Chapter 1 Introduction to Digital Systems Design

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Chapter 1 Introduction to Digital Systems Design

• ECEn 224

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Digital vs. Analog

• Analog systems represent information using
  physical quantities
• Voltage on a wire, magnetic field strength
• Digital systems represent information using
  binary digits, or bits
• 1 or 0, high or low, on or off

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Positional Number Systems

• Two discrete values are insufficient for most
  applications
• We combine bits to represent more values
• We use a positional number system for binary just
  like we do in decimal

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Positional Number Systems

• Decimal, base 10, means we have 10 digits (0-9)
• Decimal example
• 103210 1x103 0x102 3x101 2x100
• Hexadecimal, base 16, means we have 16 digits
  (0-9, A-F)
• Hexadecimal example
• 2A516 2x162 10x161 5x160 512 160 5
  677
• Binary, base 2, follows the same pattern
• Binary example
• 10112 1x23 0x22 1x21 1x20 8 0 2 1
  11
• Counting in any base is analogous to counting in
  decimal

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Digital vs. Analog

• Analog thermometer
• 0V to 10V, could be used to represent 0 to 100
  F
• Each 1/10th volt represents 1 degree
• Digital thermometer
• 7-bit binary number could be used to represent 0
  to 127 F
• Seven bits can be used to represent the numbers 0
  to 127

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Digital Precision

• How would you represent 10.5 F?
• Analog example 1.05V
• Digital example ????
• 00010102 1010
• 00010112 1110
• We must either add bits or decrease the range

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Digital Precision

• 9-bit thermometer, 0 to 127.75 F
• Each discrete number increase represents 0.25 F
• 10.5 F ? 10.5/0.25 42 1010102
• 7-bit thermometer, 0 to 12.7 F
• Each discrete number represents 12.7/127 0.1
  F
• 10.5 F ? 10.5/0.1 105 11010012
• It is not possible to represent all values
  exactly using digital representation
• Example 1/3 cant be represented in binary, just
  like it cant be represented in decimal

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Example Analog Photography

• An analog camera uses a chemical reaction in the
  film when exposed to light
• The amount of exposure is directly related to the
  amount of light that hits the film

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Example Digital Photography

• A digital camera uses an array of light-sensitive
  receptors that measure the light as a binary
  number
• Image quality is determined mostly by two
  factors
• The number of bits per pixel
• The number of pixels per image

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Example Digital Photography
1284x897 pixels, 24-bit color
100x70 pixels, 24-bit color
1284x897 pixels, 6-bit color
100x70 pixels, 6-bit color
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Analog vs. Digital Storage

• Analog storage mediums fade over time due to
  gradual physical degradation
• Photos turn yellow with time
• Cassette audio tapes lose their clarity
• Digital storage mediums dont fade like analog
• If a 0 or 1 fades it will still be a 0 or 1
• A .jpg image taken 10 years ago is exactly the
  same today

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Analog vs. Digital Storage

• Making an analog copy implies measuring the
  storage medium
• Always introduces some errors
• Copies of copies are even worse
• Making digital copies implies distinguishing 0s
  from 1s so copies are exact
• Copies can be made without any error
• Copies of copies are identical

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Analog vs. Digital Processing

• Modern computers and digital circuits make it
  easy to do extremely complex processing
• Digital processing allows precision and error to
  be exactly predicted

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Combinational vs. Sequential Circuits

• Digital circuits consist of binary inputs and
  outputs
• In combinational circuits, the output is a direct
  function of its inputs
• In sequential circuits the output depends on the
  current input and previous inputs
• Sequential circuits contain memory that tracks
  state
• A clock is used to signal when to change states

A
B
X
Y
C
D
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Combinational vs. Sequential

• Combinational example Clock chime
• Inputs seconds and minutes
• Output chime
• Behavior Output chime is 1 if and only if
  seconds is 0 and minutes is 0, 15, 30, or 45.
• Sequential example Counter
• Inputs inc and clk
• Output count
• Behavior Increment count on clk edge if and only
  if inc is 1