left-most bits with

zero if necessary), for examples,

• 1001001010B = 0010 0100 1010B = 24AH

• 10001011001011B = 0010 0010 1100 1011B = 22CBH


Exercises (Number Systems Conversion)

Convert the following decimal numbers into binary and hexadecimal

numbers:

• 108

• 4848

• 9000


Answers……………

• 108 = 1101100 = 6C

• 4848 = 1001011110000 = 12F0

• 9000 = 10001100101000 = 2328



Convert the following binary numbers into hexadecimal and

decimal numbers:

• 1000011000

• 10000000

• 101010101010



• 1000011000 = 218H = 536D

• 10000000 = 80H = 128D

• 101010101010 = AAAH = 2730D



Convert the following hexadecimal numbers into binary and

decimal numbers:

• ABCDE

• 1234

• 80F



• ABCDE = 10101011110011011110 = 703710D

• 1234 = 1001000110100 = 4660D

• 80F = 100000001111 = 2063D



Convert the following decimal numbers into binary equivalent:

• 19.25D

• 123.456D



• 19.25 = 10011.01

• 123.456 = 1111011.01110100…


Can you identify the forms of the data in use?


Answer…..

The different forms of data are text, image,audio,video….


Image

Image

Audio Audio

Video

Text

Different Forms of Data


All software, music, documents, and any other information that is

processed by a computer, is also stored using binary.


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Data in any form (text, audio, video) is represented in binary form only

in computers.


Figure : Representation of Different forms of data

Amount of storage space required

Different types of data require different amounts of storage space.


Data Storage

One extended-ASCII character in a text file

(eg 'A')1 byte

The word 'Monday' in a document 6 bytes

A plain-text email 2 KB

64 pixel x 64 pixel GIF 12 KB

Hi-res 2000 x 2000 pixel RAW photo 11.4 MB

Three minute MP3 audio file 3 MB

One minute uncompressed WAV audio file 15 MB

One hour film compressed as MPEG4 4 GB

Bit number patterns

• Computer systems and files have limits that are measured in bits.

For example, image and audio files have bit depth.

• The bit depth reflects the number of binary numbers available,

similar to the number of combinations available on a padlock.

• The more wheels of numbers on a padlock, the more combinations

of numbers are possible.

• The greater the bit depth, the more combinations of binary numbers

are possible.


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Bit number patterns

• Every time the bit depth increases by one, the number of binary

combinations is doubled.

• A 1-bit system uses combinations of numbers up to one place value

(1).There are just two options: 0 or 1.

• A 2-bit system uses combinations of numbers up to two place values

(11).There are four options: 00, 01, 10 and 11.


Binary combinations

• These tables show how many binary combinations are available for

each bit size.

• One bit


Maximum binary number = 1

Maximum denary number = 1

Binary combinations = 2

Two bit

• Maximum binary number = 11

• Maximum denary number = 3

• Binary combinations = 4


Three bit

• Maximum binary number = 111

• Maximum denary number = 7

• Binary combinations = 8


Bit depth Max (binary) Max (denary)Combinations

available

1 1 1 2

2 11 3 4

3 111 7 8

4 1111 15 16

5 11111 31 32


A 1-bit image can have 2 colours,

a 4-bit image can have 16 colours,

an 8-bit image can have 256 colours,

and a 16-bit image can have 65,536 colours.

Encoding and Decoding

• Encoding is the process of putting a sequence of characters (letters,

numbers, punctuation, and certain symbols) into a specialized digital

format for efficient transmission or transfer.

• Decoding is the opposite process -- the conversion of a digital signal

into a sequence of characters.

• Encoding and decoding are used in data communications,

networking, and storage.


• Everything on a computer is represented as streams of binary

numbers.

• Audio, images and characters all look like binary numbers

in machine code.

• These numbers are encoded in different data formats to give them

meaning,

eg the 8-bit pattern 01000001 could be

the number 65,

the character 'A', or

a colour in an image.


Encoding formats• Encoding formats have been standardised to help compatibility across

different platforms.

• audio is encoded as audio file formats, eg mp3,WAV, AAC

• video is encoded as video file formats, eg MPEG4, H264

• text is encoded in character sets, eg ASCII, Unicode

• images are encoded as file formats, eg BMP, JPEG, PNG

• The more bits used in a pattern, the more combinations of valuesbecome available.

• This larger number of combinations can be used to represent manymore things, eg a greater number of different symbols, or morecolours in a picture.


Character sets

• Every word is made up of symbols or characters.

• When you press a key on a keyboard, a number is generated that represents the symbol for that key.

• This is called a character code.

• A complete collection of characters is a character set.


Numbers are generated

that represent keyboard

symbols

Representing Character



A standard

QWERTY

keyboard

A keyboard with

Japanese characters

• Different languages use different keyboard layouts.

• For example, a French keyboard has an é.

• If we were writing in Japanese or Arabic, we would need even more

choices of characters.

• In theory, anyone can create a character set.

• But it is important that computers can communicate so we use

global standards for character sets.


