Programmable Logic Controllers Third Edition

Programmable Logic Controllers Third Edition Frank D. Petruzella McGraw-Hill

Chapter 4 Fundamentals of Logic

These two states can be defined as “high” or “low”, “on” or “off”, “yes” or “no”, and “1” or “0”. high, on, yes, 1 5V Binary Signal low, off, no, 0 The Binary Concept Many things can be thought of as existing in one of two states.

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. 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.

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

7. The symbol shown is that of a(an) • _________ . • AND gate • OR gate • NAND gate • inverter 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)

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

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

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

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. Hard Wired versus Programmed Logic The term hardwired logic refers to logic control functions that are determined by the way devices are interconnected.

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

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.

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

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

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

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

13. Which gate logic shown represents the Boolean equation: ( A + B ) C = Y (b) (a) (c) (d)

Programmable Logic Controllers Third Edition