In combinational logic, what is the key difference between a half-adder and a full-adder when adding single-bit operands?

Introduction / Context:Adders are the building blocks of arithmetic logic units (ALUs). Understanding the structural difference between a half-adder and a full-adder helps explain how multi-bit adders are assembled in ripple-carry and look-ahead designs.

Given Data / Assumptions:

• Half-adder inputs: A and B; outputs: SUM and CARRY.
• Full-adder inputs: A, B, and Cin (carry-in); outputs: SUM and Cout (carry-out).
• Single-bit operands are being added in each stage.

Concept / Approach:A full-adder extends the half-adder by accepting a third input (Cin), enabling correct multi-bit addition by propagating carry from the less significant stage. The half-adder cannot incorporate an incoming carry, so it is generally used only in the least significant stage or in educational contexts.

Step-by-Step Solution:1) Identify half-adder limitation: only two inputs (A,B) → cannot add a prior carry.2) Identify full-adder enhancement: adds Cin so the total is A + B + Cin.3) Therefore, the essential difference is the presence of a carry-in in the full-adder.4) Hence the correct statement: Full-adder has a carry-in.

Verification / Alternative check:Examine ripple-carry adder diagrams: only the least significant stage could be a half-adder; all higher stages require a full-adder to accept the carry from the previous stage.

Why Other Options Are Wrong:Half-adder has a carry-in: false by definition.Half-adder lacks carry-out: incorrect; it does output carry when A and B are both 1.Full-adder lacks carry-out: false; Cout is essential for cascading.

Common Pitfalls:Confusing SUM and CARRY roles or assuming both adders accept Cin. Only the full-adder incorporates the incoming carry for proper multi-bit addition.

Final Answer:Full-adder has a carry-in.