computer systems data representation 1221644513950568 9

7/31/2019 Computer Systems Data Representation 1221644513950568 9

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Higher Computing

Mr Arthur


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Course Outline

3 Main Units Computer Systems = 40 hours

Software Development = 40 hours

Artificial Intelligence = 40 hours Assessment

3 End of Unit Assessments (NABS)

Practical Coursework Tasks (/60 or 30%)

Written Exam (/140 or 70%)


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Computer Systems

5 units in the Computer Systems Section

1. Data Representation = 6 hours

2. Computer Structure = 7 hours

3. Peripherals = 5 hours4. Networking = 9 hours

5. Computer Software = 9 hours


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Aims of Lesson 1

1. How are numbers, text and imagesrepresented inside the computer system?

2. Discussing the 2 state computer system

3. Converting positive whole numbers to binaryand vice versa

4. Playing Binary Bingo


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Data Representation

100 billionswitches per sq. cm
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3Den%26sa%3DN


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Data Storage

Numbers, Text, andImages are all storedas a series of 1s and 0s

inside the computersystem.

These series of 1s and0s are made up of

pulses of electricityfrom 1 volt to 5 volts
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Decimal Counting System

When we represent numbers we use the decimalcounting system, for example

123,000

100,000 10,000 1,000 100 10 1

1 2 3 0 0 0

Since the computer is 2 state, the binary counting

system goes up by the power 2, rather than 10 i.e256 128 64 32 16 8 4 2 1


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How Positive Whole Numbers areStored

34

128 64 32 16 8 4 2 1

0 0 1 0 0 0 1 0

= 32 + 2

134

128 64 32 16 8 4 2 1

1 0 0 0 0 1 1 0

= 128 + 4 + 2


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Binary back to Decimal

1011 0011

128 64 32 16 8 4 2 1

1 0 1 1 0 0 1 1

= 128 + 32 + 16 + 2 + 1

=179


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Binary to Decimal

1. What is the decimalrepresentation of thefollowing 8 bits using

2s complement(a) 0001 0110

(b) 1000 1100

(c) 0111 0011

2. What is the 8 bitrepresentation of thefollowing decimal

numbers(a) 174

(b) 121

(c) 71


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Binary Bingo

42

81

21

16

121

73

101 75

127

13

209

32

56

175

192

186 176

121


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Data Storage

1 or 0 = 1 bit

8 bits = 1 byte

1024 bytes = 1 kilobyte

1024 kilobytes = 1 megabyte

1024 megabytes = 1 gigabyte


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Aims of Lesson 2

1. Representation of negative whole numbers

2. The 2s complement system


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Representing NegativeNumbers

The signed bit method

0000 0001 = 1

0000 0000 = 01000 0001 = -1

1000 0010 = -2

1000 0011 = -31000 0100 = -4


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Representing NegativeNumbers

There is a problem with this method??

Using 8 bits you can only store the decimalnumbers from

128 64 32 16 8 4 2 1

1 1 1 1 1 1 1 1

= 64 +32+16+8+4+2+1 = -127

128 64 32 16 8 4 2 10 1 1 1 1 1 1 1

=64+32+16+8+4+2+1=127

Rather than -255 to 255


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2s Complement

What is the 8 bit twos complement representation ofthe decimal number -101

101

128 64 32 16 8 4 2 10 1 1 0 0 1 0 1

Invert numbers

1 0 0 1 1 0 1 0

+1-101

1 0 0 1 1 0 1 1


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Negative Whole Numbers

What is the decimal representation of thefollowing 8 bits using 2s complement

1 0 1 0 1 1 1 1

You invert every number0 1 0 1 0 0 0 0

Then add 1

0 1 0 1 0 0 0 1

128 64 32 16 8 4 2 1

64+16+1

-81


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2s Complement Questions

1. What is the decimalrepresentation of thefollowing 8 bits using

2s complement(a) 1000 1011

(b) 1100 1100

(c) 1001 0111

(d) 1110 1100

2. What is the 8 bit twos

complementrepresentation of the

following decimalnumbers

(a) -45

(b) -121

(c) -176

(d) -71


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Aims of Lesson 3

1. So far we have looked at representingpositive and negative whole numbers usingbinary

2. We are now going to look at therepresentation of non whole numbers usingthe floating point system


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Representing Non WholeNumbers

How do we represent the number 128.75 inbinary?

