## TRUE or FALSE condition

To understand **programmable logic controllers (PLCs)** and their applications, you must first understand the logic concepts behind them. We’ll will explain the relationship between Boolean algebra and logic contact symbology, so that you will be ready to learn about PLC processors and ladder logic functions and diagrams.

The binary concept shows how physical quantities (binary variables) that can exist in one of two states can be represented as **1** or **0**.

Now, you will see how statements that combine two or more of these binary variables can result in either a

TRUE or FALSE condition, represented by1and0, respectively.

Programmable logic controllers (PLCs) make decisions based on the results of these kinds of logical statements.

Operations performed by digital equipment, such as programmable controllers, are based on three fundamental ladder logic functions – **AND, OR, and NOT**. These functions combine binary variables to form statements. Each function has a rule that determines the statement outcome (TRUE or FALSE) and a symbol that represents it.

## Ladder Logic Functions

There are many control situations requiring actions to be initiated when a certain combination of conditions is realized. Thus, for an **automatic drilling machine**, there might be the condition that the drill motor is to be activated when the limit switches are activated that indicate the presence of the workpiece and the drill position as being at the surface of the workpiece.

Such a situation involves the

AND logic function, condition A and condition B having both to be realized for an output to occur. This section is a consideration of such logic functions.

Make sure you read the first part of this article “PLC Ladder Diagrams for Electrical Engineers (Beginners)”. **Now let’s talk about the six most used logic functions in PLC ladder programming //**

### 1. AND logic function

Figure 1a shows a situation where an output is not energized unless two, normally open, switches are both closed. Switch A and switch B have both to be closed, which thus gives an **AND logic situation**. We can think of this as representing a control system with two inputs A and B (Figure 1b). Only when A and B are both on is there an output.

Thus if we use **1** to indicate an **on signal** and **0** to represent an **off signal**, then for there to be a 1 output we must have A and B both 1.

Such an operation is said to be controlled by a logic gate and the relationship between the inputs to a logic gate and the outputs is tabulated in a form known as a

truth table.

**Thus for the AND gate we have //**

Inputs | Output | |

A | B | |

0 | 0 | 0 |

0 | 1 | 0 |

1 | 0 | 0 |

1 | 1 | 1 |

An example of an AND gate is an **interlock control system** for a machine tool so that it can only be operated when the safety guard is in position and the power switched on.

**Figure 2a** shows an **AND gate system on a ladder diagram**.

The ladder diagram starts with **| |**, a normally open set of contacts labeled input A, to represent switch A and in series with it **| |**, another normally open set of contacts labeled input B, to represent switch B. The line then terminates with O to represent the output. For there to be an output, both input A and input B have to occur, i.e., input A and input B contacts have to be closed (**Figure 2b**).

In general //On a ladder diagram contacts in a horizontal rung, i.e., contacts in series, represent the logical AND operations.

### 2. OR logic function

Figure 3a shows an electrical circuit where an output is energized when switch A or B, both normally open, are closed. This describes an **OR logic gate** (Figure 3b) in that input A or input B must be on for there to be an output.

**The truth table is //**

Inputs | Output | |

A | B | |

0 | 0 | 0 |

0 | 1 | 1 |

1 | 0 | 1 |

1 | 1 | 1 |

Figure 11.10a shows an **OR logic gate system on a ladder diagram**, Figure 4b showing an equivalent alternative way of drawing the same diagram.

The ladder diagram starts with **| |**, normally open contacts labeled **input A**, to represent **switch A** and in parallel with it **| |**, normally open contacts labeled input B, to represent switch B. Either input A or input B have to be closed for the output to be energized (Figure 4c). The line then terminates with O to represent the output.

In general //Alternative paths provided by vertical paths from the main rung of a ladder diagram, i.e., paths in parallel representlogical OR operations.

An example of an OR gate control system is a conveyor belt transporting bottled products to packaging where a deflector plate is activated to deflect bottles into a reject bin if either the weight is not within certain tolerances or there is no cap on the bottle.

### 3. NOT logic function

Figure 5a shows an electrical circuit controlled by a switch that is normally closed. When there is an input to the switch, it opens and there is then no current in the circuit. This illustrates a **NOT gate** in that there is an output when there is no input and no output when there is an input (Figure 5c). The gate is sometimes referred to as an **inverter**.

**The truth table is //**

Input A | Output |

0 | 1 |

1 | 0 |

Figure 5b shows a NOT gate system on a ladder diagram. The input A contacts are shown as being normally closed. This is in series with the **output ( )**. With no input to input A, the contacts are closed and so there is an output. When there is an input to input A, it opens and there is then no output.

An example of a NOT gate control system is a light that comes on when it becomes dark, i.e., when there is no light input to the light sensor there is an output.

### 4. NAND logic function

Suppose we follow an **AND gate with a NOT gate** (Figure 6a). The consequence of having the NOT gate is to invert all the outputs from the AND gate. An alternative, which gives exactly the same results, is to put a NOT gate on each input and then follow that with OR (Figure 6b).

**The same truth table occurs, namely //**

Inputs | Output | |

A | B | |

0 | 0 | 1 |

0 | 1 | 1 |

1 | 0 | 1 |

1 | 1 | 0 |

Both the inputs A and B have to be 0 for there to be a 1 output. There is an output when input A and input B are not 1. The combination of these gates is termed a **NAND gate** (Figure 7).

An example of a NAND gate control system is a **warning light** that comes on if, with a machine tool, the safety guard switch has not been activated and the limit switch signalling the presence of the workpiece has not been activated.

### 5. NOR logic function

Suppose we follow an **OR gate by a NOT gate** (Figure 8a). The consequence of having the NOT gate is to invert the outputs of the OR gate. An alternative, which gives exactly the same results, is to put a NOT gate on each input and then an AND gate for the resulting inverted inputs (Figure 8b).

**The following is the resulting truth table //**

Inputs | Output | |

A | B | |

0 | 0 | 1 |

0 | 1 | 0 |

1 | 0 | 0 |

1 | 1 | 0 |

The combination of OR and NOT gates is termed a **NOR gate**. There is an output when neither input A or input B is 1.

Figure 9 shows a ladder diagram of a NOR system. When input A and input B are both not activated, there is a 1 output. When either X400 or X401 are 1 there is a 0 output.

### 6. Exclusive OR (XOR) logic function

The OR gate gives an output when either or both of the inputs are 1. Sometimes there is, however, a need for a gate that gives an output when either of the inputs is 1 but not when both are 1, i.e., has the truth table:

Inputs | Output | |

A | B | |

0 | 0 | 0 |

0 | 1 | 1 |

1 | 0 | 1 |

1 | 1 | 0 |

Such a gate is called an **Exclusive OR or XOR gate**. One way of obtaining such a gate is by using NOT, AND and OR gates as shown in Figure 10.

Figure 11 shows a **ladder diagram for an XOR gate system**.

When input A and input B are not activated then there is 0 output. When just input A is activated, then the upper branch results in the output being 1. When just input B is activated, then the lower branch results in the output being 1. When both input A and input B are activated, there is no output.

In this example of a logic gate, input A and input B have two sets of contacts in the circuits, one set being normally open and the other normally closed. With PLC programming, each input may have as many sets of contacts as necessary.

### Programmable Logic Controller Basics (VIDEO)

**References //**

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how do we NOT an input in programming?

for example if we have a NO contact and we want to NOT it, shall we define it as NC in programming?

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