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Programmable Logic Controllers Third Edition

Frank D. Petruzella McGraw-Hill

Chapter 4

Fundamentals of Logic

The Binary Concept

Many things can be thought of as existing in one

of two states.

The Binary Concept

This two-state binary concept, applied to gates,

can be the basis for making decisions.

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.

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.

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.

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

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.

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.

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

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.

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.

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.

NOT Gate Application Example 2

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.

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.

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.

- 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)

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)

6. With an AND gate, if any input is 0, the

output will be 0. (True/False)

- 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

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

Boolean Equation Example 2

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.

Circuit Development Using A Boolean Expression

Example 2

AND gate with Input B and C

Producing A Boolean Expression From A

Given Circuit Example 1

Producing A Boolean Expression From A

Given Circuit Example 2

Logic equation Y AB AB

Hard Wired versus Programmed Logic

The term hardwired logic refers to logic control

functions that are determined by the way

devices are interconnected.

Hardwired Stop/Start Motor Control Circuit

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

Hard Wired versus Programmed Logic Example 4-1

Hard Wired versus Programmed Logic Example 4-2

Hard Wired versus Programmed Logic Example 4-3

Hard Wired versus Programmed Logic Example 4-4

Hard Wired versus Programmed Logic Example 4-5

Hard Wired versus Programmed Logic Example 4-6

Hard Wired versus Programmed Logic Example 4-7

Hard Wired versus Programmed Logic Example 4-8

Hard Wired versus Programmed Logic Example 4-9

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.

Programmed AND Instruction

Programmed AND Instruction

Programmed OR Instruction

Programmed XOR Instruction

Programmed NOT Instruction

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