Combinatorial Logic

Table of Contents

Combinational logic circuits connect multiple inputs using AND, OR, or NOT gates, but do not use memory functions, meaning RS latches. More complex circuits can be formed from these basic logic functions.

Circuit design using a simple example

You receive a plant description from your customer and must develop a PLC program for this purpose. Which work steps are necessary for this? This will be shown by means of a simple example.

Example: It should be possible to switch on a motor M1 from two control points with the latching switches S1 and S2. The motor should start when either only S1 or only S2 is switched on.

Step 1: Create a Truth table

Truth table

Step 2: Create a Boolean equation from the Truth table

Only the cases in which the output has the logical state '1' are interesting here! The complete Boolean equation is:

Boolean equation

Step 3: Translate the logic equation into a Logic circuit

Logic circuit

Using a PLC you might program in LD (Ladder Diagram) or FUP (Function plan). Here the solution:

Learning PLC - XOR in LD and FUP

Note: This logic, i.e. that the output only switches when only one input has High-signal at any one time, is frequently used in automation technology. Therefore, it has its own designation and symbol:

XOR, Exclusive-Or

Example: Two out of Three Logic with Boolean Algebra

An injection molding machine may only start or continue the production process when the required operating temperature is reached and maintained. As a production stop of this installation during operation is involved with high costs, the temperature is measured by three sensors. The shut-down should only take place if at least two of the three temperature sensors report a temperature error (signal '1'). In this manner, unnecessary shut down can be prevented, which would cause high costs.

Two out of Three Logic with Boolean Algebra

Develop for this system the necessary simplified ladder diagram.