Introduction to Computer Science

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Binary codes(??????????)
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Example Representation

• Real World
• To be, or not to be that is the question
  Whether 'tis nobler in the mind to suffer The
  slings and arrows of outrageous fortune, Or to
  take arms against a sea of troubles, And by
  opposing end them? To die to sleep No more and
  by a sleep to say we end The heart-ache and the
  thousand natural shocks That flesh is heir to,
  'tis a consummation Devoutly to be wish'd.
• -- William Shakespeare - (from Hamlet Act 3,
  Scene 1)

• Computer World
• 10101000110111110000001100010101010001101100110011
  00110001011101110111111000101010110101000101101110
  11000101010110001011011101001000100010101010111010
  10101101101001011110101000110111110000001100010101
  01000110110011001100110001011101110111111000101010
  11010100010110111011000101010110001011011101001000
  10001010101011101010101101101001011110101000110111
  11000000110001010101000110110011001100110001011101
  11011111100010101011010100010110111011000101010110
  00101101110100100010001010101011101010101101101001
  0111

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Internal and External Representation of Data

• Real World
• Integers 34
• Signed Integers -156
• Decimal Numbers-23.431
• Text Hello
• Music Hey Jude
• Pictures

• Computer World
• Zeros and Ones110101

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Integer Representation

• We use a base 10 number system (Decimal)0, 1, 2,
  3, 4, 5, 6, 7, 8, 9
• 2,359

thousands
hundreds
ones
tens
100
101
102
103

• Computers use a base 2 number system (Binary)0,
  1
• 110101

20
21
22
23
24
25
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Conversion from Binary to Decimal
110101
20
21
22
23
24
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• 1x251x240x231x220x211x2053
• You Try it
• What are the following binary numbers in decimal?
• 11011
• 101100
• 110111

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Conversion from Decimal to Binary

• Perform repeated divisions by 2
• Keep track of the remainders
• 19 / 2 quotient 9 remainder 1
• 9 / 2 quotient 4 remainder 1
• 4 / 2 quotient 2 remainder 0
• 2 / 2 quotient 1 remainder 0
• 1 / 2 quotient 0 remainder 1
• Stop when the quotient is 0
• Decimal number 19 in binary is 10011
• You Try it
• Convert the following decimal numbers to binary
• 12
• 31
• 53

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Addition on Binary

• 0 0 0
• 1 0 1
• 0 1 1
• 1 1 10 (carry the 1)
• 1101 11010
• 1001 10011

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Fixed Sizes for Numbers

• On computers a fixed number of digits are
  typically used to store a number(8, 16, 32, or
  64 bits are common)
• The decimal number 3 in binary is 11, but using a
  fixed size of 8 bits it would be represented as
  00000011
• Try adding the binary numbers using a fixed size
  of 8 bits
• 11011001
• 10001011

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Internal and External Representation of Data

• Real World
• Integers 34
• Signed Integers -156
• Decimal Numbers-23.431
• Text Hello
• Music Hey Jude
• Pictures

v
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Signed Integers

• -134
• Sign/Magnitude Notation
• 110000110

magnitude

• Not frequently used on computers
• 2 numbers for zero
• Not easy to add/subtract

Sign 0 positive 1 negative
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Signed Integers

• -134
• Twos Complement Notation (for fixed size window
  16)
• Calculate the magnitude in binary0000000010000110
  
• Flip the bits1111111101111001
• Add one1111111101111010
• You Try it
• -129 -151

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Internal and External Representation of Data

• Real World
• Integers 34
• Signed Integers -156
• Decimal Numbers-23.431
• Text Hello
• Music Hey Jude
• Pictures

v
v
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Decimal Numbers

• 5.75
• Write the 5 in binary and the 0.75 in binary
• 5 101
• 0.75 0.11
• Normalize the number, keeping track of Mantissa
  and Exponent
• MxBE
• M Mantissa
• B Base (we use base 2)
• E Exponent
• Used fixed size window (16 bits)
• First bit is sign
• Next 9 bits are Mantissa
• Next bit is sign
• Last 5 bits are Exponent
• You Try It -8.25 11.5

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Text

• Fixed Size Window represents a character
• ASCII (8 bits) pg 141 in text
• Unicode (16 bits) represents 65,636
  characters

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Binary Representation of Sound and Images

• Multimedia data is sampled to store a digital
  form with or without detectable differences
• Representing sound data
• Sound data must be digitized for storage in a
  computer
• Digitizing means periodic sampling of amplitude
  values

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Binary Representation of Sound and Images
(continued)

• From samples, original sound can be approximated
• To improve the approximation
• Sample more frequently
• Use more bits for each sample value

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• Figure 4.5
• Digitization of an Analog Signal
• (a) Sampling the Original
• Signal
• (b) Recreating the
• Signal from the Sampled
• Values

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Binary Representation of Sound and Images
(continued)

• Representing image data
• Images are sampled by reading color and intensity
  values at even intervals across the image
• Each sampled point is a pixel
• Image quality depends on number of bits at each
  pixel

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Pictures

• For each pixel keep track of
• RGB values
• 0-255 (8-bit)

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Why Binary Representation

• Electronic devices are most reliable in a
  bistable environment
• Bistable environment
• Distinguishing only two electronic states
• Current flowing or not
• Direction of flow
• Computers are bistable binary representations

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Binary Storage Devices

• Magnetic core
• Historic device for computer memory
• Tiny magnetized rings flow of current sets the
  direction of magnetic field
• Binary values 0 and 1 are represented using the
  direction of the magnetic field

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• Figure 4.9
• Using Magnetic Cores to Represent Binary Values

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Binary Storage Devices (continued)

• Transistors
• Solid-state switches either permit or block
  current flow
• A control input causes state change
• Constructed from semiconductors

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• Figure 4.11
• Simplified Model of a Transistor