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Computer Systems Data Representation

by iarthur on Sep 17, 2008

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Computer Systems Data RepresentationPresentation Transcript

• Higher Computing Mr Arthur
• 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%)
• Computer Systems
• 5 units in the Computer Systems Section
• Data Representation = 6 hours
• Computer Structure = 7 hours
• Peripherals = 5 hours
• Networking = 9 hours
• Computer Software = 9 hours
• Aims of Lesson 1
• How are numbers, text and images represented inside the computer system?
• Discussing the 2 state computer system
• Converting positive whole numbers to binary and vice versa
• Playing Binary Bingo
• Data Representation 100 billion switches per sq. cm
• Data Storage
• Numbers, Text, and Images are all stored as a series of 1s and 0s inside the computer system.
• These series of 1s and 0s are made up of pulses of electricity from 1 volt to 5 volts
• Decimal Counting System
• When we represent numbers we use the decimal counting 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.e
• 256 128 64 32 16 8 4 2 1
• How Positive Whole Numbers are Stored
• 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
• 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
• Binary to Decimal
• What is the decimal representation of the following 8 bits using 2s complement
• (a) 0001 0110
• (b) 1000 1100
• (c) 0111 0011
• What is the 8 bit representation of the following decimal numbers
• (a) 174
• (b) 121
• (c) 71
• Binary Bingo
• 42
• 81
• 21
• 16
• 121
• 73
• 101
• 75
• 127
• 13
• 209
• 32
• 56
• 175
• 192
• 186
• 176
• 121
• Data Storage
• 1 or 0 = 1 bit
• 8 bits = 1 byte
• 1024 bytes = 1 kilobyte
• 1024 kilobytes = 1 megabyte
• 1024 megabytes = 1 gigabyte
• Aims of Lesson 2
• Representation of negative whole numbers
• The 2s complement system
• Representing Negative Numbers
• The signed bit method
• 0000 0001 = 1
• 0000 0000 = 0
• 1000 0001 = -1
• 1000 0010 = -2
• 1000 0011 = -3
• 1000 0100 = -4
• Representing Negative Numbers
• There is a problem with this method??
• Using 8 bits you can only store the decimal numbers 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 1
• 0 1 1 1 1 1 1 1
• =64+32+16+8+4+2+1=127
• Rather than -255 to 255
• 2s Complement
• What is the 8 bit two’s complement representation of the decimal number -101
• 101
• 128 64 32 16 8 4 2 1
• 0 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
• Negative Whole Numbers
• What is the decimal representation of the following 8 bits using 2s complement
• 1 0 1 0 1 1 1 1
• You invert every number
• 0 1 0 1 0 0 0 0
• 0 1 0 1 0 0 0 1
• 128 64 32 16 8 4 2 1
• 64+16+1
• -81
• 2s Complement Questions
• What is the decimal representation of the following 8 bits using 2s complement
• (a) 1000 1011
• (b) 1100 1100
• (c) 1001 0111
• (d) 1110 1100
• What is the 8 bit two’s complement representation of the following decimal numbers
• (a) -45
• (b) -121
• (c) -176
• (d) -71
• Aims of Lesson 3
• So far we have looked at representing positive and negative whole numbers using binary
• We are now going to look at the representation of non whole numbers using the floating point system
• Representing Non Whole Numbers
• How do we represent the number 128.75 in binary?
• 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
• 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
• Mantissa
• Exponent
• 6
• 8 4 2 1
• 0 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 using floating point 32 16 8 4 2 1 0.5 0.25 0.125 0.0625
• Representing Non Whole Numbers
• Mantissa relates to the precision of the number you can represent i.e 34.44454321
• Exponent relates to the range of the number
• 1111 = 15
• 1111 1111 = 255
8 4 2 1 0.5 0.25 0.125 0.075 0.0375 0.01875 0.009375
• 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
• Aims of Lesson 4
• So far we have looked at representing positive and negative whole numbers using binary
• We have also looked at representing non whole numbers using floating point.
• Today we are going to practice converting storage capacities from bit, byte, kilobyte, megabyte, gigabyte, terabyte
• Discuss how text is represented in a computer system
• 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
• Storage Conversions
• I have a 2 Gigabyte IPOD Classic. How many 512Kb songs can I store on the IPOD?
• Convert 2Gb to Kb
• 2 X 1024 = 2048Mb
• 2048 X 1024 = 2,097,152Kb
• 512Kb
• 4096 Songs
• Storage Conversion Questions
• I have a memory card for a Digital Camera with a capacity of 4Gb. How many 460Kb images can I store on the memory card?
• Mr Haggarty has recently been working as a DJ at weekends. He has bought an external hard disk to back up songs. How many 4Mb songs would he be able to fit on the 80Gb hard disk?
• Solutions
• 4Gb X 1024 = 4096Mb
• 4096 X 1024 = 4,194,304Kb
• 460Kb
• = 9118 images
• 80Gb X 1024 = 81920Mb
• 4Mb
• = 20,480 songs
• How is Text Represented
• ASCII
• Each key on the keyboard is converted into a binary code using 7 bits
• Using 7 bits i.e 2 = 128 characters can be represented
• Character Set
• A list of all the characters which the computer can process
• Control Characters
