Identify the Boolean equation that correctly represents the two-input exclusive-OR (XOR) function in standard sum-of-products or equivalent Boolean form.

Introduction / Context:
The exclusive-OR (XOR) function outputs 1 when its inputs differ and 0 when they are the same. It is fundamental in parity generation, adders (sum output), and data comparison circuits. Recognizing its Boolean forms is essential for simplification and hardware realization.

Given Data / Assumptions:

• Two inputs: A and B.
• Standard Boolean operators: * for AND, + for OR, and ~ for NOT.
• Equivalent XOR forms exist; we focus on a correct canonical expression.

Concept / Approach:
By definition, XOR is true when exactly one of the inputs is 1. Translating that into Boolean algebra yields the canonical sum-of-products: A*~B + ~A*B. This covers the two cases (1,0) and (0,1) while excluding (0,0) and (1,1).

Step-by-Step Solution:

Verification / Alternative check:
Another well-known XOR identity is (A + B) * ~(A*B). Expanding shows it reduces to A*~B + ~A*B, confirming equivalence. Truth-table evaluation also verifies the mapping.

Why Other Options Are Wrong:
A*B + ~A*~B is XNOR (true when inputs are equal). A + B is OR (true when any input is 1, including both). A*B is AND (true only when both are 1). None of these match the XOR behavior of “one but not both.”

Common Pitfalls:
Confusing XOR with OR, or picking the XNOR form by mistake. Also, forgetting the valid alternative XOR form (A + B) * ~(A*B) can cause uncertainty when simplifying expressions.

Final Answer:
A*~B + ~A*B