Full-adder inputs: How many input signals must a full adder accept to produce a sum and carry output?

Introduction / Context:The full adder (FA) is the fundamental 1-bit arithmetic cell inside multi-bit adders. It extends the half adder by considering a carry-in from a less significant position, enabling chained (ripple or look-ahead) operation.

Given Data / Assumptions:

• Outputs: Sum (S) and Carry-out (Cout).
• We are discussing a standard full adder block.

Concept / Approach:A full adder must combine two operand bits along with a carry-in bit. Thus, its three inputs are traditionally labeled A, B, and Cin.

Step-by-Step Solution:Inputs required: A, B (the bits to add) and Cin (carry from the previous, less significant stage).Outputs produced: Sum S and carry out Cout to the next more significant stage.Therefore, the required number of inputs is 3.

Verification / Alternative check:Canonical equations: S = A ⊕ B ⊕ Cin and Cout = AB + ACin + BCin, confirming dependence on three inputs.

Why Other Options Are Wrong:2 inputs describes a half adder, not a full adder.4 or more inputs would be nonstandard and unnecessary for 1-bit addition with carry-in.

Common Pitfalls:Confusing the half adder (two inputs) with the full adder, or assuming Cin is optional in a chained adder.

Final Answer:3