• You can check what character encoding your web browser is

using by looking in your browser settings:

• Mozilla Firefox >Tools > Page Info: Encoding

• Microsoft Internet Explorer >View > Encoding

• Google Chrome >Tools > Encoding



Text Encoding

• Characters are usually encoded as integer values using the

encoding schemes.

• The associations between numbers and text are known

collectively as a character encoding scheme.


ASCII - American Standard Code for Information Interchange

• Focus on unaccented, English letters.

• Every letter, number, capital, etc

• Represented by codes 0-127.

• Space, 32; “A”, 65; “a”, 97.

• Only the 7-bit patterns were standardized under ASCII.

• Standard 8-bit ASCII codes

• start with a zero-valued bit (followed by 7-bit ASCII code).


• “Extended ASCII” codes start with a one-valued bit;

• these codes are not standard and vary in meaning among different

manufactures and equipment.

• First 32 patterns (when written in hexadecimal, any patterns starting with

0 or 1): control codes;

• the most common of these are 0Ah (Line Feed) and 0Dh (Carriage

Return).


Table : ASCII Chart


EBCDIC (Extended Binary Coded Decimal

Interchange Code)

• Developed by IBM.

• Restricted mainly to IBM or IBM compatible mainframes.

• Conversion software to/from ASCII available.

• Common in archival data.

• Character codes differ from ASCII.


ASCII EBCDIC

Space 2016 4016

A 4116 C116

b 6216 8216

• Unicode uses between 8 and 32 bits per character

• so it can represent characters from languages from all around the world.

• It is commonly used across the internet.

• As it is larger than ASCII, it might take up more storage space when saving documents.

• Global companies, like Facebook and Google, would not use the ASCII character set because their users communicate in many different languages.


Unicode


• Multilingual: defines codes for

• Nearly every character-basedalphabet.

• Large set of ideographs forChinese, Japanese andKorean.

• Composite characters forvowels and syllabic clustersrequired by some languages.

• Allows software modifications forlocal-languages.


ASCII only contains 127 characters

though an extended version exists with 257 characters

This is by far not enough as it is too restrictive to the English language.

UNICODE was developed to alleviate this problem:

the latest version, UNICODE 5.1.0 contains more than 100,000

characters, covering most existing languages.

For more information, see:

http://www.unicode.org/versions/Unicode5.1.0/

http://www.unicode.org/versions/Unicode5.1.0/

How Did Photography Go Digital?


PIXELS


Pixels


Image Encoding


• Binary representation of bitmap images

• All bitmap images are stored as array of pixels.

• A monochrome images store

• 1 for black pixel and

• 0 for a white pixel

• (or vice versa depending on the encoding protocol)

• It could also be necessary to store the dimensions of the image.


• This image could be represented as following 35 binary digits (5 bytes):

• 00100 01010 01010 10001 11111 10001 00000


Show how to encode

Answer

Color Images


Representing Color


• Each pixel of the rose flower

is to be defined using 24

bits(8 bits/ color RGB)

• The first 8 bits specifying the

shade of red,

• The next 8 bits specifying the

shade of green and

• The last 8 bits specifying the

shade of blue.

Color Images


Black and White Image


Black and White


Improve Efficiency


Color Images


Image - 1



1 1 1 1 1 1 1 1 1

1 1 1 0 1 0 1 1 1

1 1 1 1 0 1 1 1 1

1 1 1 0 1 0 1 1 1

1 1 1 1 0 1 1 1 1

1 1 1 1 0 1 1 1 1

1 1 0 0 0 0 0 1 1

1 1 1 0 0 0 1 1 1

1 1 1 0 0 0 1 1 1

Image - 2



1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1

1 1 0 0 1 0 0 1 1

1 1 0 0 1 0 0 1 1

1 1 1 1 1 1 1 1 1

1 0 0 1 1 1 0 0 1

1 1 0 1 1 1 0 1 1

1 1 1 0 0 0 1 1 1

1 1 1 1 1 1 1 1 1

Image - 3



1 1 1 1 1 1 1 1 1

1 1 0 1 1 1 0 1 1

1 0 0 0 1 0 0 0 1

1 0 0 0 0 0 0 0 1

1 0 0 0 0 0 0 0 1

1 1 0 0 0 0 0 1 1

1 1 1 0 0 0 1 1 1

1 1 1 1 0 1 1 1 1

1 1 1 1 1 1 1 1 1

Image - 4



1 1 1 1 0 1 1 1 1

1 1 1 0 0 0 1 1 1

1 1 0 0 0 0 0 1 1

1 0 0 0 0 0 0 0 1

1 1 0 0 0 0 0 1 1

1 1 0 0 0 0 0 1 1

1 1 0 0 1 0 0 1 1

1 1 0 0 1 0 0 1 1

1 1 0 0 1 0 0 1 1

Representing Sound


Sound is produced by the vibration of a media like air or water.

Audio refers to the sound within the range of human hearing.

Naturally, a sound signal is analog, i.e. continuous in both time

and amplitude.

To store and process sound information in a computer or to

transmit it through a computer network, we must first convert the

analog signal to digital form using an analog-to-digital converter (

ADC )

The conversion involves two steps:

(1) sampling, and (2) quantization.

