Definition of a full adder: A full adder stage adds two single-bit operands along with an incoming carry (Cin) and produces a Sum and a carry-out (Cout). What does a full adder add?
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Atwo 2-bit binary numbers
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Btwo 4-bit binary numbers
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Ctwo single bits and one carry bit
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Dtwo 2-bit numbers and one carry bit
Answer
Correct Answer: two single bits and one carry bit
Explanation
Introduction / Context:A full adder is the fundamental building block for multi-bit ripple-carry adders. Understanding its inputs clarifies how larger adders are constructed by cascading stages.
Given Data / Assumptions:
- Single full-adder cell, not a 4-bit adder IC.
- Inputs: A (1 bit), B (1 bit), Cin (1 bit).
- Outputs: Sum (1 bit), Cout (1 bit).
Concept / Approach:The full adder solves a three-input addition problem at the bit level. The logic implements the equations Sum = A XOR B XOR Cin and Cout = majority(A, B, Cin), enabling carry propagation from less significant bits to more significant bits in a ripple chain.
Step-by-Step Solution:
Accept A, B, Cin as inputs.Compute Sum using cascaded XOR operations.Compute Cout using combinations of pairwise products (A*B + A*Cin + B*Cin) or a majority gate equivalence.Verification / Alternative check:Truth tables confirm that for all 8 combinations of A, B, Cin, the Sum/Cout match binary addition rules.
Why Other Options Are Wrong:Options referring to “2-bit” or “4-bit” numbers confuse a single full-adder cell with multi-bit adder ICs that contain several full-adder stages.
Common Pitfalls:Mixing up half adder vs full adder; a half adder lacks Cin and cannot be directly cascaded for accurate multi-bit addition with carry propagation.
Final Answer:two single bits and one carry bit