Key distinction between half-adder and full-adder What is the major functional difference that a full-adder provides compared to a half-adder?

Introduction / Context:
Half-adders and full-adders both compute binary sums, but only one supports carry propagation, which is essential for multi-bit addition in arithmetic logic units. This question targets your understanding of that essential extension.

Given Data / Assumptions:

• Half-adder inputs: A, B → outputs: Sum, Carry.
• Full-adder inputs: A, B, Cin → outputs: Sum, Cout.

Concept / Approach:
The full-adder’s distinguishing feature is the ability to accept a carry-in (Cin) from the previous stage, enabling chaining across multiple bit positions. Without Cin, multi-bit addition cannot propagate carry, which is why half-adders alone are insufficient for parallel addition of multi-bit numbers.

Step-by-Step Solution:
Identify missing feature in half-adder: no carry-in.Recognize full-adder adds Cin to A and B: Sum = A XOR B XOR Cin.Thus, the major difference is the carry input capability.

Verification / Alternative check:
Truth tables demonstrate that full-adders cover 8 input combinations (A, B, Cin), whereas half-adders cover 4 combinations (A, B).

Why Other Options Are Wrong:

• “Nothing basically”: Incorrect; the carry input is fundamental.
• “Handle double-digit numbers”: Number of digits is unrelated; cascading is what matters.
• “Half adders can handle only single-digit numbers”: Misleading phrasing; limitation is lack of Cin, not “digits.”

Common Pitfalls:

• Assuming two half-adders automatically equal a full-adder without the OR gate for carries.
• Confusing decimal “digits” with binary bit-widths.

Final Answer:
Full adders have a carry input capability.