design of information and control systems · 2020. 9. 27. · design of information and control...
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Design of Information and Control SystemsProgrammable Logic Controllers - Fundamentals
Institute of Information Engineering, Automation and Mathematics
22. marca 2020
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Contents
What are programmable logic controllers? (PLC)
Implementation of logic using Boolean algebra
Ladder Logic - LAD
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Programmable Logic Controller (PLC)
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Programmable Logic Controller
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Programmable Logic Controller
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Programmable Logic Controller
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Programmable Logic Controller
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Programmable Logic Controller
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Programmable Logic Controller
Electric
sourceMain
unit
Input and
output
modules
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Programmable Logic Controller
Electric
source
Main
unit
Input and
output
modules
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Programmable Logic Controller
Electric
sourceMain
unit
Input and
output
modules
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Programmable Logic Controller
Electric
sourceMain
unit
Input and
output
modules
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Programmable Logic Controller
Electric
sourceMain
unit
Input and
output
modules
Electric source:
from outlet - 230V
produces 24V forpowering the PLC andmodules
Main unit:
processor
memory
communication
peripherals
Modules:
input
output
digital/analog
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Programmable Logic Controller
PLC Siemens S7-300
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Programmable Logic Controller
PLC Siemens S7-300
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Programmable Logic Controller
PLC Siemens S7-1200
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Programmable Logic Controller
PLC Siemens S7-1200
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Programmable Logic Controller
Processor and memory
PLC
Logic
inputs outputs
switch
sensor
light
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Programmable Logic Controller
light
spınac
sensor
switch
snımac 2
tlacidlo 2
Processor and memory
PLC
Logic
inputs outputs
024V
0V
3.3V
10
1
3.3V24V
3.3V24V
00V
0V
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Programmable Logic Controller
light
spınac
sensor
switch
snımac 2
tlacidlo 2
Processor and memory
PLC
Logic
inputs outputs
024V
0V
3.3V
10
1
3.3V24V
1
3.3V24V
13.3V
24V
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Programmable Logic Controller
light
spınac
sensor
switch
snımac 2
tlacidlo 2
Processor and memory
PLC
Logic
inputs outputs
024V
0V
3.3V
1 1
3.3V24V
1
3.3V24V
13.3V
24V
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Programmable Logic Controller
light
spınac
sensor
switch
snımac 2
tlacidlo 2
Processor and memory
PLC
Logic
inputs outputs
024V
0V
3.3V
1 1
3.3V24V
1
3.3V24V
13.3V
24V
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Programmable Logic Controller
PLC performs a set of simple tasks:
reads the state of inputs
executes logical and mathematical instructions
based on results, activates/deactivates outputs
For the purpose of this lecture, PLC will perform only logical operations.
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Programmable Logic Controller
PLC performs a set of simple tasks:
reads the state of inputs
executes logical and mathematical instructions
based on results, activates/deactivates outputs
For the purpose of this lecture, PLC will perform only logical operations.
![Page 25: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/25.jpg)
Boolean algebra
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Logical operations
operate only with values 0 and 1 (yes/no, on/off, true/false)
use logical functions - values on input are mapped to values on outputcan be written down in multiple ways
logical statement (mathematical form)ladder diagram (graphical form)electrical diagram (graphical form with switches)electronic diagram (graphical form with logic gates)
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Logical operations
NOT - logical negationlogical function: Y = A
conjunction: is not
NOT gate
Truth table
A A0
1
1
0
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Logical operations
NOT - logical negationlogical function: Y = A
conjunction: is not
NOT gate
Truth table
A A0 11
0
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Logical operations
NOT - logical negationlogical function: Y = A
conjunction: is not
NOT gate
Truth table
A A0 11 0
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Logical operations
AND - logical conjunctionlogical function: Y = A · B
conjunction: and; at the same time
AND gate
Truth table
A B A · B0 0
0
0 1
0
1 0
0
1 1
1
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Logical operations
AND - logical conjunctionlogical function: Y = A · B
conjunction: and; at the same time
AND gate
Truth table
A B A · B0 0 00 1
0
1 0
0
1 1
1
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Logical operations
AND - logical conjunctionlogical function: Y = A · B
conjunction: and; at the same time
AND gate
Truth table
A B A · B0 0 00 1 01 0
0
1 1
1
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Logical operations
