In digital communications and error detection circuits, parity generators and parity checkers are commonly implemented using specific logic gates. Which type(s) of logic gates are typically used to generate a parity bit and to check parity (even or odd) in such systems?

Introduction / Context:
Parity is one of the simplest and most widely used error-detection techniques in digital systems, serial links, memory subsystems, and communication protocols. A parity generator produces a single parity bit that makes the total number of 1s either even (even parity) or odd (odd parity). A parity checker then verifies that property on reception. Understanding which logic primitives naturally realize these functions is essential in combinational logic design and exam preparation.

Given Data / Assumptions:

• Task: identify the gate type(s) used for parity generation and checking.
• Even parity requires an even count of 1s; odd parity requires an odd count.
• We assume standard two-level logic without encoded tricks.

Concept / Approach:
The XOR operation outputs 1 if and only if the number of 1s at its inputs is odd. Cascading XORs across multiple bits therefore produces an output that represents the odd-parity function. Conversely, XNOR outputs 1 if and only if the number of 1s is even. Thus, XOR naturally generates odd parity and can be inverted for even parity; XNOR naturally generates even parity and can be inverted for odd parity. Parity checkers compare the received data bits and parity bit using XOR or XNOR to verify integrity.

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