What Makes NAND & NOR Gates Universal?

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In summary, the conversation discusses the parameters that a gate must satisfy to be a universal gate, with NOR and NAND gates being the only universal gates while others are not. The ability to perform inversion is a crucial parameter for a gate to be considered universal. However, XOR gates, which can perform inversion, are not considered universal due to their inability to make other types of gates. The conversation also mentions a post in a forum thread that provides further information on this topic.
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Avichal
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I had no idea where to post questions related to Boolean algebra and logic gates, so I thought that the logic section would be good enough. If not please move it.

Anyways are there any parameters that a gate must satisfy to be a universal gate. NAND and NOR gates are universal gates while others are not. Whats so special in these gates that make them universal. So are there any parameters such that we look at them and can judge if a gate is universal or not?
 
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  • #2
NOR and NAND gates can be used to make most other types of gate, if you use enough of them.

Other gates such as the AND gate cannot, because they cannot do an inversion, no matter how you connect them.

So any desired gates that involve an inversion function can't be made with AND gates (or OR gates either). So, they are not universal gates.
 
  • #3
What about XOR gates. They can do inversion but they are not universal. So inversion is not a parameter to decide if a gate is universal
 
  • #4
Well, they must at least be able to do an inversion.

Maybe then potential universal gates have to be evaluated on their individual properties, unless you already know an answer to your own question.
 
  • #6

Related to What Makes NAND & NOR Gates Universal?

1. What are NAND and NOR gates?

NAND and NOR gates are basic logic gates that are used to perform logical operations in digital circuits. NAND stands for "NOT AND" and NOR stands for "NOT OR". These gates are made up of transistors and can be used to perform all of the basic logic operations such as AND, OR, and NOT.

2. How do NAND and NOR gates work?

NAND and NOR gates work by taking in two or more inputs and producing a single output based on the logical operation being performed. In a NAND gate, the output is only 0 when both inputs are 1, otherwise the output is 1. In a NOR gate, the output is only 1 when both inputs are 0, otherwise the output is 0. These gates can be combined to form more complex logic circuits.

3. What makes NAND and NOR gates universal?

NAND and NOR gates are universal because they can be used to create any other logic gate. This means that by using only NAND or only NOR gates, you can create a circuit that performs all of the basic logic operations, making them essential building blocks in digital circuit design.

4. Can NAND and NOR gates be used interchangeably?

Yes, NAND and NOR gates can be used interchangeably to create the same logic circuits. This is because they are duals of each other, meaning that a circuit made with NAND gates can be converted to an equivalent circuit made with NOR gates, and vice versa.

5. What are the advantages of using NAND and NOR gates?

NAND and NOR gates have several advantages, including their simplicity and versatility. They are also easy to manufacture and can be made smaller than other types of logic gates, making them ideal for use in integrated circuits. Additionally, using only NAND or NOR gates can reduce the number of components needed in a circuit, making it more efficient and cost-effective.

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