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XNOR has two definitions:

\$1^{st}:XNOR=NOT(XOR)\$

\$2^{nd}: XNOR(A,B)=\overline{A}\cdot\overline{B}+A\cdot B\$

The problem is that these definitions are not equal in Odd inputs, the second definition acts as xor at odd inputs.

is the second really a definition or is it just the SOP of the first definition at 2 inputs?

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    \$\begingroup\$ If you want to ask about odd numbers of inputs, you should make your definitions of the function for an odd number of inputs. \$\endgroup\$ – The Photon Dec 4 '18 at 21:23
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    \$\begingroup\$ These are equal. The number of inputs here are not Odd. XOR with number of inputs greater than 2 has two conflicting definitions indeed. electronics.stackexchange.com/questions/93713/… \$\endgroup\$ – Eugene Sh. Dec 4 '18 at 21:23
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XNOR is a negation of the Exclusuve OR on any number of inputs. Thus if you have n inputs, you perform

A0 + A1 + ... + An

discarding any carry bits from bit 0 (so that result remains to be 0 or 1), and then negate it.

Sounds like you are looking at the two-input implementation (e.g. from Wikipedia), and it is one of the possible ways to implement XNOR with two inputs. Three input equivalent (and optimized) circuit will look differently.

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