AND - logical conjunctionlogical function: Y = A · B
conjunction: and; at the same time
AND gate
Truth table
A B A · B0 0 00 1 01 0 01 1
1
![Page 34: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/34.jpg)
Logical operations
AND - logical conjunctionlogical function: Y = A · B
conjunction: and; at the same time
AND gate
Truth table
A B A · B0 0 00 1 01 0 01 1 1
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Logical operations
OR - logical disjunctionlogical function: Y = A + B
conjunction: or
OR gate
Truth table
A B A + B0 0
0
0 1
1
1 0
1
1 1
1
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Logical operations
OR - logical disjunctionlogical function: Y = A + B
conjunction: or
OR gate
Truth table
A B A + B0 0 00 1
1
1 0
1
1 1
1
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Logical operations
OR - logical disjunctionlogical function: Y = A + B
conjunction: or
OR gate
Truth table
A B A + B0 0 00 1 11 0
1
1 1
1
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Logical operations
OR - logical disjunctionlogical function: Y = A + B
conjunction: or
OR gate
Truth table
A B A + B0 0 00 1 11 0 11 1
1
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Logical operations
OR - logical disjunctionlogical function: Y = A + B
conjunction: or
OR gate
Truth table
A B A + B0 0 00 1 11 0 11 1 1
![Page 40: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/40.jpg)
Logical operations
NAND - negated logicalconjunction
logical function: Y = A · B
conjunction: not at the same time
NAND gate
Truth table
A B A · B0 0
1
0 1
1
1 0
1
1 1
0
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Logical operations
NAND - negated logicalconjunction
logical function: Y = A · B
conjunction: not at the same time
NAND gate
Truth table
A B A · B0 0 10 1
1
1 0
1
1 1
0
![Page 42: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/42.jpg)
Logical operations
NAND - negated logicalconjunction
logical function: Y = A · B
conjunction: not at the same time
NAND gate
Truth table
A B A · B0 0 10 1 11 0
1
1 1
0
![Page 43: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/43.jpg)
Logical operations
NAND - negated logicalconjunction
logical function: Y = A · B
conjunction: not at the same time
NAND gate
Truth table
A B A · B0 0 10 1 11 0 11 1
0
![Page 44: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/44.jpg)
Logical operations
NAND - negated logicalconjunction
logical function: Y = A · B
conjunction: not at the same time
NAND gate
Truth table
A B A · B0 0 10 1 11 0 11 1 0
![Page 45: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/45.jpg)
Logical operations
NOR - negated logicaldisjunction
logical function: Y = A + B
conjunction: neither
NOR gate
Truth table
A B A + B0 0
1
0 1
0
1 0
0
1 1
0
![Page 46: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/46.jpg)
Logical operations
NOR - negated logicaldisjunction
logical function: Y = A + B
conjunction: neither
NOR gate
Truth table
A B A + B0 0 10 1
0
1 0
0
1 1
0
![Page 47: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/47.jpg)
Logical operations
NOR - negated logicaldisjunction
logical function: Y = A + B
conjunction: neither
NOR gate
Truth table
A B A + B0 0 10 1 01 0
0
1 1
0
![Page 48: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/48.jpg)
Logical operations
NOR - negated logicaldisjunction
logical function: Y = A + B
conjunction: neither
NOR gate
Truth table
A B A + B0 0 10 1 01 0 01 1
0
![Page 49: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/49.jpg)
Logical operations
NOR - negated logicaldisjunction
logical function: Y = A + B
conjunction: neither
NOR gate
Truth table
A B A + B0 0 10 1 01 0 01 1 0
![Page 50: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/50.jpg)
Logical operations
XOR - exclusive logicaldisjunction
logical function: Y = A ⊕ B
conjunction: one or the other but notboth
XOR gate
Truth table
A B A ⊕ B0 0
0
0 1
1
1 0
1
1 1
0
![Page 51: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/51.jpg)
Logical operations
XOR - exclusive logicaldisjunction
logical function: Y = A ⊕ B
conjunction: one or the other but notboth
XOR gate
Truth table
A B A ⊕ B0 0 00 1
1
1 0
1
1 1
0
![Page 52: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/52.jpg)
Logical operations
XOR - exclusive logicaldisjunction
logical function: Y = A ⊕ B
conjunction: one or the other but notboth
XOR gate
Truth table
A B A ⊕ B0 0 00 1 11 0
1
1 1
0
![Page 53: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/53.jpg)
Logical operations
XOR - exclusive logicaldisjunction
logical function: Y = A ⊕ B
conjunction: one or the other but notboth
XOR gate
Truth table
A B A ⊕ B0 0 00 1 11 0 11 1
0
![Page 54: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/54.jpg)
Logical operations
XOR - exclusive logicaldisjunction
logical function: Y = A ⊕ B
conjunction: one or the other but notboth
XOR gate
Truth table
A B A ⊕ B0 0 00 1 11 0 11 1 0
![Page 55: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/55.jpg)
Ladder Logic
![Page 56: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/56.jpg)
Ladder Logic
PLC programming
a way to design logical controllers
program is represented graphically
![Page 57: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/57.jpg)
Ladder Logic
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Ladder Logic
Basic elements of ladder logic
Logical network
1
1
1
Normallyopen
contact
Normallyclosedcontact
input
input
0
0
1
1 1
0
![Page 59: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/59.jpg)
Ladder Logic
Basic elements of ladder logic
Logical network
1
1
1
Normallyopen
contact
Normallyclosedcontact
input
input
0
0
1
1 1
0
