Full-adder sum implementation using XOR gates: In a standard 1-bit full adder, the SUM output (S) can be realized using two exclusive-OR (XOR) gates arranged so that S = A XOR B XOR Cin. Assess this claim.

Introduction / Context: The full adder is a fundamental combinational block that sums two bits and an incoming carry. Its outputs are SUM (S) and CARRY OUT (Cout). Understanding minimal gate implementations of S helps in efficient hardware design and HDL coding.

Given Data / Assumptions:

• Inputs: A, B, Cin.
• Outputs: S = A XOR B XOR Cin, and Cout = majority(A, B, Cin) = A*B + B*Cin + A*Cin.
• Exclusive-OR gate property: X XOR Y = (X and not Y) + (not X and Y).

Concept / Approach: The XOR function is the natural expression of bitwise addition without carry. For two inputs, S2 = A XOR B. Adding Cin requires XORing that intermediate sum with Cin: S = (A XOR B) XOR Cin. This can be implemented with exactly two XOR gates in cascade.

Step-by-Step Solution:

Verification / Alternative check: Build the truth table for A, B, Cin and compute S via XOR chaining. The resulting S matches binary addition modulo 2, confirming the implementation.

Why Other Options Are Wrong: “Incorrect” ignores the standard identity. “Only correct for carry-lookahead adders” is irrelevant; the SUM path is the same across architectures. “Requires three XOR gates” overcounts the needed logic.

Common Pitfalls: Mixing SUM and CARRY logic; assuming Cout also needs XOR chaining rather than majority logic; forgetting XOR associativity (A XOR B XOR Cin is well defined).

Final Answer: Correct