What Makes NAND & NOR Gates Universal?

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SUMMARY

NAND and NOR gates are classified as universal gates due to their ability to create any other type of logic gate through combinations, including AND, OR, and NOT gates. In contrast, gates like AND and OR cannot perform inversion, which is a critical function for universality. The discussion emphasizes that while inversion is necessary, it alone does not determine a gate's universality; rather, the ability to construct other gates is the defining characteristic. Therefore, evaluating potential universal gates requires a comprehensive analysis of their individual properties.

PREREQUISITES
  • Understanding of Boolean algebra
  • Familiarity with logic gate functions
  • Knowledge of gate combinations and circuit design
  • Basic principles of digital electronics
NEXT STEPS
  • Research the construction of logic circuits using NAND and NOR gates
  • Learn about the properties of other logic gates like XOR and their limitations
  • Explore the concept of gate universality in digital design
  • Study practical applications of universal gates in circuit design
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Students of electrical engineering, digital circuit designers, and anyone interested in the fundamentals of logic gates and Boolean algebra.

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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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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.
 
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
 
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.
 

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