CHAPTER 1 SAFETY

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Programmable Logic Controllers Third Edition
Frank D. Petruzella McGraw-Hill
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Chapter 4
Fundamentals of Logic
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The Binary Concept
Many things can be thought of as existing in one
of two states.
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The Binary Concept
This two-state binary concept, applied to gates,
can be the basis for making decisions.
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Gate Decision Making
The Logical AND
Light Switch
AND Gate
High Beam Light
High Beam Switch
The automotive high beam light can only be turned
on when the light switch AND high beam switch are
on.
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Gate Decision Making
The Logical OR
Passenger Door Switch
Dome Light
OR Gate
Driver Door Switch
The automotive dome light will be turned on when
the passenger door switch OR the driver
door switch is activated.
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AND Function
The outcome or output is called Y and the input
signals are called A, B, C, etc.
Binary 1 represents the presence of a signal or
the occurrence of some event, while binary 0
represents the absence of the signal or
nonoccurrence of the event.
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AND Gate Function Application Example 1
Basic Rules
The device has two or more inputs and one output
If any input is 0, the output will be 0
If all inputs are 1, the output will be 1
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AND Gate Function Application Example 2
The AND gate operates like a series circuit. The
light will be on only when both switch A and
switch B are closed.
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OR Function
An OR gate can have any number of inputs but
only one output.
The OR gate output is 1 if one or more inputs are
1.
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OR Gate Function Application Example 1
Basic Rules
If all inputs are 0, the output will be 0
If one or more inputs are 1, the output will be 1
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OR Gate Function Application Example 2
The OR gate operates like a parallel
circuit. The light will be on if switch A or
switch B is closed.
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NOT Function
The NOT function has only one input and one
output.
The NOT output is 1 if the input is 0. The NOT
output is 0 if the input is 1.
Since the output is always the reverse of the
input it is called an inverter.
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NOT Gate Application Example 1
Acts like a normally closed pushbutton in series
with the output.
The light will be on if the pushbutton is not
pressed.
The light will be off if the pushbutton is n
pressed.
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NOT Gate Application Example 2
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NAND Function
The NAND gate functions like an AND gate with
an inverter connected to its output.
The only time the NAND gate output is 0 is when
all inputs are binary 1.
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NOR Function
The NOR gate functions like an OR gate with
an inverter connected to its output.
The only time the NAND gate output is 1 is when
all inputs are binary 0.
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XOR (exclusive-OR) Function
The XOR function has two inputs and one output.
The output of this gate is HIGH only when one
input or the other is HIGH, but not both.
It is commonly used for comparison of two binary
numbers.
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• 1. The two binary states can be defined as
• high or low
• on or off
• 1 or 0
• all of these

2. A gate can have one or more outputs but only
one input. (True/False)
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3. The ______ table shows the resulting output
for each possible gate input conditions. a. input
status c. data b. output status d.
truth
4. A light that is "off" or a switch that is
"open" would normally be represented by a binary
1. (True/False)
5. The OR function, implemented using
contacts, requires contacts connected in series.
(True/False)
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6. With an AND gate, if any input is 0, the
output will be 0. (True/False)
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• 8. Which of the following gates is commonly used
• for the comparison of two binary numbers?
• NAND
• NOR
• XOR
• NOT

9. The basic rule for an XOR function is that
if one or the other, but not both, inputs are 1
the output is 1. (True/False)
10. A NAND gate is an AND gate with an
inverter connected to the output. (True/False)
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Boolean Equation Example 1
Each logic function can be expressed in terms of
a Boolean expression
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Boolean Equation Example 2
Any combination of control can be expressed in
terms of a Boolean equation
AB
Y AB C
A B
Y (A B) C
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Boolean Equation Example 2
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Circuit Development Using A Boolean Expression
Example 1
1. AND gate with Input A and B
2. OR gate with Input C an output from
previous AND gate.
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Circuit Development Using A Boolean Expression
Example 2
AND gate with Input B and C
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Producing A Boolean Expression From A
Given Circuit Example 1
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Producing A Boolean Expression From A
Given Circuit Example 2
Logic equation Y AB AB
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Hard Wired versus Programmed Logic
The term hardwired logic refers to logic control
functions that are determined by the way
devices are interconnected.
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Hardwired Stop/Start Motor Control Circuit
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Programmed Stop/Start Motor Control Circuit
A rung is the contact symbolism required to
control an output. Each rung is a combination of
input conditions connected from left to right
with the symbol that represents the output at
the far right.
The input and output field devices remain the
same as those required for the hardwired circuit.
The instructions used are the relay equivalent
of normally open (NO) and normally closed
(NC) contacts and coils
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Hard Wired versus Programmed Logic Example 4-1
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Hard Wired versus Programmed Logic Example 4-2
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Hard Wired versus Programmed Logic Example 4-3
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Hard Wired versus Programmed Logic Example 4-4
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Hard Wired versus Programmed Logic Example 4-5
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Hard Wired versus Programmed Logic Example 4-6
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Hard Wired versus Programmed Logic Example 4-7
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Hard Wired versus Programmed Logic Example 4-8
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Hard Wired versus Programmed Logic Example 4-9
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Selecting Word-Level Logic Instructions
If you want to know when matching bits in two
different words are both ON use the AND
instruction.
If you want to know when one or both matching
bits in two different words are ON use the OR
instruction.
If you want to know when one or the other bit
of matching bits in two different words is ON use
the XOR instruction.
If you want to reverse the status of bits in a
word use the NOT instruction.
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Programmed AND Instruction
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Programmed AND Instruction
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Programmed OR Instruction
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Programmed XOR Instruction
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Programmed NOT Instruction
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11. Hardwired logic is changeable only by
altering the way devices are connected.
(True/False)
12. Each programmed rung is a combination
of input conditions connected from left to right
with the symbol that represents the output at the
far right. (True/False)
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14. The correct Boolean equation for the
combination logic gate circuit shown is
a. Y A B C D c. Y ( A B ) (
C D ) b. Y ( AB ) ( CD ) d. Y ( AB )
( CD )
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19. If you want to know when matching bits in two
different words are both "on", you would use the
_____ logic instruction. a. AND c.
XOR b. OR d. NOT
20. If you want to reverse the state of bits in a
word, you would use the ______ logic
instruction. a. AND c. XOR b. OR
d. NOT