Digital Logic Circuit Design Putting logic to use

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Digital Logic Circuit DesignPutting logic to use

• Imperial Oil Summer Institute for Computer
  Science Educators
• Erin Lester

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Introduction

• So you know and love the fundamental logic gates
• But why do you know them? How are they used in
  real life?

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Digital Design

• When studying combinational circuits, the circuit
  comes before the truth table
• But this is backwards to reality
• In circuit design, we develop a truth table and
  then use it to determine the circuit needed

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The Design Process

• Suppose you want to design an electronic circuit
  for a 2-person voting system that determines if
  the majority of the votes are yes
• How do you go about this?
• What steps are involved?

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Step 1 Declaring Variables

• When working with digital logic we must use
  Boolean values (on/off or 0/1)
• The first step is to model the systems inputs
  and outputs as Boolean values
• The 2 vote inputs can be modeled as yes/no values
  A and B
• The output, which represents a majority yes
  scenario, can be modeled as Y

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Step 2 Determine the Truth Table

• The next step is to determine the truth table -
  that is, what combinations of inputs make our
  output(s) true (i.e. 1)
• In our case the truth table is as follows

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Two different versions of the truth table
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Step 3 Simplification

• Logic functions derived from a truth table can be
  very complex
• The Boolean logic functions derived are called
  minterm expressions
• These functions are the sum of products of
  Boolean variables e.g.

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Simplification continued

• For example, suppose that instead we wanted our
  output to be on (e.g. true) if either voters
  either agree or disagree(that is there isa
  consensus)

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Simplification continued

• In this case our Boolean expression would be
• The 2 values added (that is ored) together
  correspond to the expressions for the rows in the
  truth table with 1s
• These expressions are called minterms

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Simplification continued

• Minterm expressions can be simplified using
  Boolean Algebra Laws or Karnaugh Maps (Kmaps)
• For example, the expressionsimplifies to
• This is because it is true only in all of the
  cases when B is true

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Simplification continued

• Complex Boolean expression simplification can
  also be done using software
• Simple Kmap programs exist as well
• Advantages to simplification include economics,
  clarity and aesthetics

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Step 4 Create the circuit

• At this point you are ready to create your
  circuit using logic chips and input/output
  components
• For the voting system
• inputs can be simple solid state, on/off switches
• the logic is a single AND gate (74LS08 IC)
• inputs and outputs can be shown with LEDs

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Creating the circuit

• You could have students build their circuits into
  a working model
• Ideas include traffic light systems, voting
  systems, games, alarm/sensor systems

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Your Turn

• In a group of 2-4 people, design the logic
  circuit for one of the following
• A 2 person voting system with 3 outputs majority
  for, against and tie
• A 3 person voting system with 2 outputs for and
  against
• A walk signal for a standard traffic light
• A circuit that compares two 2-bit values and
  outputs if they are the same

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Boolean Algebra Laws

• And Laws
• A1A
• A00
• AAA
• AA0
• ABBA
• (AB)CA(BC)
• A(BC)(AB)(AC)
• (AB)AB

• Or Laws
• A11
• A00
• AAA
• AA1
• ABBA
• (AB)CA(BC)
• A(BC)(AB)(AC)
• (AB)AB

Show that A B A B A
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Design Resources

• Reid, Neal E. and Wilson, Stanley L. Computer
  Science Program Design and Technology. Toronto
  John Wiley Sons, 1985, pp 334-365.

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Minterm Resources

• Minterms http//doyle.wcdsb.ca/ICE4MI/digitial_el
  ectronics/minterms.htm
• Simplification with Karnaugh maps ( minterms)
  http//doyle.wcdsb.ca/ICE4MI/digitial_electronics/
  karnaugh_maps.htm
• Karnaugh map explorer http//doyle.wcdsb.ca/ICE4M
  I/digitial_electronics/KarnaughExplorer.htm

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Boolean Algebra Resources

• Boolean algebra laws http//doyle.wcdsb.ca/ICE4MI
  /digitial_electronics/boolean_algebra_laws.htm
• Boolean algebra simplification
  http//doyle.wcdsb.ca/ICE4MI/digitial_electronics/
  boolean_simplification.htm
• Logic gate simulator http//doyle.wcdsb.ca/ICE4MI
  /LearnAndOrNot/index.html