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Combinational circuit design: A full adder circuit can be implemented using which combination of half adders and/or logic gates?

Difficulty: Medium

Correct Answer: two half adders and an OR gate

Explanation:


Introduction / Context:
A full adder is a basic combinational circuit that adds three binary inputs (two significant bits and a carry-in). It is an essential building block for arithmetic logic in CPUs. This question examines how a full adder can be constructed from smaller blocks like half adders.


Given Data / Assumptions:

  • Inputs: A, B, and Cin.
  • Outputs: Sum and Cout.


Concept / Approach:
A half adder adds two bits and produces Sum and Carry. By cascading two half adders and combining carries with an OR gate, we implement a full adder. This construction is standard in digital electronics education.


Step-by-Step Solution:

First half adder adds A and B: produces Sum1 and Carry1.Second half adder adds Sum1 and Cin: produces final Sum and Carry2.OR gate combines Carry1 and Carry2 to produce Cout.


Verification / Alternative check:

Boolean expression: Sum = A XOR B XOR Cin; Cout = (A AND B) OR (Cin AND (A XOR B)). Matches the circuit built from two half adders + OR.


Why Other Options Are Wrong:

'two half adders': missing the OR for carry combination.'NOT gate' addition is irrelevant.'three half adders': unnecessary redundancy.'one half adder and XOR': incomplete for carry-out.


Common Pitfalls:

Confusing the role of OR vs XOR in carry generation.


Final Answer:

two half adders and an OR gate
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