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A $3$-input majority gate is defined by the logic function $M(a,b,c)=ab+bc+ca$. Which one of the following gates is represented by the function $M(\overline{M(a,b,c)}, M(a,b,\overline{c}),c)$?

  1. $3$-input NAND gate
  2. $3$-input XOR gate
  3. $3$-input NOR gate
  4. $3$-input XNOR gate
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Detailed Video Solution, with Complete Analysis: https://youtu.be/ks2tg5UaQ08 

NOTE that 3-inputs XNOR gate is NOT same as 3-inputs XOR gate. XNOR gate is ALWAYS Complement of XOR gate.

A Very Important NOTE:

$XNOR$ gate with inputs $A,B,C$ is NOT same as $A \odot B \odot C .$

$XNOR-n$ gate is defined as Complement of $XOR-n$ gate.

NOTE that: 

$a \odot b \odot c = a \oplus b \oplus c$

BUT $XNOR-3 \,\, gate \neq XOR-3 \,\, gate$

The exclusive‐NOR gate is the complement of the exclusive‐OR gate, as indicated by the small circle on the output side of the graphic symbol.

Detailed Video Solution, with Complete Analysis: https://youtu.be/ks2tg5UaQ08 


3 Inputs XNOR gate, Complete Analysis: https://youtu.be/uAadNn38oFo 

XOR & XNOR functions: https://www.youtube.com/watch?v=-30dUjh6Qv4 

After watching THIS video solution, Solve this GATE EC 2010 question: https://ec.gateoverflow.in/1953/gate-ece-2010-question-12 

Answer: