![]() © Goodheart-Willcox Co., Inc.ģ2 Using K-Maps (Cont.) 5. ![]() Write the Boolean expressions for each group, and then simplify the expression. © Goodheart-Willcox Co., Inc.ģ0 Using K-Maps (Cont.) How groups wrap around the K-Map.ģ1 Using K-Maps (Cont.) 4. © Goodheart-Willcox Co., Inc.Ģ9 Using K-Maps (Cont.) Map can be considered closed, so that end boxes are grouped adjacently (top and bottom, or left and right). Each group should be as large as possible. The same 1 can be used in two or more overlapping groups. © Goodheart-Willcox Co., Inc.Ģ8 Using K-Maps (Cont.) Every 1 in adjacent cells must be included in a group. © Goodheart-Willcox Co., Inc.Ģ7 Using K-Maps (Cont.) Each group must contain an even number of binary 1s. Follow the rules below for grouping the 1s in the K-Map that lead to simplifying the expression. © Goodheart-Willcox Co., Inc.Ģ6 Using K-Maps (Cont.) 3. Therefore, for a two-variable (A and B) input table, there will be 22 boxes, or 4 boxes. As stated, for an n-variable input truth table, there will be 2n boxes. © Goodheart-Willcox Co., Inc.Ģ5 Using K-Maps Use the following steps to simplify the Boolean expressions using K-Maps: Select an appropriate K-Map that has the correct number of input boxes, such as two-input and three-input. For an n-variable input truth table, there are 2n boxes in a Karnaugh map. Use columns and rows to represent each term in a truth table. © Goodheart-Willcox Co., Inc.Ģ3 Karnaugh Maps (K-Map) Graphical representations of truth tables. Three methods used to simplify Boolean expressions: Karnaugh maps. © Goodheart-Willcox Co., Inc.Ģ2 Simplifying Boolean Expressions (Cont.) ![]() Use the gate logic to PLC ladder diagram conversion routine to create the PLC ladder logic diagram. To convert a truth table to a PLC ladder logic diagram: Find its simplified Boolean expression. XNOR logic gate symbol, its Boolean expression, and its truth table. XOR logic gate symbol, its Boolean expression, and its truth table. © Goodheart-Willcox Co., Inc.ġ8 NOR Gate A two-input NOR logic gate symbol, its Boolean expression, and its truth table. © Goodheart-Willcox Co., Inc.ġ7 NAND Gate Two-input NAND logic gate symbol, Boolean expression, and its truth table. © Goodheart-Willcox Co., Inc.ġ6 OR Gate Two-input OR logic gate symbol, its Boolean expression, and its truth table. © Goodheart-Willcox Co., Inc.ġ5 AND Gate Two-input AND logic gate symbol, its Boolean expression, and its truth table. Function is simulated by the electric circuit displayed. © Goodheart-Willcox Co., Inc.ġ4 NOT Gate Output is the inverse of the input. © Goodheart-Willcox Co., Inc.ġ3 Gate Symbols For every combinational and sequential logic device. © Goodheart-Willcox Co., Inc.ġ2 Truth Tables In Boolean algebra, a table contains the digital input and output points. Logic low: Represented by the absence of a voltage potential. Logic high: Represented by the presence of a voltage potential. ![]() False state: Represented by the number zero, called logic low or logic zero. True state: Represented by the number one, called logic high or logic one in Boolean algebra. Boolean algebra: Two states are true and false. © Goodheart-Willcox Co., Inc.ĩ Boolean Expressions Every gate logic function has its own equation called a Boolean expression. An inherent delay time is always present. Have outputs that depend on their inputs as well as time. © Goodheart-Willcox Co., Inc.Ħ Logic Gates NOT. © Goodheart-Willcox Co., Inc.ĭo not require clock pulses to operate. Convert PLC ladder logic diagrams to logic gate circuits and Boolean expressions. Convert Boolean expressions to PLC ladder logic diagrams. © Goodheart-Willcox Co., Inc.Ĥ Objectives Use the Logic Converter instrument in NI Multisim to create logic tables and Boolean expressions from logic gate circuits. Create Boolean expressions and logic gate circuits from truth tables. ![]() And when Input ( I1) is released then coil( Q1 is off.2 Programming Logic Gate Functions in PLCsħ Programming Logic Gate Functions in PLCsģ Objectives Describe combinational and sequential logic gate circuits.Ĭreate PLC ladder logic programs for NOT, AND, OR, NAND, NOR, XOR, and XNOR logic gates. When ( I1) is pressed then the coil ( Q1) is on. In the case of PLC ladder, there will be a push button to provide input. Logic Gate Truth Table for NOT Gate: Input (I1) When the input is high then the output is low and vice-versa. In electronics, NOT GATE is also called an ‘ Inverter’ or ‘ Buffer’. Let’s see the explanation for each logic gate with PLC implementation, 1. Note: The circuit diagrams are connected to make and break input (I) and output (Q) contact in series and parallel circuits.įor all the circuit diagram, we are representing inputs ( I1) and ( I2) as switches, output ( Q1) as coil/lamp. Basically, there are seven types of logic gates as below. Different types of ladder logic diagram that perform different logic gate functions. ![]()
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