In today's post we are gonna implement few complex logical gates. Its not gonna be much difficult if you have the basic concepts. I am just pointing out few important points here. While implementing any gate in ladder logic, always consider rung as an electrical line having HIGH voltage at one end and LOW voltage at the other, while the inputs are simple switches. Voltage will be supplied to the output only when switch is closed i.e. input is HIGH, otherwise the output will remain OFF. You should also have a look at Introduction to Logic Gates.

You have seen in previous post, while implementing OR gate we have used a second switch in parallel which ends at the first rung so overall its a single rung having two inputs in parallel so input can come either from first switch or from second one. So, now let's start implementing some complex logical gates in Ladder Logic for PLC. Today, we are gonna implement these logic gates:

- NAND Logical gate in Ladder Logic for PLC
- NOR Logical gate in Ladder Logic for PLC
- XOR Logical gate in Ladder Logic for PLC
- XNOR Logical gate in Ladder Logic for PLC

#### NAND Logical gate in Ladder Logic for PLC

- NAND gate is another type of logical gate, which is normally used. NAND gate is nothing but a simple NOT of AND gate. In simple words, if we add a NOT gate in front of AND gate, we get NAND gate. The truth tablel of NAND gate is shown in the below figure:

- It is quite obvious from the truth table of NAND gate that the output will be OFF only when both the inputs will be ON otherwise output will remain ON. So, now lets implement this gate in ladder logic programming.
- The below image shows the implementation of NAND logical gate in Ladder Logic form:

- Now, if you understand the above figure, then its quite obvious. We have used both inputs in normally closed form so when both inputs are OFF the output will be ON. If we get X0 ON then in still we will get the HIGH voltage from X1. If we make X1 ON then we get HIGH voltage from X0, but if we get both X0 and X1 ON then our Y0 will get OFF. Again we are using inputs in normally closed form so when our actual input is OFF then our X0 is closed. :)

#### NOR Logical gate in Ladder Logic for PLC

- In NOR gate, we simple place a NOT gate in front of OR gate. Its truth table is shown in below figure:

- From the truth taable of NOR gate, its quite obvious that its output will be ON when both of its input goes OFF otherwise the output will remain ON. Lets implement this NOR logical gate in Ladder Logic diagram.
- The below figure shows the NOR logical gate in ladder logic diagram:

- If you got the ladder logic form of NAND gate, then its not gonna be much problem. Simple two normally closed inputs are placed in series, so now when any of them gets ON, then output will get OFF.

- If you have noticed, whenever NOT gate is involved somewhere, we use normally closed inputs.

#### XOR Logical gate in Ladder Logic for PLC

- The truth table of XOR gate is shown in below figure:

- From the truth table, we can get this thing that, output will ON only when the inputs are in opposite states and output will be OFF when inputs are in same state.
- The ladder logic implementation of XOR gate is shown in below figure:

- Now it has gone a little complex but lets understand how's its working. We have placed X0 and X1 in series and also in parallel, but in first string X0 is normally open and X1 is normally closed while in second string X0 is normally closed and X1 is normally open.
- Now, what we need to do is if both inputs are in same state we need to turn OFF the output. That's what we are doing in above logic diagram. Let's say X0 and X1 both are OFF then the normally open switches will be OFF and they wont let the HIGH voltage pass and hence our Y0 will remain OFF. And if both are ON then the normally closed will be OFF and again Y0 will remain OFF.
- Now if X0 is ON and X1 is OFF, then the first string will connect and our output will ON, and if X0 is OFF while X1 is ON then our second string will connect and will make our output ON. Quite simple and easy.

#### XNOR Logical gate in Ladder Logic for PLC

- Last but not the least XNOR gate, if we add NOT gate in front of XOR gate we get XNOR gate, let's have a look at its truth table below:

- So, in XNOR gate, we get our output ON when both inputs are in same state otherwise its OFF. Let's implement it in ladder logic form below:

- Now in this ladder logic diagram, we are getting introduced with a new symbol, till now we have used normally open output but here for the first time, we are using normally closed output Y0.
- It's exactly the same logic as we used for XOR gate, but the only difference is ere we are using normally closed output. So, simple when the output is gets ON, its actually OFF and when it gets OFF its actually ON ;)
- I hope now you got the clear concept of How to do programming using Ladder Logic and what's its difference with Microcontrollers like Arduino or PIC Microcontroller etc.