Adder selection – should a half adder be used whenever a carry input is required in an adder stage?

Introduction / Context:
Adders come in two basic building blocks: half adders and full adders. A half adder has no carry input; a full adder accepts a carry in (Cin). The choice depends on whether a stage must add two bits only or two bits plus an incoming carry.

Given Data / Assumptions:

• Binary addition across multiple bit positions.
• LSB stage has no incoming carry; higher stages typically do.
• Goal: determine which block to use when Cin is required.

Concept / Approach:
A half adder computes Sum = A XOR B and Carry = A * B. A full adder computes Sum = A XOR B XOR Cin and Cout = (A * B) + (Cin * (A XOR B)). Therefore, whenever a carry input is required, a full adder—not a half adder—must be used.

Step-by-Step Solution:

Verification / Alternative check:
Standard ripple-carry adders: LSB stage can be a half adder; all higher stages are full adders to accept carry propagation.

Why Other Options Are Wrong:
It is not limited to LSB, ripple mode, or delay issues; the functional requirement (Cin) dictates using a full adder.

Common Pitfalls:
Trying to feed an external carry into a half adder by ad hoc wiring; this breaks the defined logic equations.

Final Answer:
Incorrect