Discussion
What is the expression for sum of a full adder with 2 input bits a, b and carry bit c ?
Answer: A
The sum is \(a \oplus b \oplus c\).
A full adder adds three bits. The sum bit is 1 when an odd number of the inputs are 1 (one 1 gives sum 1, two give sum 0 with a carry, three give sum 1 with a carry), which is exactly the XOR of all three: \(S = a \oplus b \oplus c\). The carry is \(ab + bc + ca\).
\(\overline{a \oplus b \oplus c}\) is the complement, wrong in every row. \(a \wedge b \wedge c\) is 1 only when all three are 1, and \(a \vee b \vee c\) is 1 whenever any is 1, so neither is the sum.
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