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Programmable Logic Controllers

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Chapter 4 Part 1 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 AND Gate Light Switch High Beam Switch High Beam Light The automotive high beam light can only be turned on when the light switch AND high beam switch are on. The Logical AND

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Gate Decision Making OR Gate Passenger Door Switch Driver Door Switch Dome Light The automotive dome light will be turned on when the passenger door switch OR the driver door switch is activated. The Logical OR

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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 If all inputs are 1, the output will be 1 If any input is 0, the output will be 0 Basic Rules The device has two or more inputs and one output

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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 If one or more inputs are 1, the output will be 1 Basic Rules If all inputs are 0, the output will be 0

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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 The light will be on if the pushbutton is not pressed. Acts like a normally closed pushbutton in series with the output. 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 output of this gate is HIGH only when one input or the other is HIGH, but not both. The XOR function has two inputs and one output. It is commonly used for comparison of two binary numbers.

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1. The two binary states can be defined as: (a) high or low (b) on or off (c) 1 or 0 (d) all of these 2. A gate can have one or more outputs but only one input. (True/False)

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3. The ______ table shows the resulting output for each possible gate input conditions. a. input status c. data b. output status d. truth 4. A light that is "off" or a switch that is "open" would normally be represented by a binary 1. (True/False) 5. The OR function, implemented using contacts, requires contacts connected in series. (True/False)

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

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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) 8. Which of the following gates is commonly used for the comparison of two binary numbers? (a) NAND (b) NOR (c) XOR (d) NOT

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Gate Boolean Equations A B 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

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Circuit Development Using A Boolean Expression – Example 2

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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

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