Chapter
7Programming Logic
Gate Functions in PLCs
Permission granted to reproduce for educational use only.© Goodheart-Willcox Co., Inc.
Objectives
• Describe combinational and sequential logic gate circuits.
• Create PLC ladder logic programs for NOT, AND, OR, NAND, NOR, XOR, and XNOR logic gates.
• Create Boolean expressions and logic gate circuits from truth tables.
Permission granted to reproduce for educational use only.© Goodheart-Willcox Co., Inc.
Objectives
• Use the Logic Converter instrument in NI Multisim to create logic tables and Boolean expressions from logic gate circuits.
• Convert Boolean expressions to PLC ladder logic diagrams.
• Convert PLC ladder logic diagrams to logic gate circuits and Boolean expressions.
Permission granted to reproduce for educational use only.© Goodheart-Willcox Co., Inc.
Combinational Logic Gates
• Do not require clock pulses to operate.• Outputs depend only on their inputs.• Outputs are generated instantaneously.• Simply called logic gates.
Permission granted to reproduce for educational use only.© Goodheart-Willcox Co., Inc.
Logic Gates
• NOT.• AND.• OR.• NAND.• NOR.• XOR (exclusive OR).• XNOR (exclusive NOR).
Permission granted to reproduce for educational use only.© Goodheart-Willcox Co., Inc.
Sequential Logic Devices
• Have outputs that depend on their inputs as well as time.
• Require clock pulses. • An inherent delay time is always
present.• Flip-flop devices.
Permission granted to reproduce for educational use only.© Goodheart-Willcox Co., Inc.
Sequential Logic Circuit
Permission granted to reproduce for educational use only.© Goodheart-Willcox Co., Inc.
Boolean Expressions
• Every gate logic function has its own equation called a Boolean expression.
• Boolean algebra:– Two states are true and false.
Permission granted to reproduce for educational use only.© Goodheart-Willcox Co., Inc.
Boolean Expressions (Cont.)
• True state:– Represented by the number one, called
logic high or logic one in Boolean algebra. • False state:
– Represented by the number zero, called logic low or logic zero.
Permission granted to reproduce for educational use only.© Goodheart-Willcox Co., Inc.
Boolean Expressions (Cont.)
• Logic high:– Represented by the presence of a voltage
potential.– Represented with five volts (+5 V).
• Logic low:– Represented by the absence of a voltage
potential. – Represented with zero volts (0 V).
Permission granted to reproduce for educational use only.© Goodheart-Willcox Co., Inc.
Truth Tables
• In Boolean algebra, a table contains the digital input and output points.
• This table is called a truth table.
Permission granted to reproduce for educational use only.© Goodheart-Willcox Co., Inc.
Gate Symbols
• For every combinational and sequential logic device.
• Used to create logic gate circuits.
Permission granted to reproduce for educational use only.© Goodheart-Willcox Co., Inc.
NOT Gate
• Output is the inverse of the input.
• Sometimes called an inverter.
• Function is simulated by the electric circuit displayed.
Permission granted to reproduce for educational use only.© Goodheart-Willcox Co., Inc.
AND Gate
• Two-input AND logic gate symbol, its Boolean expression, and its truth table.
Permission granted to reproduce for educational use only.© Goodheart-Willcox Co., Inc.
OR Gate
• Two-input OR logic gate symbol, its Boolean expression, and its truth table.
Permission granted to reproduce for educational use only.© Goodheart-Willcox Co., Inc.
NAND Gate
• Two-input NAND logic gate symbol, Boolean expression, and its truth table.
Permission granted to reproduce for educational use only.© Goodheart-Willcox Co., Inc.
NOR Gate
• A two-input NOR logic gate symbol, its Boolean expression, and its truth table.
Permission granted to reproduce for educational use only.© Goodheart-Willcox Co., Inc.
XOR (exclusive OR) Gate
• XOR logic gate symbol, its Boolean expression, and its truth table.
Permission granted to reproduce for educational use only.© Goodheart-Willcox Co., Inc.
XNOR (exclusive NOR) Gate
• XNOR logic gate symbol, its Boolean expression, and its truth table.
Permission granted to reproduce for educational use only.© Goodheart-Willcox Co., Inc.
Simplifying Boolean Expressions
• To convert a truth table to a PLC ladder logic diagram:– Find its simplified Boolean expression. – Use the gate logic to PLC ladder diagram
conversion routine to create the PLC ladder logic diagram.
Permission granted to reproduce for educational use only.© Goodheart-Willcox Co., Inc.
Simplifying Boolean Expressions (Cont.)
• Three methods used to simplify Boolean expressions:– Karnaugh maps.– Quine-McCluskey routine.– Electronic simulation software.
Permission granted to reproduce for educational use only.© Goodheart-Willcox Co., Inc.
Karnaugh Maps (K-Map)
• Graphical representations of truth tables. – Use columns and rows to represent each
term in a truth table. – For an n-variable input truth table, there
are 2n boxes in a Karnaugh map. – A box for every line in the truth table.
