# How to design an XOR with these gates?

• jean28
In summary, to design an XOR gate with AND, OR, and NOT gates, you will need to build an OR gate, two AND gates with inverted inputs, and a final AND gate which will be the XOR gate. This process can also be done using NAND or NOR gates. In total, five gates are needed - one OR gate, two AND gates, and two NOT gates. An XOR gate can also be designed using other logic gates, but the number and type of gates may differ. The function of an XOR gate is to output a 0 if the inputs are the same, and a 1 if the inputs are different, achieved by using a combination of AND, OR, and NOT gates.
jean28
I need to design an XOR with 2 NANDS, 1 NOR, and 3 inverters. Is it possible? I can't seem to find how to do it now.

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Consider that the XOR of A and B can be written as:
(A OR B) AND ~(A AND B)

And recall that NOR is ~(OR) and that NAND is ~(AND) (NOT OR and NOT AND)

And that ~(~(A)) is just A

Then you can use up that exact quantity and type of gate!

Last edited:

## 1. How do I design an XOR gate with AND, OR, and NOT gates?

To design an XOR gate with AND, OR, and NOT gates, you can follow these steps:

• First, build an OR gate using two inputs and one output.
• Next, build two AND gates using the same inputs as the OR gate, but with one inverted input for each AND gate.
• Connect the output of the OR gate to the inputs of the two AND gates.
• Finally, connect the outputs of the two AND gates to the inputs of a third AND gate. This final AND gate will be the XOR gate, and its output will be the desired result.

## 2. Can I design an XOR gate using only NAND or NOR gates?

Yes, an XOR gate can be designed using only NAND or NOR gates. You can follow the same steps as above, but instead of using AND gates, use NAND or NOR gates.

## 3. How many gates do I need to design an XOR gate?

To design an XOR gate using AND, OR, and NOT gates, you will need a total of five gates - one OR gate, two AND gates, and two NOT gates.

## 4. Can I design an XOR gate with other types of logic gates?

Yes, an XOR gate can be designed using other types of logic gates such as XOR, XNOR, and NAND gates. However, the number of gates and the design process may vary depending on the types of gates used.

## 5. How does an XOR gate work?

An XOR gate, also known as an exclusive OR gate, outputs a 0 if both inputs are the same, and outputs a 1 if the inputs are different. This is achieved by using a combination of AND, OR, and NOT gates to create a logical circuit that produces the desired output based on the input values.

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