![Page 60: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/60.jpg)
Ladder Logic
Basic elements of ladder logic
Logical network
1
1
1
Normallyopen
contact
Normallyclosedcontact
input
input
0
0
1
1 1
0
![Page 61: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/61.jpg)
Ladder Logic
Basic elements of ladder logic
Logical network
1
1
1
Normallyopen
contact
Normallyclosedcontact
input
input
1
0
1
1 1
1
![Page 62: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/62.jpg)
Ladder Logic
Basic elements of ladder logic
Logical network
1
1
1
Normallyopen
contact
Normallyclosedcontact
input
input
1
1
1
1 0
1
![Page 63: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/63.jpg)
Ladder Logic
Example: light bulb control
a single room with 3 light switches
pressing of either switch will result in bulb turning on
![Page 64: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/64.jpg)
Ladder Logic
Example: light bulb control
ovl adaci e prvky(vstupy)
ovl adany prvok(vystup)
zdroj el ektri ny
switch 1
switch 2
switch 3
light bulb
![Page 65: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/65.jpg)
Ladder Logic
Example: light bulb control
ovl adaci e prvky(vstupy)
ovl adany prvok(vystup)
zdroj el ektri ny
switch 1
switch 2
switch 3
light bulb
electrical source
![Page 66: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/66.jpg)
Ladder Logic
Example: light bulb control
ovl adaci e prvky(vstupy)
ovl adany prvok(vystup)
zdroj el ektri ny
switch 1
switch 2
switch 3
light bulb
electrical source
control elements(inputs)
![Page 67: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/67.jpg)
Ladder Logic
Example: light bulb control
ovl adaci e prvky(vstupy)
zdroj el ektri ny
switch 1
switch 2
switch 3
light bulb
electrical source
control elements(inputs)
controlled element(output)
![Page 68: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/68.jpg)
Ladder Logic
Example: light bulb control
ovl adaci e prvky(vstupy)
zdroj el ektri ny
switch 1
switch 2
switch 3
light bulb
switch 1 = 0
switch 3 = 0switch 2 = 0
light = 0
![Page 69: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/69.jpg)
Ladder Logic
Example: light bulb control
ovl adaci e prvky(vstupy)
zdroj el ektri ny
switch 1
switch 2
switch 3
light bulb
switch 1 = 1
switch 3 = 0switch 2 = 0
light = 1
![Page 70: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/70.jpg)
Ladder Logic
Example: light bulb control
ovl adaci e prvky(vstupy)
zdroj el ektri ny
switch 1
switch 2
switch 3
light bulb
switch 1 = 1
switch 3 = 0switch 2 = 0
light = 1
![Page 71: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/71.jpg)
Ladder Logic
Example: light bulb control
ovl adaci e prvky(vstupy)
zdroj el ektri ny
switch 1
switch 2
switch 3
light bulb
switch 1 = 0
switch 3 = 0switch 2 = 1
light = 1
![Page 72: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/72.jpg)
Ladder Logic
Example: light bulb control
ovl adaci e prvky(vstupy)
zdroj el ektri ny
switch 1
switch 2
switch 3
light bulb
switch 1 = 0
switch 3 = 0switch 2 = 1
light = 1
![Page 73: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/73.jpg)
Ladder Logic
Example: light bulb control
ovl adaci e prvky(vstupy)
zdroj el ektri ny
switch 1
switch 2
switch 3
light bulb
switch 1 = 0
switch 3 = 1switch 2 = 0
light = 1
![Page 74: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/74.jpg)
Ladder Logic
Example: light bulb control
ovl adaci e prvky(vstupy)
zdroj el ektri ny
switch 1
switch 2
switch 3
light bulb
switch 1 = 0
switch 3 = 1switch 2 = 1
light = 1
![Page 75: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/75.jpg)
Ladder Logic
Example: light bulb control
ovl adaci e prvky(vstupy)
zdroj el ektri ny
switch 1
switch 2
switch 3
light bulb
The bulb is ON ifat least ONE
of the switches ispressed.
![Page 76: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/76.jpg)
Ladder Logic
Example: car engine start
The engine will start only if the key is present, the brake pedal is stepped on,and driver presses start button.
All of these requirements (inputs) must be fulfilled at the same time.
![Page 77: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/77.jpg)
Ladder Logic
Example: car engine start
key break button
start
brake
![Page 78: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/78.jpg)
Ladder Logic
Example: car engine start
key break button
start
brake
![Page 79: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/79.jpg)
Ladder Logic
Example: car engine start
key break button
start
brake
![Page 80: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/80.jpg)
Ladder Logic
Example: car engine start
key break button
start
brake
![Page 81: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/81.jpg)
Ladder Logic
Example: car engine start
key break button
start
brake
![Page 82: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/82.jpg)
Ladder Logic
Example: car engine start
key break button
start
brake
![Page 83: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/83.jpg)
Ladder Logic
Example: car engine start
key break button
start
brake
![Page 84: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/84.jpg)
Ladder Logic
Example: car engine start
key break button
start
brake
![Page 85: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/85.jpg)
Ladder Logic
Example: car engine start
key break button
start
brake
![Page 86: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/86.jpg)
Ladder Logic
Example: car engine start
key break button
start
brake
![Page 87: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/87.jpg)
Ladder Logic
Example: car engine start
key break button
start
All the inputs must be active at the same time.