Permission granted to reproduce for educational use only.© Goodheart-Willcox Co., Inc.
Karnaugh Maps (K-Map) (Cont.)
Permission granted to reproduce for educational use only.© Goodheart-Willcox Co., Inc.
Using K-Maps
• Use the following steps to simplify the Boolean expressions using K-Maps:
1. Select an appropriate K-Map that has the correct number of input boxes, such as two-input and three-input. As stated, for an n-variable input truth table, there will be 2n boxes. Therefore, for a two-variable (A and B) input table, there will be 22 boxes, or 4 boxes.
2. Plot only the terms in which Y = 1.
Permission granted to reproduce for educational use only.© Goodheart-Willcox Co., Inc.
Using K-Maps (Cont.)
3. Follow the rules below for grouping the 1s in the K-Map that lead to simplifying the expression.
Permission granted to reproduce for educational use only.© Goodheart-Willcox Co., Inc.
Using K-Maps (Cont.)
• Each group must contain an even number of binary 1s.
Permission granted to reproduce for educational use only.© Goodheart-Willcox Co., Inc.
Using K-Maps (Cont.)
• Every 1 in adjacent cells must be included in a group.
• The same 1 can be used in two or more overlapping groups. Each group should be as large as possible.
Permission granted to reproduce for educational use only.© Goodheart-Willcox Co., Inc.
Using K-Maps (Cont.)
• Map can be considered closed, so that end boxes are grouped adjacently (top and bottom, or left and right).
Permission granted to reproduce for educational use only.© Goodheart-Willcox Co., Inc.
Using K-Maps (Cont.)
• How groups wrap around the K-Map.
Permission granted to reproduce for educational use only.© Goodheart-Willcox Co., Inc.
Using K-Maps (Cont.)
4. Write the Boolean expressions for each group, and then simplify the expression.
Permission granted to reproduce for educational use only.© Goodheart-Willcox Co., Inc.
Using K-Maps (Cont.)
5. Sum common variables from each group to create simplified sum of product (SOP) Boolean expression.
Permission granted to reproduce for educational use only.© Goodheart-Willcox Co., Inc.
Quine-McCluskey Routine
• For more than five input variables, a better method for simplifying Boolean expressions.
• Complicated method that uses the Boolean algebraic simplification rules to find the simplified Boolean expression.
• Might be used in an advanced course.
Permission granted to reproduce for educational use only.© Goodheart-Willcox Co., Inc.
Electronic Simulation Software
• Easiest method to find simplified Boolean expression: – Enter input and output data.– Solves and simplifies the expression.– NI Multisim is an example of this software.
Permission granted to reproduce for educational use only.© Goodheart-Willcox Co., Inc.
NI Multisim Software
• Open NI Multisim program. • From the Instruments toolbar, click
the Logic Converter icon. • Click a space in the work area to place
the converter. • Double-click the Logic Converter
image to open the Logic Converter dialog box.
Permission granted to reproduce for educational use only.© Goodheart-Willcox Co., Inc.
Creating PLC Ladder Logic Diagrams from Logic Gate Circuits
• Convert each gate to its equivalent ladder logic diagram.
Permission granted to reproduce for educational use only.© Goodheart-Willcox Co., Inc.
Creating PLC Ladder Logic Diagrams from Boolean Expressions
• Some manufacturers use Boolean expressions to program PLCs.
Example• Create the PLC ladder logic diagram
for the following Boolean expression.
Y = A′ + B + CD + EB
Permission granted to reproduce for educational use only.© Goodheart-Willcox Co., Inc.
Creating PLC Ladder Logic Diagrams from Boolean Expressions (Cont.)
• To create the diagram, each rung or each portion of a rung is created by replacing the Boolean letter with the inputs that match.
Permission granted to reproduce for educational use only.© Goodheart-Willcox Co., Inc.
PLC Ladder Logic Diagrams from Boolean Expressions
Permission granted to reproduce for educational use only.© Goodheart-Willcox Co., Inc.
Creating Logic Gate Circuits from PLC Ladder Logic Diagrams
• Converting to logic gate circuits: – Find Boolean expression that represents
ladder logic diagram. – Draw the logic gate circuit using the
Boolean expression similar. – Use logic converter instrument in NI
Multisim program to find truth tables and Boolean expressions.
Permission granted to reproduce for educational use only.© Goodheart-Willcox Co., Inc.
Creating Logic Gate Circuits from PLC Ladder Logic Diagrams (Cont.)
• Create the logic gate circuit for the PLC ladder logic diagram displayed.
Permission granted to reproduce for educational use only.© Goodheart-Willcox Co., Inc.
Creating Logic Gate Circuits from PLC Ladder Logic Diagrams (Cont.)
• Turn the PLC ladder logic diagram into a Boolean expression as shown in the ladder diagram.