128 + 0.5 + 0.25 = 128.75

128 64 32 16 8 4 2 1 0.5 0.25 0.125 0.0625

1 0 0 0 0 0 0 0 1 1 0 0


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Mantissa and Exponent

Mantissa

Exponent

8

8 4 2 1

1 0 0 0

128 64 32 16 8 4 2 1 0.5 0.25 0.125 0.0625

1 0 0 0 0 0 0 0 1 1 0 0

1 0 0 0 0 0 0 0 1 1 0 0


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Mantissa

Exponent

6

8 4 2 10 1 1 0

1 0 0 1 1 0 0 0 1 0

1 0 0 1 1 0 0 0 1 0

How do we represent the number 38.125 usingfloating point

32 16 8 4 2 1 0.5 0.25 0.125 0.0625


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Representing Non WholeNumbers

Mantissa relates to the precision of thenumber you can represent i.e 34.44454321

Exponent relates to the range of the number

1111 = 151111 1111 = 255

8 4 2 1 0.5 0.25 0.125 0.075 0.0375 0.01875 0.009375


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What is the decimal number if the Mantissa is

10010011 and the exponent is 0101

Exponent

8 4 2 1

0 1 0 1

= 5

Mantissa

1 0 0 1 0 0 1 1

Mantissa and Exponent

16 8 4 2 1 0.5 0.25 0.125

16 + 2 + 0.25 + 0.125 =18.375


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Aims of Lesson 4

1. So far we have looked at representingpositive and negative whole numbers usingbinary

2. We have also looked at representing nonwhole numbers using floating point.

3. Today we are going to practice convertingstorage capacities from bit, byte, kilobyte,

megabyte, gigabyte, terabyte4. Discuss how text is represented in a

computer system


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Storage Capacities

0 or 1 = 1 bit

8 bits = 1 byte

1024 bytes = 1 Kilobyte

1024 Kilobytes = 1 Megabyte

1024 Megabytes = 1 Gigabyte

1024 Gigabytes = 1 Terabyte


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Storage Conversions

I have a 2 Gigabyte IPOD Classic. How many512Kb songs can I store on the IPOD?

Convert 2Gb to Kb

2 X 1024 = 2048Mb

2048 X 1024 = 2,097,152Kb

512Kb 4096 Songs


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Storage Conversion Questions

1. I have a memory card for a Digital Camerawith a capacity of 4Gb. How many 460Kbimages can I store on the memory card?

2. Mr Haggarty has recently been working as aDJ at weekends. He has bought an externalhard disk to back up songs. How many 4Mb

songs would he be able to fit on the 80Gbhard disk?


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Solutions

4Gb X 1024 = 4096Mb

4096 X 1024 =4,194,304Kb

460Kb

= 9118 images

80Gb X 1024 =81920Mb

4Mb

= 20,480 songs


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How is Text Represented

ASCII

Each key on the keyboardis converted into a binarycode using 7 bits

Using 7 bits i.e 2 = 128characters can berepresented

Character Set

A list of all the characterswhich the computer canprocess

Control Characters

Codes 0 to 31 are nonprintable characters

7

Character Binary Decimal

tab 000 1001 9

return 000 1101 13

space 010 0000 32

! 010 0001 33

010 0010 34

1 011 0001 49

A 100 0001 65

a 110 0001 97


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How is Text Represented

Unicode (Universal Code) Each key on the keyboard is converted into a binary code

using 16 bits

Using 16 bits i.e 2 = 65,536 characters can be

represented Can represent Latin, Roman, Japanese characters

Advantages More characters can be represented

Disadvantages Takes up more than twice as much space for each

character

16


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Aims of Lesson 5

Last Lessons

Representing positivewhole numbers as binary

Representing negative

whole numbers using 2scomplement

Non whole numbers usingmantissa and exponent

Storage calculations

Looked at how text isrepresented using ASCIIand Unicode

Todays Lesson

1. Discuss graphicrepresentation

2. Calculate storage

capacities of colour Bit Mapgraphics

3. Bit Map v Vector


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BIT Map GraphicsSCREEN MEMORY

