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Computer Systems Data Representation

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Higher Computing Mr Arthur
Course Outline ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Computer Systems ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Aims of Lesson 1 ,[object Object],[object Object],[object Object],[object Object]
Data Representation 100 billion switches per sq. cm
Data Storage ,[object Object],[object Object]
Decimal Counting System ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
How Positive Whole Numbers are Stored ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Binary back to Decimal ,[object Object],[object Object],[object Object],[object Object],[object Object]
Binary to Decimal ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Binary Bingo ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Data Storage ,[object Object],[object Object],[object Object],[object Object],[object Object]
Aims of Lesson 2 ,[object Object],[object Object]
Representing Negative Numbers ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Representing Negative Numbers ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
2s Complement ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Negative Whole Numbers ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
2s Complement Questions ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Aims of Lesson 3 ,[object Object],[object Object]
Representing Non Whole Numbers ,[object Object],[object Object],[object Object],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 ,[object Object],[object Object],[object Object],[object Object],[object Object],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
[object Object],[object Object],[object Object],[object Object],[object Object],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 ,[object Object],[object Object],[object Object],[object Object],8 4 2 1 0.5 0.25 0.125 0.075 0.0375 0.01875 0.009375
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],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 ,[object Object],[object Object],[object Object],[object Object]
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 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Storage Conversion Questions ,[object Object],[object Object]
Solutions ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
How is Text Represented ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],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 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],16
Aims of Lesson 5 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
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 ,[object Object],[object Object],[object Object],Pixel Pattern using 8x8 grid Pixel Pattern using 16x16 grid
Calculating Storage Capacities of Bit Mapped Images ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],7
Bit Map V Vector Graphics ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Aims of Lesson 6 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
True Colour ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],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 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Aims of Lesson 7 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Compression ,[object Object],[object Object],[object Object],[object Object]
Lossless Compression ,[object Object],[object Object],COLOUR = 10011000 11100000 e.g. 16 bits NUMBER OF THE SAME PIXELS = 32 100000 STORAGE REQUIRED = 16 BITS + 6 BITS = 22 BITS
Lossy Compression ,[object Object],[object Object],[object Object],[object Object]
Data Representation – Learning Aims ,[object Object],[object Object],[object Object],[object Object],[object Object]
Data Representation – Learning Aims ,[object Object],[object Object],[object Object],[object Object],[object Object]

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Computer Systems Data Representation

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  • 5. Data Representation 100 billion switches per sq. cm
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  • 26. 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
  • 27.
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  • 33. 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
  • 34.
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  • 36.
  • 37.
  • 38.
  • 39. Bit Depths Bit Depth = 2 bits 01 10 11 00
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