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Inst Tools > Blog > PLC Tutorials > From Boolean Algebra to PLC Logic

From Boolean Algebra to PLC Logic

In this article, a simple example will teach you the conversion from Boolean algebra to PLC logic.

Last updated: March 28, 2024 5:28 am
Editorial Staff
PLC Tutorials
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In this article, a simple example will teach you the conversion from Boolean algebra to PLC logic.

Contents
Boolean Algebra to PLC LogicVideoDigital InputsDigital OutputsPLC ProgrammingPLC Program DescriptionTest Results

Note: The PLC logic shown here is for educational use only for students and technicians to learn the basics.

Boolean Algebra to PLC Logic

Problem Statement

Design a PLC ladder logic for the following Boolean Expression.

We are using toggle Inputs to control the output.

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

Video

Watch the video to learn this PLC program example.

PLC Ladder Diagram for the given Boolean Expression

Digital Inputs

The inputs listed below.

A: I0.0

B: I0.1

C: I0.2

D: I0.3

Digital Outputs

The outputs listed below.

Y: Q0.0

PLC Programming

Find the equivalent plc program for the given Boolean expression.

Boolean Algebra to PLC Logic

PLC Program Description

  • In this program, we used Schneider Electric PLC software. You can use any brand of PLC software.
  • In the above PLC program, Normally Open Contacts are used for input A, input B, input C, and input D.
  • Input A and Input B are connected in parallel, thus implementing OR Logic Gate.
  • There is again the implementation of OR Logic Gate as Input C and Input D are connected in parallel.
  • There is also implementation of AND Logic Gate as A+B is connected in series with C+D.
  • For the output Y (Q0.0) to be ON, either Input A or Input B should be ON and either Input C or Input D should be ON.
  • If input A and input C are ON or If input A and input D are ON or If input B and input C are ON or input B and input D are ON, then the output Y (Q0.0) will be ON.

Test Results

Now check the PLC program simulation results.

When Input A and Input C are ON

Boolean Algebra for PLC

When Input A and Input C are turned ON, the output Y (Q0.0) will turn ON. The inputs are taken as Normally Open Contacts and when in true state, the signal will pass through these contacts.

As a result, the output Y (Q0.0) will turn ON. If only one input is turned ON i.e., either input A or input C is turned ON, then the output Y Q(0.0) will not turn ON.

When Input A and Input D are ON

PLC Logic design with boolean expression

Y (Q0.0) will turn ON when Input A and Input D are turned ON. These inputs are used as Normally Open Contacts and when in true states, the signal will flow through these contacts which results in turning ON the output Y (Q0.0).

For the output Y (Q0.0) to turn ON, both the inputs should be ON. If only one input i.e., if input A or Input D is turned ON, then the output Y (Q0.0) will not turn ON.

When Input B and Input C are ON

Boolean to Ladder Logic Converter

The signal will flow through Input B and Input C as these inputs are taken as Normally Open Contacts. When the input B and input C are in true state, the output Y (Q0.0) will turn ON.

So, both the inputs i.e., input B and input C should be ON and then only the output Y (Q0.0) will turn ON. Turning ON only one input will not turn ON the output Y (Q0.0).

When Input B and Input D are ON

Boolean expression for the given PLC ladder program

As Normally Open Contacts used for Input A and Input B are in the true state, the signal will pass through these two Inputs and Y(Q0.0) will turn ON.

The output Y (Q0.0) will turn ON only if both these inputs are turned ON otherwise it will remain OFF.

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