Computer Systems Data Representation

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]

Computer Systems Data Representation

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Computer Systems Data Representation