Chapter 3 Logic Gates and Boolean Algebra Part 1

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Chapter 3 Logic Gates and Boolean Algebra Part 1
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Objectives

• Three basic logic operations AND, OR, NOT
• Operation of logic circuits and construction of
  truth tables
• Timing diagrams for the various logic-circuit
  gates
• Boolean expression for the logic circuits
• Implement logic circuits using AND, OR, NOT
• Simplify logic expressions
• DeMorgans theorem
• Using NAND or NOR to implement a circuit
• Alternate gate symbols vs. standard logic-gate
  symbols
• Active high Active low

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3-1 Boolean Constants and variables

• Boolean constants and variables are allowed to
  have only two possible values, 0 or 1.
• Boolean 0 and 1 do not represent actual numbers
  but instead represent the state of a voltage
  variable, or what is called its logic level.
• 0/1 and Low/High are used most of the time.
• Three Logic operations AND, OR, NOT
• Logic Gates
• Digital circuits constructed from diodes,
  transistors, and resistors whose output is the
  result of a basic logic operation(OR, AND, NOT)
  performed on the inputs.

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3-2 Truth Tables

• How a logic circuits output depends on the logic
  levels present at the inputs.

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3-3 OR Operation with OR gates

• Truth Table and circuit symbol

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3-3 symbol and truth table for a three-input OR
gate
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Summary of OR operation

• Produce a result of 1 whenever any input is 1.
  Otherwise 0.
• An OR gate is a logic circuit that performs an OR
  operation on the circuit's input
• The expression xAB is read as x equals A OR B

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Example of the use of an OR gate in an Alarm
system
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Example 2
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Example3
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Review Questions

• What is the only set of input conditions that
  will produce a LOW output for any OR gate?
• Write the Boolean expression for a six-input OR
  gate
• If the A input in previous example is permanently
  kept at the 1 level, what will the resultant
  output waveform be?

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3-4 And Operation with And Gates

• Truth Table and Gate symbol

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Truth Table and Symbol for a three-input AND gate
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Summary of the AND operation

• The AND operation is performed the same as
  ordinary multiplication of 1s and 0s.
• An AND gate is a logic circuit that performs the
  AND operation on the circuits inputs.
• An AND gate output will be 1 only for the case
  when all inputs are 1 for all other cases the
  output will be 0.
• The expression xAB is read as x equals A AND B.