Discussion
What is the expression for even parity for 3 bits a, b, c ?
Answer: A
The expression is \(a \oplus b \oplus c\).
XOR of several bits is 1 when an odd number of them are 1. The even-parity bit must be 1 exactly in those cases, so that data plus parity bit together contain an even number of 1s. So the even-parity generator is \(P = a \oplus b \oplus c\).
Check a = 1, b = 0, c = 0: one 1, so P must be 1 to make the count even, and \(1 \oplus 0 \oplus 0 = 1\). The complement \(\overline{a \oplus b \oplus c}\) is the odd-parity bit. AND and OR of the bits do not track the count of 1s at all.
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