Standard XOR behavior — choose the correct complete truth-table output Select the correct 2-input XOR truth table description for all input combinations (A,B → Y).

Introduction / Context:The exclusive-OR (XOR) gate outputs logic 1 when its inputs differ and outputs logic 0 when they are the same. This fundamental pattern drives applications such as parity generation, binary addition without carry, and conditional inversion.

Given Data / Assumptions:

• Two binary inputs A and B.
• XOR is defined as Y = A ⊕ B.
• “Differ” means exactly one of A or B equals 1.

Concept / Approach:Use the definition “1 when inputs are unequal.” That is equivalent to the Boolean expression Y = A · B̄ + Ā · B, or to Y = (A + B) · (Ā + B̄). This ensures Y=0 for 00 and 11, and Y=1 for 01 and 10.

Step-by-Step Solution:A=0, B=0 → equal → Y=0.A=0, B=1 → different → Y=1.A=1, B=0 → different → Y=1.A=1, B=1 → equal → Y=0.

Verification / Alternative check:Implement XOR with two ANDs, two inverters, and one OR as Y = A·B̄ + Ā·B; simulate or hand-evaluate to see the same outputs. Another check: think of binary addition without carry; sum bit is XOR of inputs.

Why Other Options Are Wrong:Each incorrect option either asserts 1 when inputs are equal or assigns 0 to one of the unequal cases, contradicting the XOR definition.

Common Pitfalls:Confusing XOR with OR (which is 1 if any input is 1) or with XNOR (which is 1 when inputs are equal).

Final Answer:00→0, 01→1, 10→1, 11→0