Lesson 1 The Basic Principles of Digital Systems

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Lesson 1 The Basic Principles of Digital Systems

• David L. Koehler

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Two Basic Types of Variables

• Analog
• Digital

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What are Variables?

• Variable An identified number object that can
  accommodate change.
• Age (may be analog or digital)
• Body Weight (may be analog or digital)
• Body Height (usually digital in inches)
• (By contrast, a Constant is an identified number
  object that does not change.)

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What is an Analog Variable?

• A variable that can be assigned any level
  according to any arbitrary resolution.
  Associated with measuring.
• Temperature, Pressure, Distance, Voltage, Current

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What is a Digital Variable?

• Digital variables have steps abrupt changes with
  no possibility of any intermediate levels.
  Associated with counting discrete instances
  rather than measuring a property.
• Counting the leaves in a given book
• Counting the cents in a quantity of money
• Counting the steps in a flight of stairs
• Counting students in a class section

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What are Functions?

• Function A rule for translating one variable
  into another variable.
• Example Fahrenheit degrees (Celsius degrees X
  180/100) 32

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Signals are functions.

• Signals are quantities impressed on a carrier.
• Easier or cheaper to transmit from place to
  place.
• Easier to process accurately through intermediate
  functions.
• Easier to record.
• Common carriers for signals
• Current in a conductor
• Voltage between conductors
• Low pressure air in a pipe or tube.
• Light beam (heliograph, flashing light, fiber
  optic)
• Radio wave
• Mechanical linkage (pull chain, tracker)

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Analog Signals

• A signal is a representation of a measured
  quantity.
• Signal representation facilitates transmitting,
  processing, and recording a quantity.
• An analog signal smoothly changes (not step)
  from one level to another.

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Digital Signals

• Changes stepwise from one level to another.

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Whats a Digital Logic Level?

• Digital Logic has only TWO SIGNAL LEVELS
• True, False
• 1,0
• 5V, 0V
• On, Off
• High, Low

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What is positive logic?

• True or 1 is represented by a higher value
  (voltage).
• False or 0 is represented by a lower value
  (voltage).
• Many other conventions are used but positive
  logic is very common.

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How are numbers represented electrically.

• Quite often voltage is used as the carrier of a
  digital signal.
• True or 1 is commonly represented by 5VDC.
• False or 0 is commonly represented by 0VDC.

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So much for 1 and 0, how about larger numbers?

• At any node, the voltage will be either 0VDC or
  5VDC representing 0 or 1.
• To represent numbers greater than 1, we need more
  nodes.
• The largest number represented by n nodes is
  2n-1. Thus it takes 4 nodes to represent the
  number 15.

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What is the Positional Numbering System?

• Integers are weighted depending on their position
  from the radix point.
• In the decimal system we call the radix point the
  decimal point.

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Decimal is a positional number system.

• In the decimal number (123), the most significant
  digit stands for 100 counters, the least
  significant digit stands for 3 counters.
• Positional weights are related to powers of 10.

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Binary is a positional number system.

• Positional weights are related to powers of 2.

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Binary, Hex, and Decimal

• Each hex digit corresponds to a four bit binary
  value.
• Hex is just shorthand for binary.

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Converting Hex to Decimal

• Power of 16 multipliers
• Decimal equivalents of hex characters

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Periodic Digital Waveforms

• Constant high time
• Constant low time
• Constant duty cycle
• Constant period

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Aperiodic Waveforms

• Low time varies
• High time varies
• Duty Cycle varies
• Period varies

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Pulse Analysis

• Rise time and fall time between 10 and 90
• Pulse width between 50 points

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Glossary

• Amplitude
• Analog
• Aperiodic waveform
• Binary number system
• Continuous
• Digital
• Digital waveform
• Discrete

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Glossary

• Duty Cycle
• Edge
• Fall time tf
• Falling edge
• Frequency
• Hexadecimal number system
• Leading edge
• Least Significant Bit
• Logic High

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Glossary

• Logic level
• Logic LOW
• Most Significant Bit
• Negative Logic
• Period (T)
• Periodic waveform
• Positional notation
• Positive Logic
• Pulse
• Pulse width tw

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Glossary

• Radix point
• Rise time tr
• Rising edge
• Time High
• Time Low
• Trailing edge