Transcript Chapter 3 Logic Gates and Boolean Algebra

Chapter 3 Logic Gates and
Boolean Algebra – Part 1
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Objectives
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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
– DeMorgan’s 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
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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
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How a logic circuit’s output depends on the logic levels
present at the inputs.
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3-3 OR Operation with OR gates
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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
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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 x=A+B 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
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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
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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
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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 circuit’s 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 x=AB is read as “x equals A AND B.”
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