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Chapter 3
Basic Logic Gates
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Objectives

You should be able to:
Describe the operation and use of AND gates and
OR gates.
 Construct truth tables for AND and OR gates.
 Draw timing diagrams for AND and OR gates.
 Use timing analysis to describe the operation of an
ENABLE function.
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Objectives
(Continued)
Sketch external connections to IC chips to
implement AND and OR logic circuits.
 Explain how to use a logic pulser and a logic probe
to troubleshoot digital ICs.
 Describe the operation and use of NAND and NOR
gates.
 Construct truth tables for NAND and NOR gates.

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Objectives
(Continued)
Draw timing diagrams for NAND and NOR gates.
 Use the outputs of a Johnson shift counter to
generate specialized waveforms using combinations
of the five basic gates.
 Develop a comparison of Boolean equations and
truth tables for the five basic gates.
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Logic Gates are the building blocks of Digital
Electronic Circuits
Logic Gates have one Output Terminal and one
or more Input Terminals
The Output will be High (1) or Low (0),
depending on the value of the Inputs and the
type of Gate
The AND Gate

The output, X, is HIGH if input A AND input
B are both HIGH.
If A = 1 and B = 1, then X = 1.
 If A = 0 or B = 0, then X = 0.
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The AND Gate
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The AND Gate
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Boolean Equation: X = A•B or X = AB
Read as “X equals A AND B”
 Can have more than two inputs
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Number of input/output combinations = 2N
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N = number of input bits
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The OR Gate
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The output at X will be HIGH whenever input
A OR input B is HIGH or both are HIGH
If A = 1 and/or B = 1, then X = 1
 If A = 0 and B = 0, then X = 0
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The OR Gate
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The OR Gate
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Boolean Equation: X = A + B
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Read as, “ X = A or B”
Can have more than two inputs
Number of combinations = 2N

N = number of input bits
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Timing Analysis
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Timing diagrams are used to analyze the output
response to varying inputs
Oscilloscope
Display plots voltage versus time
 Dual-trace can display two waveforms at a time.
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Logic analyzer
Can display state tables that show binary levels on
signal lines
 Can display up to 16 waveforms at a time
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Timing Analysis
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Timing Analysis
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Determine the gate output
for the input waveforms
below.
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Enable and Disable Functions
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Enable function using AND gate
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Enable and Disable Functions
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Disable function using OR gate
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Using Integrated Circuit Logic
Gates
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Enable and Disable
Pin Connections
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Introduction to
Troubleshooting Techniques
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The procedure used to find the fault or
trouble in a circuit.
Logic Probe shows voltage level
Indicator lamp glows strongly if high
 Lamp is off if output is low
 Glows dimly if floating
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Floating - open circuit, neither high nor low
Logic Pulser – provides a known digital signal
to a circuit
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Discussion Points

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Describe how a logic probe and pulser could
be used to troubleshoot an AND gate.
Describe how a logic probe and pulser could
be used to troubleshoot an OR gate.
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The Inverter
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Used to complement (invert) a digital signal
When A = 1, X = 0
 When A = 0, X = 1
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The Inverter
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Truth Table
Boolean Equation: X = A
Inversion bar
NOT gate
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The NAND Gate
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Same as the AND gate except that its output
is inverted
If A = 1 and B = 1, X = 0
 If A = 0 or B = 0, A = 1
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The NAND Gate
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Truth Table
Boolean Equation: X = AB
Multiple inputs - the output is always HIGH
unless all inputs go HIGH
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The NOR Gate
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Same as the OR gate except that its output is
inverted
If A = 1 or B = 1, X = 0
 If A = 0 and B = 0, X = 1
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The NOR Gate
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Truth Table
Boolean Equation: X = A + B
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Logic Gate Waveform Generation
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Repetitive waveform
Waveform generator
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Johnson shift counter
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Discussion Point
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Which Johnson counter outputs must be
connected to a 3-input AND gate to enable
only CP #4?
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Discussion Point
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Sketch the output waveform resulting from
inputting the Johnson counter outputs
shown:
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Using IC Logic Gates
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Hex - six gates
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Using IC Logic Gates
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Quad - four gates
Three-, four-, and eight-input configurations
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Common IC Logic Gates
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IEEE/IEC Standard Logic
Symbols
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Discussion Point
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Briefly describe the operation of each of the
basic logic gates:
AND
 OR
 NOT (inverter)
 NAND
 NOR
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Discussion Point
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Create a truth table for a three input NAND
gate.
Write the Boolean equation for a 3 input OR
gate.
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Discussion Point
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Sketch the output waveform (X) for the 2-input
AND gate shown.
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Discussion Point

Sketch the output waveforms for the Johnson shift
counter outputs shown:
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Discussion Point
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Determine the problem (if any) with the 7427 NOR
IC using the logic probe results shown:
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Summary
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The AND gate requires that all inputs are
HIGH in order to get a HIGH output.
The OR gate outputs a HIGH if any of its
inputs are HIGH.
An effective way to measure the precise timing
relationships of digital waveforms is with an
oscilloscope or a logic analyzer.
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Summary
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Beside providing the basic logic functions, AND
and OR gates can also be used to enable or
disable a signal to pass from one point to
another.
There are several integrated circuits available in
both TTL and CMOS that provide the basic
logic functions.
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Summary
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Two important troubleshooting tools are the
logic pulser and the logic probe. The pulser is
used to inject pulses into a circuit under test.
The probe reads the level at a point in a circuit
to determine is it is HIGH, LOW, or floating.
An inverter provides an output that is the
complement of its input.
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Summary
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A NAND gate outputs a LOW when all of its
inputs are HIGH.
A NOR gate outputs a HIGH when all of its
inputs are LOW.
Specialized waveforms can be created by using a
repetitive waveform generator and the basic
gates.
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Summary
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Manufacturers’ data manuals are used by the
technician to find the pin configuration and
operating characteristics for the ICs used in
modern circuitry.
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