For two inputs, XOR is one when the inputs differ; XNOR is one when they match. Repeated XOR gives the parity of a wider input group: one for an odd number of ones and zero for an even number. This connects gate logic directly to error checking.
Worked example
For A = 1 and B = 0, XOR is 1 and XNOR is 0. For data 1011, calculate 1 XOR 0 XOR 1 XOR 1 = 1. That value is also the even-parity bit needed to make the complete transmitted group contain an even number of ones.
What to watch for
For more than two inputs, repeated XOR means odd parity. It does not mean exactly one input is high.
Try it yourself
What is 1 XOR 1 XOR 0 XOR 0?
Answer: The first two ones cancel under XOR, leaving zero. The group has an even number of ones.
How to study this topic
Begin with settled Boolean values, then consider the physical signal and the device's electrical limits. A logic symbol explains a function; its data sheet explains which voltages, currents and delays are permitted.
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Digital Electronics