brake
![Page 88: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/88.jpg)
Ladder Logic
Light bulb example
The light will turn on if:
switch 1 is pressed
OR
switch 2 is pressed
OR
switch 3 is pressed
Logical disjunction: LIGHT = S1 + S2 + S3
![Page 89: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/89.jpg)
Ladder Logic
Light bulb example
The light will turn on if:
switch 1 is pressed
OR
switch 2 is pressed
OR
switch 3 is pressed
Logical disjunction: LIGHT = S1 + S2 + S3
![Page 90: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/90.jpg)
Ladder Logic
Light bulb example
The light will turn on if:
switch 1 is pressed
OR
switch 2 is pressed
OR
switch 3 is pressed
Logical disjunction: LIGHT = S1 + S2 + S3
![Page 91: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/91.jpg)
Ladder Logic
Light bulb example
The light will turn on if:
switch 1 is pressed
OR
switch 2 is pressed
OR
switch 3 is pressed
Logical disjunction: LIGHT = S1 + S2 + S3
![Page 92: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/92.jpg)
Ladder Logic
Light bulb example
The light will turn on if:
switch 1 is pressed
OR
switch 2 is pressed
OR
switch 3 is pressed
Logical disjunction: LIGHT = S1 + S2 + S3
![Page 93: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/93.jpg)
Ladder Logic
Light bulb example
The light will turn on if:
switch 1 is pressed
OR
switch 2 is pressed
OR
switch 3 is pressed
Logical disjunction: LIGHT = S1 + S2 + S3
![Page 94: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/94.jpg)
Ladder Logic
Light bulb example
The light will turn on if:
switch 1 is pressed
OR
switch 2 is pressed
OR
switch 3 is pressed
Logical disjunction: LIGHT = S1 + S2 + S3
![Page 95: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/95.jpg)
Ladder Logic
Engine start example
The engine will start if:
key is present
AND
brake pedal is stepped on
AND
start button is pressed
Logical conjunction: START = KEY · BRAKE · BUTTON
![Page 96: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/96.jpg)
Ladder Logic
Engine start example
The engine will start if:
key is present
AND
brake pedal is stepped on
AND
start button is pressed
Logical conjunction: START = KEY · BRAKE · BUTTON
![Page 97: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/97.jpg)
Ladder Logic
Engine start example
The engine will start if:
key is present
AND
brake pedal is stepped on
AND
start button is pressed
Logical conjunction: START = KEY · BRAKE · BUTTON
![Page 98: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/98.jpg)
Ladder Logic
Engine start example
The engine will start if:
key is present
AND
brake pedal is stepped on
AND
start button is pressed
Logical conjunction: START = KEY · BRAKE · BUTTON
![Page 99: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/99.jpg)
Ladder Logic
Engine start example
The engine will start if:
key is present
AND
brake pedal is stepped on
AND
start button is pressed
Logical conjunction: START = KEY · BRAKE · BUTTON
![Page 100: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/100.jpg)
Ladder Logic
Engine start example
The engine will start if:
key is present
AND
brake pedal is stepped on
AND
start button is pressed
Logical conjunction: START = KEY · BRAKE · BUTTON
![Page 101: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/101.jpg)
Ladder Logic
Engine start example
The engine will start if:
key is present
AND
brake pedal is stepped on
AND
start button is pressed
Logical conjunction: START = KEY · BRAKE · BUTTON
![Page 102: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/102.jpg)
Logical operations in LAD
![Page 103: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/103.jpg)
Logical operations in LAD
NOT - logical negationlogical function: Y = A
conjunction: is not
Y
A
NOT in LAD
Truth table
A A0 11 0
![Page 104: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/104.jpg)
Logical operations in LAD
NOT - logical negationlogical function: Y = A
conjunction: is not
Y
A
NOT in LAD
Truth table
A A0 11 0
![Page 105: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/105.jpg)
Logical operations in LAD
AND - logical conjunctionlogical function: Y = A · B
conjunction: and; at the same time
Y
A B
AND in LAD
Truth table
A B A · B0 0 00 1 01 0 01 1 1
![Page 106: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/106.jpg)
Logical operations in LAD
AND - logical conjunctionlogical function: Y = A · B
conjunction: and; at the same time
Y
A B
AND in LAD
Truth table
A B A · B0 0 00 1 01 0 01 1 1
![Page 107: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/107.jpg)
Logical operations in LAD
