Consider the XOR of three bits A$,$ B$,$ and C$,$ which can either be two two$-$bit XOR gates strung

together, or a single three$-$bit XOR gate:

a$.$ What is the truth table for this circuit?

b$.$ When there is an even number of $1\text{'}$s in the input $($we call this even parity$),$ what is the

output?

c$.$ When there is an odd number of $1\text{'}$s in the input $($we call this odd parity$),$ what is the

output?