Parity and XOR behavior: an XOR gate (extended to multiple inputs) asserts logic-1 for input words containing how many 1-bits?

Introduction / Context:XOR (exclusive-OR) is central to parity computations and error detection. When generalized to more than two inputs, XOR outputs 1 precisely when the count of 1-bits at its inputs is odd.

Given Data / Assumptions:

• XOR is associative and commutative over binary inputs.
• Multiple-input XOR equals 1 if an odd number of inputs are 1.
• Even number of 1s yields 0.

Concept / Approach:Define XOR truth for two inputs: 0⊕0=0, 0⊕1=1, 1⊕0=1, 1⊕1=0. Extending iteratively shows that XOR acts as a parity detector: it toggles with each encountered 1.

Step-by-Step Solution:

Verification / Alternative check:Test examples: with three inputs 1,1,1 → 1⊕1⊕1 = 1; with four 1s → 1⊕1⊕1⊕1 = 0.

Why Other Options Are Wrong:

Common Pitfalls:Confusing XOR with OR; OR outputs 1 when any input is 1, regardless of parity.

Final Answer:odd