OR - logical disjunctionlogical function: Y = A + B
conjunction: or
Y
A
B
OR in LAD
Truth table
A B A + B0 0 00 1 11 0 11 1 1
![Page 108: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/108.jpg)
Logical operations in LAD
OR - logical disjunctionlogical function: Y = A + B
conjunction: or
Y
A
B
OR in LAD
Truth table
A B A + B0 0 00 1 11 0 11 1 1
![Page 109: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/109.jpg)
Logical operations in LAD
NAND - negated logicalconjunction
logical function: Y = A · B
conjunction: not at the same time
Y
A
B
NAND in LAD
Truth table
A B A · B0 0 10 1 11 0 11 1 0
![Page 110: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/110.jpg)
Logical operations in LAD
NAND - negated logicalconjunction
logical function: Y = A · B
conjunction: not at the same time
Y
A
B
NAND in LAD
Truth table
A B A · B0 0 10 1 11 0 11 1 0
![Page 111: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/111.jpg)
Logical operations in LAD
NOR - negated logicaldisjunction
logical function: Y = A + B
conjunction: neither
Y
A B
NOR in LAD
Truth table
A B A + B0 0 10 1 01 0 01 1 0
![Page 112: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/112.jpg)
Logical operations in LAD
NOR - negated logicaldisjunction
logical function: Y = A + B
conjunction: neither
Y
A B
NOR in LAD
Truth table
A B A + B0 0 10 1 01 0 01 1 0
![Page 113: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/113.jpg)
Logical operations in LAD
XOR - exclusive logicaldisjunction
logical function: Y = A ⊕ B
conjunction: one or the other but notboth
Y
A B
A B
XOR in LAD
Truth table
A B A ⊕ B0 0 00 1 11 0 11 1 0
![Page 114: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/114.jpg)
Logical operations in LAD
XOR - exclusive logicaldisjunction
logical function: Y = A ⊕ B
conjunction: one or the other but notboth
Y
A B
A B
XOR in LAD
Truth table
A B A ⊕ B0 0 00 1 11 0 11 1 0
![Page 115: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/115.jpg)
Construction of LAD from logical statements
D = (A · B) + C
C D
A B
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Construction of LAD from logical statements
D = (A · B) + C
C D
A B
![Page 117: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/117.jpg)
Construction of LAD from logical statements
D = (A · B) + C
C D
A B
![Page 118: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/118.jpg)
Construction of LAD from logical statements
D = (A · B) + C
C D
A B
![Page 119: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/119.jpg)
Construction of LAD from logical statements
D = (A · B) + C
C D
A B
![Page 120: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/120.jpg)
Construction of LAD from logical statements
D = (A · B) + C
C D
A B
![Page 121: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/121.jpg)
Construction of LAD from logical statements
D = (A · B) + C
C D
A B
![Page 122: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/122.jpg)
Construction of LAD from logical statements
D = (A · B) + C
C D
A B
![Page 123: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/123.jpg)
Construction of LAD from logical statements
X = (A · ∼B) + (B · ∼A)
A BX
A B
![Page 124: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/124.jpg)
Construction of LAD from logical statements
X = (A · ∼B) + (B · ∼A)
A BX
A B
![Page 125: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/125.jpg)
Construction of LAD from logical statements
X = (A · ∼B) + (B · ∼A)
A BX
A B
![Page 126: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/126.jpg)
Construction of LAD from logical statements
X = (A · ∼B) + (B · ∼A)
A BX
A B
![Page 127: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/127.jpg)
Construction of LAD from logical statements
X = (A · ∼B) + (B · ∼A)
A BX
A B
![Page 128: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/128.jpg)
Construction of LAD from logical statements
X = (A · ∼B) + (B · ∼A)
A BX
A B
![Page 129: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/129.jpg)
Construction of LAD from logical statements
X = (A · ∼B) + (B · ∼A)
A BX
A B
![Page 130: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/130.jpg)
Construction of LAD from logical statements
X = (A · ∼B) + (B · ∼A)
X
A B
A B
![Page 131: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/131.jpg)
Construction of LAD from logical statements
X = (A · ∼B) + (B · ∼A)
X
A B
A B
![Page 132: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/132.jpg)
Construction of LAD from logical statements
X = (A · ∼B) + (B · ∼A)
X
A B
A B
![Page 133: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/133.jpg)