Sound Encoding

Sampling

Sampling is the process of examining the value of a continuous

function at regular intervals.

Sampling usually occurs at uniform intervals, which are referred

to as sampling intervals.

Sound can also be stored in a computer as binary codes

To represent the varying values of a soundwave, it’s height must be

measured at regular intervals and the measurements given binary codes.

This process is called Sampling and the number of samples taken in a

second is called the sampling rate

The sampled measurements make up the digital sound file

Sampling rate

Analogue signal

Time

Am

pli

tud

e

Quantization

Quantization is the process of limiting the value of a sample of a

continuous function to one of a predetermined number

of allowed values, which can then be represented by a

finite number of bits.

Quantization

The number of bits used to store each intensity defines the

accuracy of the digital sound:

Adding one bit makes the sample twice as accurate

How much space do we need to store one minute of music?

- 60 seconds

- 44,100 samples

-16 bits (2 bytes) per sample

- 2 channels (stereo)

S = 60x44100x2x2 = 10,534,000 bytes ≈ 10 MB !!

1 hour of music would be more than 600 MB !

Sound Encoding



• Sound Data As Bytes: Sound occurs

naturally as an analog wave.

• The data is represented as a pair of

decimal number.

• The first part representing the time

and the second part representing

the voltage value {0000 — low and

1111-high}

• A microphone translates the change in air pressure and converts it to

a wave form.

• A converter within the sound card of the computer takes readings

each second.

• These readings are positions (voltages, actually) on the wave in

relation to the zero line.

• They are recorded and converted from decimal to binary numbers.

• The process of measuring and recording the voltage of the

signal is called sampling.


• Using 2 bit sampling to represent the audio signal ...


11100100

t1 t2 t3 t4 t10


• At t1 : 01


11100100

t1 t2 t3 t4 t10


• AT t2 it is : 00

• We have 01 00


11100100

t1 t2 t3 t4 t10


• At t3 it is: 01

• We have 01 00 01


11100100

t1 t2 t3 t4 t10


• The complete wave is represented by specifying the region to which it

belongs i.e at time 1 it is in region 01, at time 2 it is in 00… and so on .

• Here we are not representing time as we are sampling continuously at

time = 1, 2, 3…


11100100

01 00 01 01 11

01 10 01 11 01

The complete representation of the

signal is….

Inside the computer, however, all data is stored as

numbers:

• Numbers – are stored as numbers, obviously!

• Text characters are stored as a code that represents each – e.g.

ASCII.

• Images are stored as numbers representing the amounts of red,

green and blue for each pixel.

• Sounds are stored as numbers representing the loudness at given

intervals.


Data Compression

• To reduce the volume of data to be transmitted (text, fax,

images).

• To reduce the bandwidth required for transmission and to

reduce storage requirements (speech, audio, video).


Classification

• Lossless compression

• Lossless compression for legal and medical documents, computer

programs.

• Lossy compression

• Digital audio, image, video where some errors or loss can be

tolerated.


Video and Audio Compression

• Video and Audio files are very large. Unless we develop and

maintain very high bandwidth networks (Gigabytes per second or

more) we have to compress the data.

• Relying on higher bandwidths is not a good option.

• Compression becomes part of the representation or coding scheme

which have become popular audio, image and video formats.


Run-length Encoding

• This encoding method is frequently applied to images (or pixels

in a scan line).

• It is a small compression component used in JPEG

compression.

• In this instance, sequences of image elements X1, X2, …, Xn

are mapped to pairs (c1, l1), (c1, l2), …, (cn, ln)

where ci represent image intensity or colour and

li the length of the ith run of pixelsDepartment of CSE,Coimbatore

Run-length Encoding

Department of CSE,Coimbatore Figure: An encoded figure

Run Length Code


Run Length encoding – 8 X 8


• A Sequence:

111122233333311112222

Can be encoded as:

(1,4),(2,3),(3,6),(1,4),(2,4)

• In the first row we have 3 white pixels followed by 3 black pixels, 5

white pixels, 4 black pixels and 3 white pixels hence it is encoded as

(3,3,5,4,3).

The image is represented as {(3,3,5,4,3), (1,6,3,7,1) …….}

Start with white pixel always…


How would AAAAAAA be encoded?

*n5*x9ccc*h6 some other text *k8eee is decoded as what?



AAAAAAA is encoded as *A7

*n5*x9ccc*h6 some other text *k8eee is decoded as …

nnnnnxxxxxxxxxccchhhhhh some other text

kkkkkkkkeee

What has been described?

• Number systems and conversion between different bases.

• The data encoding schemes for text, color, image and sound.

• Compression technique and how data can be compressed using

RLE method.

Credits

Foundations of Computer Science --- Behrouz Forouzan, Firouz Mosharral

www.bbc.co.uk › Home › KS3 › Computing › Data representation

Google imagesDepartment of CSE,Coimbatore

Date post:	05-Feb-2021
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1.3 Data Encoding · 2019. 5. 20. · Bits and binary •All computer data is represented using...

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