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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. These two states can be defined as “high” or “low”, “on” or “off”, “yes” or “no”, and “1” or “0”. 5V high, on, yes, 1 low, off, no, 0 Binary Signal

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The Binary Concept This two-state binary concept, applied to gates, can be the basis for making decisions. The gate is a device that has one or more inputs with which it will perform a logical decision and produce a result at its one output.

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**Gate Decision Making The Logical AND Light Switch AND High Beam Gate**

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 OR Dome Gate**

Light 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**

If the power is “on” (1) and the pressure switch is not closed (0), the warning indicator will be “on” Low-pressure indicating circuit When the pressure rises to close the pressure switch, the warning indicator will be switched "off"

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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**

6. With an AND gate, if any input is 0, the output will be (True/False) 7. The symbol shown is that of a(an) _________ . AND gate OR gate NAND gate inverter

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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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**Gate Boolean Equations**

Y AND Y = A B Gate Boolean Equation OR A B Y Y = A + B NOT A Y Y = A

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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**

AB Y = AB + C A + B Y = (A + B) C

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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. Hardwired logic can be implemented using relays and relay ladder schematics. Hardwired logic is fixed: it is changeable only by altering the way devices are connected.

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**Hardwired Stop/Start Motor Control Circuit**

Ladder rung Ladder rail Control scheme is drawn between two vertical supply lines.

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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**

There is a 1 at B3:10 only when Source A and B bits are 1 and input A is true

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**Programmed AND Instruction**

There is a 1 at B3:10 only when Source A and B bits are 1 and input A is true

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**Programmed OR Instruction**

There is a 1 at B3:20 when either or both the Source A or B bits are 1

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**Programmed XOR Instruction**

There is an output only when Source A and B bits are different

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**Programmed NOT Instruction**

The bits from B3:9 are sent to B3:10 and inverted when input A is true

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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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**13. Which gate logic shown represents the Boolean**

equation: ( A + B ) C = Y (a) (b) (c) (d)

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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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**15. The correct Boolean equation for the combination logic gate circuit shown is:**

a. Y = ( A + B + C ) D c. Y = ( AB + C ) D b. Y = ( A + B ) ( C + D ) d. Y = ( ABC ) D

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**16. The correct Boolean equation for the combination logic gate circuit shown is:**

a. Y = A B C c. Y = A + B + C b. Y = ( A B ) C d. Y = ( AB ) + ( BC )

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**17. The correct Boolean equation for the ladder**

logic program shown is: a. Y = (A B) + (CD) c. Y = A + B + C + D b. Y = (A+B ) (C+D) d. Y = ABCD

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**18. The correct Boolean equation for the ladder**

logic program shown is: a. Y = (A B) + (CD) c. Y = A + B + C + D b. Y = AB (C+D) d. Y = ABC + D

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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

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