• Codes 0 to 31 are non printable characters
7 97 110 0001 a 65 100 0001 A 49 011 0001 1 34 010 0010 ‘ 33 010 0001 ! 32 010 0000 space 13 000 1101 return 9 000 1001 tab Decimal Binary Character
• 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
• More characters can be represented
• Takes up more than twice as much space for each character
16
• Aims of Lesson 5
• Last Lessons
• Representing positive whole numbers as binary
• Representing negative whole numbers using 2s complement
• Non whole numbers using mantissa and exponent
• Storage calculations
• Looked at how text is represented using ASCII and Unicode
• Today’s Lesson
• Discuss graphic representation
• Calculate storage capacities of colour Bit Map graphics
• Bit Map v Vector
• BIT Map Graphics SCREEN MEMORY PIXEL MEMORY REQUIRED 8 BITS X 8 BITS = 64 BITS = 8 BYTES Bit Map = the graphic is made up from a series of pixels
• Graphics Resolution
• The smaller the size of the pixels, the finer the detail of the image
• 800 x 600 pixels lower quality than 1024 x 768
• As the number of pixels increases so does the storage space required
Pixel Pattern using 8x8 grid Pixel Pattern using 16x16 grid
• Calculating Storage Capacities of Bit Mapped Images
• Storage Requirements = total number of pixels * number of bits used for each pixel
• This picture of Mr Haggarty has a resolution of 300dpi. The image is 2 inches by 4 inches in 128 colours
• 300 X 2 = width 600 pixels
• 300 X 4 = height 1200 pixels
• Total pixels = 600 X 1200 = 720,000 pixels
• Each pixel = 7 bits i.e. 2 = 128 colours
• 720,000 X 7 = 5,040,000 bits / 8 = 630,000 bytes
• 630,000 / 1024 = 615Kb
7
• Bit Map V Vector Graphics
• Bit Map Graphic
• Bit map packages paint pictures by changing the colour of the pixels
• Known as “Paint Packages”
• When shapes overlap, the one on top rubs out the other
• When you save a file the whole screen is saved
• The resolution of the image is fixed when you create the image
• Vector Graphic
• Work by drawing objects on the screen
• Known as “Draw Packages”
• When shapes overlap they remain as separate objects
• Only the object attributes are stored taking up much less space
• Resolution Independent
• Aims of Lesson 6
• Last Lessons
• Representing positive whole numbers as binary
• Representing negative whole numbers using 2s complement
• Non whole numbers using mantissa and exponent
• Storage calculations
• Looked at how text is represented using ASCII and Unicode
• Discuss graphic representation
• Calculate storage capacities of colour Bit Map graphics
• Bit Map v Vector
• Today’s Lesson
• Discuss true colour
• Complete Data Representation Questions
• Read chapter in the book
• 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 between adjacent shades of grey when looking at more than 200 shades between black and white Bit Depth = 2 bit
• Bit Depths Bit Depth = 2 bits 01 10 11 00
• Solutions
• Question 1
• 2 inches X 90 = 180 pixels
• 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 = 1000 pixels
• 3 inches X 200 = 600 pixels
• 1000 X 600 = 600,000 pixels in total
• 128 colours = 2 power 7
• 600,000 X 7 = 4,200,000 bits
• 4,200,000/8 = 525,000 bytes
• 525,000 / 1024 = 512.7Kb
• Aims of Lesson 7
• Last Lessons
• Representing positive whole numbers as binary
• Representing negative whole numbers using 2s complement
• Non whole numbers using mantissa and exponent
• Storage calculations
• Looked at how text is represented using ASCII and Unicode
• Discuss graphic representation
• Calculate storage capacities of colour Bit Map graphics
• Bit Map v Vector
• True Colour
• Today’s Lesson
• Data Compression
• Complete Data Representation Questions Sheet
• Read chapter in the book
• Compression
• Data compression means reducing the size of a file in order to save backing storage space.
• 2 types of compression
• Lossless compression
• Lossy compression
• Lossless Compression
• Lossless means that none of the original data is lost
• One method of lossless compression involves counting repeating pixels
COLOUR = 10011000 11100000 e.g. 16 bits NUMBER OF THE SAME PIXELS = 32 100000 STORAGE REQUIRED = 16 BITS + 6 BITS = 22 BITS
• Lossy Compression
• Lossy compression involves sacrificing some of the data in order to reduce the file size
• Deliberately losing some types of information that our eyes and brains usually ignore
• Lossy is only suitable if the loss of data will not cause the file to become useless
• JPEG is a file format that uses lossy compression to reduce file sizes
• Data Representation – Learning Aims
• Representation of positive numbers in binary up to 32 bits
• Conversion from binary to decimal and vice versa
• Representation of negative numbers using 2s complement
• Representation of non whole numbers using floating point with mantissa and exponent
• Conversion to and from bit, byte, kilobyte, megabyte, gigabyte, terabyte
• Data Representation – Learning Aims
• Unicode and its advantages over ASCII
• Description of the bit map method of graphics representation
• Description of the relationship between bit depth and the number of colours represented up to 24 bit depth
• Vector graphics
• Relationship between bit depth and file size