How to design an XOR with these gates?

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SUMMARY

Designing an XOR gate using 2 NAND gates, 1 NOR gate, and 3 inverters is achievable. The XOR function can be expressed as (A OR B) AND ~(A AND B). By applying the definitions of NOR and NAND, specifically that NOR is ~(OR) and NAND is ~(AND), the required gates can be effectively utilized to construct the XOR logic. This method confirms that the specified quantity and types of gates are sufficient for the design.

PREREQUISITES
  • Understanding of basic logic gates: NAND, NOR, and NOT (inverter)
  • Familiarity with Boolean algebra and logic expressions
  • Knowledge of how to manipulate logic gate functions
  • Experience with digital circuit design concepts
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  • Research the implementation of XOR using only NAND gates
  • Study the properties and applications of NOR gates in digital circuits
  • Explore advanced Boolean algebra techniques for simplifying logic expressions
  • Learn about digital circuit simulation tools for testing gate designs
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Electronics engineers, digital circuit designers, and students studying logic design will benefit from this discussion on constructing an XOR gate using specific types of logic gates.

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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!
 
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