Construction of logical statements from LAD
E
A
D C B
F
A = ∼D+ E +∼F( )·C ∼B·
![Page 134: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/134.jpg)
Construction of logical statements from LAD
E
A
D C B
F
A = ∼D+ E +∼F( )·C ∼B·
![Page 135: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/135.jpg)
Construction of logical statements from LAD
E
A
D C B
F
A = ∼D+ E +∼F( )·C ∼B·
![Page 136: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/136.jpg)
Construction of logical statements from LAD
E
A
D C B
F
A = ∼D+ E +∼F( )·C ∼B·
![Page 137: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/137.jpg)
Construction of logical statements from LAD
E
A
D C B
F
A = ∼D+ E +∼F( )·C ∼B·
![Page 138: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/138.jpg)
Construction of logical statements from LAD
E
A
D C B
F
A = ∼D+ E +∼F( )·C ∼B·
![Page 139: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/139.jpg)
Construction of logical statements from LAD
E
A
D C B
F
A = ∼D+ E +∼F( )·C ∼B·
![Page 140: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/140.jpg)
Construction of logical statements from LAD
E
A
D C B
F
A = ∼D+ E +∼F( )·C ∼B·
![Page 141: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/141.jpg)
Construction of logical statements from LAD
E
A
D C B
F
A = ∼D+ E +∼F( )·C ∼B·
![Page 142: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/142.jpg)
Construction of logical statements from LAD
E
A
D C B
F
A = ∼D+ E +∼F( )·C ∼B·
![Page 143: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/143.jpg)
Simplification of logical statements
B
Y
A B D
A
Y = D · (D · (A · B +∼B · A) +∼D · C · A)
D
A
C D
A B
Y
Y = D ·A
![Page 144: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/144.jpg)
Simplification of logical statements
![Page 145: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/145.jpg)
Basic axioms
Idempotency:A + A = A A · A = A
Associativity:(A + B) + C = A + (B + C) (A · B) · C = A · (B · C)
Commutative property:A + B = B + A A · B = B · A
Distributivity:A+(B·C) = (A+B)·(A+C) A · (B+C) = (A ·B)+(A ·C)
Identity:A + 0 = A A + 1 = 1 A · 0 = 0 A · 1 = A
Complement:A +∼A = 1 A · ∼A = 0
![Page 146: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/146.jpg)
Simplification of logical statements
Y = D · (D · (A · B +∼B · A) +∼D · C · A)
Y = D · (D · (A · B +∼B · A) +∼D · C · A)Y = D · (D · A · (B +∼B) +∼D · C · A)Y = D · (D · A · (B +∼B) +∼D · C · A)
Y = D · (D · A · 1 +∼D · C · A)Y = D · (D · A +∼D · C · A)Y = D · (D · A +∼D · C · A)
Y = D · A · (D +∼D · C)Y = D · A · (D +∼D · C)
Y = D · A · D + D · A · ∼D · CY = D · A · D + D · A · ∼D · C
Y = D · A · D + 0 · A · CY = D · A · D
Y = D · A
![Page 147: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/147.jpg)
Simplification of logical statements
Y = D · (D · (A · B +∼B · A) +∼D · C · A)Y = D · (D · (A · B +∼B · A) +∼D · C · A)
Y = D · (D · A · (B +∼B) +∼D · C · A)Y = D · (D · A · (B +∼B) +∼D · C · A)
Y = D · (D · A · 1 +∼D · C · A)Y = D · (D · A +∼D · C · A)Y = D · (D · A +∼D · C · A)
Y = D · A · (D +∼D · C)Y = D · A · (D +∼D · C)
Y = D · A · D + D · A · ∼D · CY = D · A · D + D · A · ∼D · C
Y = D · A · D + 0 · A · CY = D · A · D
Y = D · A
![Page 148: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/148.jpg)
Simplification of logical statements
Y = D · (D · (A · B +∼B · A) +∼D · C · A)Y = D · (D · (A · B +∼B · A) +∼D · C · A)
Y = D · (D · A · (B +∼B) +∼D · C · A)
Y = D · (D · A · (B +∼B) +∼D · C · A)Y = D · (D · A · 1 +∼D · C · A)
Y = D · (D · A +∼D · C · A)Y = D · (D · A +∼D · C · A)
Y = D · A · (D +∼D · C)Y = D · A · (D +∼D · C)
Y = D · A · D + D · A · ∼D · CY = D · A · D + D · A · ∼D · C
Y = D · A · D + 0 · A · CY = D · A · D
Y = D · A
![Page 149: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/149.jpg)
Simplification of logical statements
Y = D · (D · (A · B +∼B · A) +∼D · C · A)Y = D · (D · (A · B +∼B · A) +∼D · C · A)
Y = D · (D · A · (B +∼B) +∼D · C · A)Y = D · (D · A · (B +∼B) +∼D · C · A)
Y = D · (D · A · 1 +∼D · C · A)Y = D · (D · A +∼D · C · A)Y = D · (D · A +∼D · C · A)
Y = D · A · (D +∼D · C)Y = D · A · (D +∼D · C)
Y = D · A · D + D · A · ∼D · CY = D · A · D + D · A · ∼D · C
Y = D · A · D + 0 · A · CY = D · A · D
Y = D · A
![Page 150: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/150.jpg)
Simplification of logical statements
Y = D · (D · (A · B +∼B · A) +∼D · C · A)Y = D · (D · (A · B +∼B · A) +∼D · C · A)
Y = D · (D · A · (B +∼B) +∼D · C · A)Y = D · (D · A · (B +∼B) +∼D · C · A)
Y = D · (D · A · 1 +∼D · C · A)
Y = D · (D · A +∼D · C · A)Y = D · (D · A +∼D · C · A)
Y = D · A · (D +∼D · C)Y = D · A · (D +∼D · C)
