3 input XOR Gate is not same as 3 input XNOR Gate
3 input XNOR is not same as cascading two 2 input XNOR gates
A XNOR B XNOR C !=
(A XNOR (B XNOR C))
N-input XNOR gate is complement of N-input XOR gate
Wikipedia definition:
The XNOR gate (sometimes XORN'T, ENOR, EXNOR or NXOR and pronounced as Exclusive NOR) is a digital logic gate whose function is the logical complement of the exclusive OR (XOR) gate.
*XOR gate(odd function) is odd parity checker and even parity generator
*XNOR(even function) is Even parity checker and Odd parity generator
For N(fanin)>2,
XOR gate can be associated:
a XOR b XOR c = (a XOR( b XOR c ))=((a XOR b) XOR c)
For n>=2,
Odd input XNOR gate cannot be associated:
a XNOR b XNOR c != (a XNOR( b XNOR c ))=((a XNOR b) XNOR c)
Even input XNOR gate can be associated