PIXEL

MEMORY REQUIRED

8 BITS X 8 BITS = 64 BITS

= 8 BYTES

Bit Map = the graphic is made upfrom a series of pixels


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Graphics Resolution

The smaller the size ofthe pixels, the finer thedetail of the image

800 x 600 pixels lowerquality than 1024 x 768

As the number of pixelsincreases so does the

storage space required

Pixel Patternusing 8x8 grid

Pixel Patternusing 16x16 grid


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Bit Map V Vector Graphics

Bit Map Graphic

Bit map packages paintpictures by changing thecolour of the pixels

Known as Paint Packages When shapes overlap, the

one on top rubs out theother

When you save a file the

whole screen is saved

The resolution of the imageis fixed when you create theimage

Vector Graphic

Work by drawing objects onthe screen

Known as Draw Packages

When shapes overlap theyremain as separate objects

Only the object attributesare stored taking up muchless space

Resolution Independent


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Aims of Lesson 6

Last Lessons Representing positive whole

numbers as binary Representing negative



Storage calculations Looked at how text is

represented using ASCIIand Unicode

Discuss graphicrepresentation

Calculate storage capacitiesof colour Bit Map graphics

Bit Map v Vector

Todays Lesson1. Discuss true colour

Todays Tasks1. Complete Data

Representation Questions

2. Read chapter in the book

Bit D th 1 bit


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True Colour

Bit Depth (Colour Depth) The number of bits used to represent colours in the

graphic 1 bit = black or white 2 bits = 4 colours 3 bits = 8 colours 8 bits = 256 colours 24 bits = 16,777,216 colours this is true colour

True Colour 24 bits

8 bits for red 8 bits for blue 8 bits for green

Bit Depth = 1 bit

Human eye cannot

distinguish betweenadjacent shades ofgrey when looking atmore than 200shades betweenblack and white

Bit Depth = 2 bit
http://images.google.com/imgres?imgurl=http://www.photoshopessentials.com/images/essentials/16-bit/6-colors.gif&imgrefurl=http://www.photoshopessentials.com/essentials/16-bit/&h=304&w=362&sz=8&hl=en&start=4&um=1&usg=__SVbFEA3WVuyrG2BWXiQ3LNxSLXQ=&tbnid=3lkFOTzTp1tB6M:&tbnh=102&tbnw=121&prev=/images%3Fq%3Dred%2Bgreen%2Bblue%26um%3D1%26hl%3Den


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Bit DepthsBit Depth = 2 bits

01

10

11

00


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Solutions

Question 1

2 inches X 90 = 180 pixels


180 X 180 = 32,400 pixels

in total 256 colours = 2 power 8

32,400 X 8 = 259,200 bits

259,200/8 = 32,400 bytes

32,400 / 1024 = 31.6Kb

Question 2

5 inches X 200 = 1000pixels


1000 X 600 = 600,000pixels in total

128 colours = 2 power 7

600,000 X 7 = 4,200,000bits

4,200,000/8 = 525,000bytes

525,000 / 1024 = 512.7Kb

Ai f L 7


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Aims of Lesson 7

Last Lessons Representing positive whole

numbers as binary Representing negative



Storage calculations Looked at how text is

represented using ASCIIand Unicode

Discuss graphicrepresentation

Calculate storage capacitiesof colour Bit Map graphics

Bit Map v Vector True Colour

Todays Lesson1. Data Compression

Todays Tasks1. Complete Compression task2. Issue Scholar logins

3. Complete DataRepresentation QuestionsSheet

4. Read chapter in the book


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Compression

Data compressionmeans reducing thesize of a file in order to

save backing storagespace.

2 types of compression

Lossless compression

Lossy compression


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Lossless Compression

Lossless means thatnone of the originaldata is lost

One method of losslesscompression involvescounting repeatingpixels

COLOUR = 10011000 11100000 e.g. 16 bits

NUMBER OF THE SAME PIXELS = 32

100000

STORAGE REQUIRED = 16 BITS + 6 BITS =22 BITS


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Lossy Compression

Lossy compression involvessacrificing some of the datain order to reduce the filesize

Deliberately losing some

types of information that oureyes and brains usuallyignore

Lossy is only suitable if theloss of data will not causethe file to become useless

JPEG is a file format thatuses lossy compression toreduce file sizes

D R i L i


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Data Representation Learning

Aims

1. Representation of positive numbers in binary up to32 bits

2. Conversion from binary to decimal and vice versa3. Representation of negative numbers using 2s

complement4. Representation of non whole numbers using

floating point with mantissa and exponent5. Conversion to and from bit, byte, kilobyte,

megabyte, gigabyte, terabyte

D R i L i


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Data Representation Learning

Aims

6. Unicode and its advantages over ASCII

7. Description of the bit map method of graphicsrepresentation

8. Description of the relationship between bit depthand the number of colours represented up to 24 bitdepth

9. Vector graphics

10. Relationship between bit depth and file size

computer systems data representation 1221644513950568 9

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