Half adder vs full adder capability: A full adder adds three one-bit inputs (A, B, and a carry-in), whereas a half adder adds exactly two one-bit inputs with no carry-in. Evaluate the statement that “a half adder adds 1-1/2 bits.”

Introduction / Context:Adders are fundamental building blocks in arithmetic logic units. It is crucial to distinguish the functional inputs of a half adder and a full adder to design multi-bit adders properly.

Given Data / Assumptions:

• Half adder inputs: A and B (single bits); outputs: Sum and Carry-out.
• Full adder inputs: A, B, and Cin; outputs: Sum and Cout.
• No timing or speed enhancements are implied.

Concept / Approach:The “1-1/2 bits” phrase is informal and misleading. A half adder adds exactly two one-bit inputs and produces a two-bit result (Sum and Carry-out). A full adder explicitly incorporates carry-in so that adders can be chained bit by bit to form a ripple-carry adder.

Step-by-Step Solution:

Verification / Alternative check:To create multi-bit adders, chain one half adder only at the least significant stage (with Cin = 0), then use full adders for higher bits where Cin is non-zero.

Why Other Options Are Wrong:“Correct — 1.5 bits” is not a formal concept. Cascading or propagation delay does not redefine the basic inputs of a half adder.

Common Pitfalls:Assuming a half adder can handle incoming carry; attempting to cascade half adders alone will fail for multi-bit addition with carries.

Final Answer:Incorrect — a half adder adds two 1-bit inputs (no carry-in).