Digital Logic Tutorial and Design

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• Digital Logic Tutorial and Design
• http//www.electronicsteacher.com

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Digital Logic Lab(A mini-lab experience)

• We are going to build both a combination lock and
  a flashing railroad crossing signal using digital
  logic devices
• To build these circuits we will draw upon
  knowledge or resources developed by several areas
  of electrical engineering
• First, we will need to learn a little about
  digital logic

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Some Definitions

• Definition Discrete System - a system with a
  finite number of sizes or measures
• Shoes, Dresses, Pants, Bolts, Pencils
• Definition Digital System - a Discrete System
  with only two values of system variables 1 and
  0
• True/False Yes/No Male/Female On/Off
• Lets compare digital and continuous (analog)
  systems
• Digital signals are binary analog signals are
  real-valued numbers
• Digital is less susceptible to noise

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Analog Waveform
5
Voltage (V)
Time
0
Digital Waveform
5
1
1
Voltage (V)
0
Time
0
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AND Operator

• Lets look at the relationship between the
  semantic and logical operator known as the AND
  operator
• Consider
• If the car is fueled AND the engine works,
• then the engine will start

AND Operator Truth Table

• AND means that both conditions must be true in
  order for the conclusion to be true

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Digital AND

• We can build an electrical device that performs
  the logical AND operation on voltage equivalents
  of logic values
• An AND gate has the
• electrical schematic

For digital logic True 1 is 5 volts False 0
is 0 volts

• Practice with the Excel spreadsheet

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OR Operator

• Another basic operator is the OR
• Consider
• If I have cash OR a credit card,
• then I can pay the bill
• OR works such that the output is true, if either
  of the two inputs is true

OR Operator Truth Table
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NOT Operator/Inverter Gate

• The NOT gate reverses the input

NOT Operator Truth Table

• All digital computers are built using only three
  gate types AND, OR, and NOT

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XOR (Exclusive OR) Operator

• Lets look at the relationship between the
  semantic and logical operator known as the XOR
  operator
• Consider a biological example
• If gender A XOR gender B,
• then reproduction is possible
• XOR works such that output is activated (equal to
  one) if both inputs are of a different value
• Try the Excel spreadsheet exercise

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Digital XOR

• We can build an electrical device that performs
  the logical XOR operation on voltage equivalents
  of logic values
• An XOR gate has the
• electrical schematic

XOR Operator Truth Table
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Digital Combination Lock

• Design and Software Simulation

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Multi-Input AND Gate

• AND gates can be built with any number of inputs
• Consider the symbol for the 4-input AND gate

• F is true only when all the inputs are true (1s)
• Using the Excel workbook EE-WISE-DigitalLab,
  open the Digital Locks worksheet, and test this
  circuit

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Digital Combination Lock

• Using 3 two-input AND gates, we could build a
  combination lock that requires a four-digit code,
  specifically 1 1 1 1
• The number of inputs could be increased by using
  more and more AND gates

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Digital Combination Lock

• We could build a combination lock that only uses
  the AND gate, but that would be of little use
  since everyone would know our combination, namely
  1 1 1 1
• To build a more interesting combination lock, we
  will utilize the NOT (inverter) gate

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Digital Combination Lock

• Lets build a combination lock whose input (key
  code) combination is 0 1 1 0

1
0
AND
1
AND
1
1
1
AND
1
0
1

• Is there any other combination that works?

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Picking a Digital Lock

• Use the truth table below to record the lock
  outputs for the different lock combinations in
  the Pick the Locks worksheet

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Digital Railroad Crossing Signal

• Design and Software Simulation

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Digital Railroad Crossing Signal

• Now, lets develop a digital circuit whose output
  changes over time
• We are all familiar with a railroad crossing
  signal that alternates flashing red lights
• In addition to constructing the digital
  combination lock, we will build the railroad
  crossing signal in the lab, so lets begin by
  designing the circuit

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Railroad Crossing Signal Design

• Here we will need some type of timing signal that
  will tell the lights when to turn on and off
• The problem is that we seemingly need two timing
  signals since one light is on while the other is
  off, and vice versa
• A digital logic implementation can allow us to
  save cost by using only a single timing signal
• The design effort is then one of considering
  which gate(s) need to be used to achieve the
  alternating signal patterns

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Railroad Crossing Signal
Turn-on voltage puts out a constant 5 volts
1 AND 0 outputs 0 1 AND 1 outputs 1
0/1
AND
1
Square wave is being repeatedly turned on then off
0/1
XOR
1/0
1 XOR 0 outputs 1 1 XOR 1 outputs 0
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Railroad Crossing Signal Simulation

• The Railroad Xing Simulation worksheet may be
  used in Excel to view (over time) the activation
  of the RR crossing lights
• Note that this Excel simulation uses some
  advanced features of Excel such as iteration and
  conditional formatting to achieve the software
  simulation