What is the expression for sum of a full adder with 2 input bits a, b and…

2026

What is the expression for sum of a full adder with 2 input bits a, b and carry bit c ?

  1. A.

    a ⊕ b ⊕ c

  2. B.

    (a ⊕ b ⊕ c)'

  3. C.

    a ∧ b ∧ c

  4. D.

    a ∨ b ∨ c

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Correct answer: A

A full adder is a digital circuit that adds three binary inputs: two significant bits (a and b) and an incoming carry bit (c). The output sum represents the least significant bit of this addition. In binary arithmetic, adding three bits results in a 1 if an odd number of inputs are 1. The XOR operation (⊕) outputs true only when an odd number of inputs are true. Therefore, the sum expression is a ⊕ b ⊕ c. This matches Option A.\nOption B represents the complement of the sum, which is incorrect for the sum output itself. Option C (a ∧ b ∧ c) represents a majority function or carry-out condition where all inputs are 1, not the sum. Option D (a ∨ b ∨ c) is true if any input is 1, which does not correctly model binary addition logic. Thus, the correct expression for the sum output of a full adder is a ⊕ b ⊕ c.

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