Y = D · A · D + D · A · ∼D · CY = D · A · D + D · A · ∼D · C
Y = D · A · D + 0 · A · CY = D · A · D
Y = D · A
![Page 151: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/151.jpg)
Simplification of logical statements
Y = D · (D · (A · B +∼B · A) +∼D · C · A)Y = D · (D · (A · B +∼B · A) +∼D · C · A)
Y = D · (D · A · (B +∼B) +∼D · C · A)Y = D · (D · A · (B +∼B) +∼D · C · A)
Y = D · (D · A · 1 +∼D · C · A)Y = D · (D · A +∼D · C · A)
Y = D · (D · A +∼D · C · A)Y = D · A · (D +∼D · C)Y = D · A · (D +∼D · C)
Y = D · A · D + D · A · ∼D · CY = D · A · D + D · A · ∼D · C
Y = D · A · D + 0 · A · CY = D · A · D
Y = D · A
![Page 152: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/152.jpg)
Simplification of logical statements
Y = D · (D · (A · B +∼B · A) +∼D · C · A)Y = D · (D · (A · B +∼B · A) +∼D · C · A)
Y = D · (D · A · (B +∼B) +∼D · C · A)Y = D · (D · A · (B +∼B) +∼D · C · A)
Y = D · (D · A · 1 +∼D · C · A)Y = D · (D · A +∼D · C · A)Y = D · (D · A +∼D · C · A)
Y = D · A · (D +∼D · C)Y = D · A · (D +∼D · C)
Y = D · A · D + D · A · ∼D · CY = D · A · D + D · A · ∼D · C
Y = D · A · D + 0 · A · CY = D · A · D
Y = D · A
![Page 153: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/153.jpg)
Simplification of logical statements
Y = D · (D · (A · B +∼B · A) +∼D · C · A)Y = D · (D · (A · B +∼B · A) +∼D · C · A)
Y = D · (D · A · (B +∼B) +∼D · C · A)Y = D · (D · A · (B +∼B) +∼D · C · A)
Y = D · (D · A · 1 +∼D · C · A)Y = D · (D · A +∼D · C · A)Y = D · (D · A +∼D · C · A)
Y = D · A · (D +∼D · C)
Y = D · A · (D +∼D · C)Y = D · A · D + D · A · ∼D · CY = D · A · D + D · A · ∼D · C
Y = D · A · D + 0 · A · CY = D · A · D
Y = D · A
![Page 154: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/154.jpg)
Simplification of logical statements
Y = D · (D · (A · B +∼B · A) +∼D · C · A)Y = D · (D · (A · B +∼B · A) +∼D · C · A)
Y = D · (D · A · (B +∼B) +∼D · C · A)Y = D · (D · A · (B +∼B) +∼D · C · A)
Y = D · (D · A · 1 +∼D · C · A)Y = D · (D · A +∼D · C · A)Y = D · (D · A +∼D · C · A)
Y = D · A · (D +∼D · C)Y = D · A · (D +∼D · C)
Y = D · A · D + D · A · ∼D · CY = D · A · D + D · A · ∼D · C
Y = D · A · D + 0 · A · CY = D · A · D
Y = D · A
![Page 155: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/155.jpg)
Simplification of logical statements
Y = D · (D · (A · B +∼B · A) +∼D · C · A)Y = D · (D · (A · B +∼B · A) +∼D · C · A)
Y = D · (D · A · (B +∼B) +∼D · C · A)Y = D · (D · A · (B +∼B) +∼D · C · A)
Y = D · (D · A · 1 +∼D · C · A)Y = D · (D · A +∼D · C · A)Y = D · (D · A +∼D · C · A)
Y = D · A · (D +∼D · C)Y = D · A · (D +∼D · C)
Y = D · A · D + D · A · ∼D · C
Y = D · A · D + D · A · ∼D · CY = D · A · D + 0 · A · C
Y = D · A · DY = D · A
![Page 156: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/156.jpg)
Simplification of logical statements
Y = D · (D · (A · B +∼B · A) +∼D · C · A)Y = D · (D · (A · B +∼B · A) +∼D · C · A)
Y = D · (D · A · (B +∼B) +∼D · C · A)Y = D · (D · A · (B +∼B) +∼D · C · A)
Y = D · (D · A · 1 +∼D · C · A)Y = D · (D · A +∼D · C · A)Y = D · (D · A +∼D · C · A)
Y = D · A · (D +∼D · C)Y = D · A · (D +∼D · C)
Y = D · A · D + D · A · ∼D · CY = D · A · D + D · A · ∼D · C
Y = D · A · D + 0 · A · CY = D · A · D
Y = D · A
![Page 157: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/157.jpg)
Simplification of logical statements
Y = D · (D · (A · B +∼B · A) +∼D · C · A)Y = D · (D · (A · B +∼B · A) +∼D · C · A)
Y = D · (D · A · (B +∼B) +∼D · C · A)Y = D · (D · A · (B +∼B) +∼D · C · A)
Y = D · (D · A · 1 +∼D · C · A)Y = D · (D · A +∼D · C · A)Y = D · (D · A +∼D · C · A)
Y = D · A · (D +∼D · C)Y = D · A · (D +∼D · C)
Y = D · A · D + D · A · ∼D · CY = D · A · D + D · A · ∼D · C
Y = D · A · D + 0 · A · C
Y = D · A · DY = D · A
![Page 158: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/158.jpg)
Simplification of logical statements
Y = D · (D · (A · B +∼B · A) +∼D · C · A)Y = D · (D · (A · B +∼B · A) +∼D · C · A)
Y = D · (D · A · (B +∼B) +∼D · C · A)Y = D · (D · A · (B +∼B) +∼D · C · A)
Y = D · (D · A · 1 +∼D · C · A)Y = D · (D · A +∼D · C · A)Y = D · (D · A +∼D · C · A)
Y = D · A · (D +∼D · C)Y = D · A · (D +∼D · C)
Y = D · A · D + D · A · ∼D · CY = D · A · D + D · A · ∼D · C
Y = D · A · D + 0 · A · CY = D · A · D
Y = D · A
![Page 159: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/159.jpg)
Simplification of logical statements
Y = D · (D · (A · B +∼B · A) +∼D · C · A)Y = D · (D · (A · B +∼B · A) +∼D · C · A)
Y = D · (D · A · (B +∼B) +∼D · C · A)Y = D · (D · A · (B +∼B) +∼D · C · A)
Y = D · (D · A · 1 +∼D · C · A)Y = D · (D · A +∼D · C · A)Y = D · (D · A +∼D · C · A)
Y = D · A · (D +∼D · C)Y = D · A · (D +∼D · C)
