Parity testing with XOR networks: for an XOR-based parity checker, what outputs occur for even-parity input words versus odd-parity input words?

Introduction / Context:
Parity checkers determine whether the number of 1-bits in a word is even or odd. XOR gates form the core of simple parity circuits because their output is 1 for odd parity and 0 for even parity.

Given Data / Assumptions:

• Parity checker constructed from cascaded XORs.
• Definition: “even-parity word” → even count of 1s; “odd-parity word” → odd count of 1s.
• Output convention: logic-low = 0, logic-high = 1.

Concept / Approach:
Because XOR toggles its output for each input bit equal to 1, the final output equals 1 if the number of toggles is odd; equals 0 if even. Hence, even parity → 0, odd parity → 1.

Step-by-Step Solution:

Verification / Alternative check:
Test a 4-bit word with two 1s (even): XOR output 0. Test with three 1s (odd): XOR output 1. This matches the stated mapping.

Why Other Options Are Wrong:

Common Pitfalls:
Mixing up conventions when an additional inverter is used after XOR (some designs invert the output to signal “OK” on even parity). Here, pure XOR output is assumed.

Final Answer:
low, high