Information Representation

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Information Representation
2
Computer Architecture
3
Memory

• Memory is a collection of cells, each with a
  unique physical address for random (direct)
  access
• memory is divided into fixed-length units or
  words
• Information that is stored in memory cells is in
  binary coded format
• Instructions that make up programs
• Data text symbols, numbers, images, etc.

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Information Representation

• The Binary System Using On/Off Electrical
  States to Represent Data Instructions
• The binary system has only two digits--0 and 1.
• Bit - binary digit
• Byte - group of 8 bits used to represent one
  character, digit, or other value

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Representing Information withBit Combinations

• To encode entities (e.g., symbols), we need to
  assign a unique number to each entity (e.g.,
  social security number). Binary encoding means
  that we assign a unique combinations of bits to
  each object.
• One bit can be either 0 or 1. Therefore, one bit
  can represent only two things.
• To represent more than two things, we need
  multiple bits. Two bits can represent four things
  because there are four combinations of 0 and 1
  that can be made from two bits 00, 01, 10,11.
• If we want to represent more than four things, we
  need more than two bits. In general, 2n bits can
  represent 2n things because there are 2n
  combinations of 0 and 1 that can be made from n
  bits.
• Q how many bits do we need to encode all the 37
  people in the class?

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Information Representation

• Kilobyte approx. 1000 bytes (actually 210 1024
  bytes)
• Megabyte approx. 1,000,000 bytes (one million)
• Gigabyte approx. 1,000,000,000 bytes (one
  billion)
• Terabyte approx. 1 trillion bytes
• Petabyte approx. 1 quadrillion bytes

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Representing Text and Symbols

• To represent a text document in digital form, we
  simply need to be able to represent every
  possible character that may appear.
• There are finite number of characters to
  represent. So the general approach for
  representing characters is to list them all and
  assign each a number (represented in binary).
• An encoding scheme is simply a list of characters
  and the codes used to represent each one.
• To represent symbols, computers must use a
  standard encoding scheme, so that the same
  symbols have the same codes across different
  computers.

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ASCII Encoding Scheme

• ASCII stands for American Standard Code for
  Information Interchange. The ASCII character set
  originally uses 8 bits to represent each
  character, allowing for 256 (or 28) unique
  characters.

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Representing Text and Symbols

• ASCII - the binary code most widely used with
  microcomputers
• EBCDIC - used with large computers
• Unicode - uses two bytes for each character
  rather than one

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The Parity Bit
Parity bit - an extra bit attached to the end of
a byte for purposes of checking for accuracy

• Even parity - sum of bits must come out even
• Ex given code 01010101, the extended code is
  010101010
• Ex given code 01101101, the extended code is
  011011011
• Odd parity - sum of bits must come out odd

Even parity scheme
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Representing Numbers

• The binary number system
• Decimal is base 10 0,1,2,3,4,5,6,7,8,9
• Binary is base 2 0,1
• Any decimal number can be converted to binary by
  doing base conversion from base 10 to base 2.
• Any binary number can be converted to decimal by
  doing base conversion from base 2 to base 10.

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Number base 10 - decimal
The Decimal Number 101

• 102 101 100
• 100s 10s 1s
• 1 0 1
• x 1
  1
• x10
  0
• x100 100
• 
  101

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Number base 2 - binary
The Binary Number 101

• 22 21 20
• 4s 2s 1s
• 1 0 1
• x 1
  1
• x 2
  0
• x 4
  4
• 
  5

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Binary Conversion - Examples
1 0 1 1 0 1
32 0 8 4 0 1 45
20
21
22
23
24
25
1
2
4
8
16
32
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Binary Conversion - Examples
1 0 1 0 1 1 0
64 0 16 0 4 2 0 86
1
2
4
8
16
32
64
Easier way to remember Just add the values for
each position where there is a 1
2
4
8
16
32
64
1
128
128 32 16 4 1 181
1 0 1 1 0 1 0 1
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Hexadecimal Representation

• Hexadecimal (Hex) Base 16
• Hex digits 0, 1, 2, , 9, A, B, C, D, E, F

Decimal Hex Binary
8 8 1000
9 9 1001
10 A 1010
11 B 1011
12 C 1100
13 D 1101
14 E 1110
15 F 1111
Decimal Hex Binary
0 0 0000
1 1 0001
2 2 0010
3 3 0011
4 4 0100
5 5 0101
6 6 0110
7 7 0111
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Hexadecimal Representation

• Hex can be used as a short hand for long binary
  strings
• Use one Hex digit to represent every group of 4
  bits
• Start from the right and an go left grouping 4
  bit sequences
• Add leading 0s if the last group has less then 4
  bits

1 0 1 0 1 1 0 1 0 1 1 0
1 0 1 0 1 1 0 1 0 1 1 0
D
A
6
0 1 0 1 1 0 1 1
1 0 1 1 0 1 1
5
B
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Hexadecimal Representation

• What is Hex 4C8F in binary?

4 C 8 F
1111
1000
1100
0100
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Representing Images as Bit maps

• Image is collection of dots (pixels)
• Pixel picture element
• Black white one bit per pixel
• Color each pixel represented by combination of
  green, red, blue in varying intensity, to form
  all colors. Three bytes per pixel one byte (8
  bits) for each color intensity, 0-255 value
• Usually each byte is represented in Hex
• D4 7F 59 ? red (D4), green (7F), blue (59)
• For example, D4 is binary 1101 0100 which is
  decimal value 212
• Bit maps are not efficient
• 3 byte/pixel, for 1280 x 1024 pixels several
  megabytes
• Image cannot be enlarged, since pixels get bigger
  and image gets grainy or blocky
• .GIF and .JPEG formats compress images

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Image Formats

• GIF
• Graphics Interchange Format
• Developed by Compuserve (ISP)
• Stores only 256 colors
• Loses some picture quality but is simple and fast
• Common in computer action games
• JPEG (JPG)
• Joint Photographic Experts Group
• Stores differences between adjacent pixels, not
  absolute values
• Uses variable-length data (values take a minimum
  number of bits to store), uses only 5 of the
  space of bitmaps

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Image Formats

• Vector Images
• Pixels are not mapped
• Equations for the lines and curves making up the
  image are stored
• Image is stored as the instructions for drawing
  the image
• Images are easily scaled
• Modern type fonts are vector images
• Used in computer aided design (CAD) systems for
  blueprint drawings
• Good for three-dimensional drawings
• Windows metafile (.wmf) or Visio (.vsd)
• Cannot produce photographic images