Y = D · A · D + D · A · ∼D · CY = D · A · D + D · A · ∼D · C
Y = D · A · D + 0 · A · CY = D · A · D
Y = D · A
![Page 160: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/160.jpg)
Simplification of logical statements
A = ∼B · (C · (∼D + E + C) +∼F · C)
A = ∼B · (C · (∼D + E + C) +∼F · C)A = ∼B · (C · ∼D + C · E + C · C +∼F · C)A = ∼B · (C · ∼D + C · E + C · C +∼F · C)
A = ∼B · (C · ∼D + C · E + C +∼F · C)A = ∼B · (C · ∼D + C · E + C +∼F · C)
A = ∼B · C · (∼D + E + 1 +∼F)A = ∼B · C · (∼D + E + 1 +∼F)
A = ∼B · C · 1A = ∼B · C
![Page 161: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/161.jpg)
Simplification of logical statements
A = ∼B · (C · (∼D + E + C) +∼F · C)A = ∼B · (C · (∼D + E + C) +∼F · C)
A = ∼B · (C · ∼D + C · E + C · C +∼F · C)A = ∼B · (C · ∼D + C · E + C · C +∼F · C)
A = ∼B · (C · ∼D + C · E + C +∼F · C)A = ∼B · (C · ∼D + C · E + C +∼F · C)
A = ∼B · C · (∼D + E + 1 +∼F)A = ∼B · C · (∼D + E + 1 +∼F)
A = ∼B · C · 1A = ∼B · C
![Page 162: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/162.jpg)
Simplification of logical statements
A = ∼B · (C · (∼D + E + C) +∼F · C)A = ∼B · (C · (∼D + E + C) +∼F · C)
A = ∼B · (C · ∼D + C · E + C · C +∼F · C)
A = ∼B · (C · ∼D + C · E + C · C +∼F · C)A = ∼B · (C · ∼D + C · E + C +∼F · C)A = ∼B · (C · ∼D + C · E + C +∼F · C)
A = ∼B · C · (∼D + E + 1 +∼F)A = ∼B · C · (∼D + E + 1 +∼F)
A = ∼B · C · 1A = ∼B · C
![Page 163: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/163.jpg)
Simplification of logical statements
A = ∼B · (C · (∼D + E + C) +∼F · C)A = ∼B · (C · (∼D + E + C) +∼F · C)
A = ∼B · (C · ∼D + C · E + C · C +∼F · C)A = ∼B · (C · ∼D + C · E + C · C +∼F · C)
A = ∼B · (C · ∼D + C · E + C +∼F · C)A = ∼B · (C · ∼D + C · E + C +∼F · C)
A = ∼B · C · (∼D + E + 1 +∼F)A = ∼B · C · (∼D + E + 1 +∼F)
A = ∼B · C · 1A = ∼B · C
![Page 164: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/164.jpg)
Simplification of logical statements
A = ∼B · (C · (∼D + E + C) +∼F · C)A = ∼B · (C · (∼D + E + C) +∼F · C)
A = ∼B · (C · ∼D + C · E + C · C +∼F · C)A = ∼B · (C · ∼D + C · E + C · C +∼F · C)
A = ∼B · (C · ∼D + C · E + C +∼F · C)
A = ∼B · (C · ∼D + C · E + C +∼F · C)A = ∼B · C · (∼D + E + 1 +∼F)A = ∼B · C · (∼D + E + 1 +∼F)
A = ∼B · C · 1A = ∼B · C
![Page 165: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/165.jpg)
Simplification of logical statements
A = ∼B · (C · (∼D + E + C) +∼F · C)A = ∼B · (C · (∼D + E + C) +∼F · C)
A = ∼B · (C · ∼D + C · E + C · C +∼F · C)A = ∼B · (C · ∼D + C · E + C · C +∼F · C)
A = ∼B · (C · ∼D + C · E + C +∼F · C)A = ∼B · (C · ∼D + C · E + C +∼F · C)
A = ∼B · C · (∼D + E + 1 +∼F)A = ∼B · C · (∼D + E + 1 +∼F)
A = ∼B · C · 1A = ∼B · C
![Page 166: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/166.jpg)
Simplification of logical statements
A = ∼B · (C · (∼D + E + C) +∼F · C)A = ∼B · (C · (∼D + E + C) +∼F · C)
A = ∼B · (C · ∼D + C · E + C · C +∼F · C)A = ∼B · (C · ∼D + C · E + C · C +∼F · C)
A = ∼B · (C · ∼D + C · E + C +∼F · C)A = ∼B · (C · ∼D + C · E + C +∼F · C)
A = ∼B · C · (∼D + E + 1 +∼F)
A = ∼B · C · (∼D + E + 1 +∼F)A = ∼B · C · 1
A = ∼B · C
![Page 167: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/167.jpg)
Simplification of logical statements
A = ∼B · (C · (∼D + E + C) +∼F · C)A = ∼B · (C · (∼D + E + C) +∼F · C)
A = ∼B · (C · ∼D + C · E + C · C +∼F · C)A = ∼B · (C · ∼D + C · E + C · C +∼F · C)
A = ∼B · (C · ∼D + C · E + C +∼F · C)A = ∼B · (C · ∼D + C · E + C +∼F · C)
A = ∼B · C · (∼D + E + 1 +∼F)A = ∼B · C · (∼D + E + 1 +∼F)
A = ∼B · C · 1A = ∼B · C
![Page 168: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/168.jpg)
Simplification of logical statements
A = ∼B · (C · (∼D + E + C) +∼F · C)A = ∼B · (C · (∼D + E + C) +∼F · C)
A = ∼B · (C · ∼D + C · E + C · C +∼F · C)A = ∼B · (C · ∼D + C · E + C · C +∼F · C)
A = ∼B · (C · ∼D + C · E + C +∼F · C)A = ∼B · (C · ∼D + C · E + C +∼F · C)
A = ∼B · C · (∼D + E + 1 +∼F)A = ∼B · C · (∼D + E + 1 +∼F)
A = ∼B · C · 1
A = ∼B · C
![Page 169: Design of Information and Control Systems · 2020. 9. 27. · Design of Information and Control Systems Programmable Logic Controllers - Fundamentals Institute of Information Engineering,](https://reader034.vdocuments.site/reader034/viewer/2022052616/60aa78294b798826b85d89a4/html5/thumbnails/169.jpg)
Simplification of logical statements
A = ∼B · (C · (∼D + E + C) +∼F · C)A = ∼B · (C · (∼D + E + C) +∼F · C)
A = ∼B · (C · ∼D + C · E + C · C +∼F · C)A = ∼B · (C · ∼D + C · E + C · C +∼F · C)
A = ∼B · (C · ∼D + C · E + C +∼F · C)A = ∼B · (C · ∼D + C · E + C +∼F · C)
A = ∼B · C · (∼D + E + 1 +∼F)A = ∼B · C · (∼D + E + 1 +∼F)
A = ∼B · C · 1A = ∼B · C