Implement XNOR using NAND gates ?

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SUMMARY

The minimum number of NAND gates required to implement an XNOR function is 5. The implementation starts with two NAND gates to invert inputs A and B, followed by three additional NAND gates to create the necessary logic for the XNOR operation. This configuration effectively combines the functions of AND and OR gates using NAND gates. The discussion highlights a common misconception regarding the number of gates needed, clarifying that the correct answer is not among the provided multiple-choice options.

PREREQUISITES
  • Understanding of digital logic gates, specifically NAND gates.
  • Knowledge of Boolean algebra and logic functions such as XOR and XNOR.
  • Familiarity with logic circuit design principles.
  • Basic skills in simplifying logic expressions.
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  • Research how to implement XOR using only NAND gates.
  • Learn about the principles of digital circuit minimization techniques.
  • Explore the design of combinational logic circuits using NAND gates.
  • Study the applications of XNOR gates in digital systems.
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Electronics engineers, computer scientists, and students studying digital logic design who are interested in optimizing logic gate implementations.

rclakmal
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what is minimum number of NAND gates to implement XOR?
i thought it in this way .first i found how many NAND gates are need to to implement XOR .
if the two input it 'A' nd 'B'
then
XOR function =A'B+AB'
so i need two NAND gates to invert A and B
then for two AND gates i need another 4 NAND gates as each AND gate need 2 NAND gates .
then for final OR gate i need another 3 NAND gate .
so this will give the XOR function .To make it XNOR i need another NAND gate

so total number of NAND gates=2+4+3+1=10

but in my MCQ question it has only
a)3 b)4 c)5 d)6

i don't how to implement XNOR in one of above answers ,totally by NAND gates .can somebody help me ?
Thanks !
 
Physics news on Phys.org
Three NAND gates can be combined to produce the double AND plus OR function. The rest are just those required for the invert operations.
 
ok thnaks !and i found some good ideas from wikepedia also !
 

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