Understanding full adders in arithmetic logic design: Which statement about full adders is correct in the context of building a parallel adder?

Introduction / Context:Binary adders are foundational to arithmetic/logic units. A half adder sums two bits without a carry-in. A full adder sums two bits plus a carry-in, making it the standard cell in multi-bit adders. This item checks practical implementation details of a parallel adder chain.

Given Data / Assumptions:

• We are building a multi-bit parallel (ripple) adder.
• The least significant bit (LSB) often has Cin = 0.
• Higher-order bits must accept the carry from the previous stage.

Concept / Approach:If the LSB stage never receives a carry-in, a half adder suffices at that position. All remaining stages must be full adders because they require a carry input from the prior stage.

Step-by-Step Solution:Identify LSB Cin: for plain addition, Cin(0) = 0.LSB hardware: half adder can be used, reducing gate count.All other bits: full adders required to accept propagated carry.Hence the correct statement is that the first stage may be a half adder.

Verification / Alternative check:Many textbooks present a “1 half adder + (n−1) full adders” implementation for an n-bit ripple adder when there is no external carry-in.

Why Other Options Are Wrong:Decimal addition requires BCD adders, not simple binary full adders.Full adders are not used to make half adders (it is the other way around conceptually).A full adder has three inputs (A, B, Cin), not “limited to two.”“No carry input” contradicts the full-adder definition.

Common Pitfalls:Forgetting that certain systems include an external carry-in, in which case even the LSB must be a full adder.

Final Answer:In a parallel full adder, the first stage may be a half adder.