Discussion
The minimal number of literals in any POS expression for a full adder Sum function is
Answer: C
The minimal POS form of the full-adder Sum has 12 literals.
The Sum output is the three-input XOR, which is 0 exactly when an even number of inputs are 1: the input combinations 000, 011, 101 and 110. No two of these differ in a single bit, so no maxterms can be merged on a Karnaugh map, and the minimal product of sums is all four maxterms:
\[ \begin{aligned} S &= (A+B+C)(A+\bar{B}+\bar{C}) \\ &\quad \cdot (\bar{A}+B+\bar{C})(\bar{A}+\bar{B}+C) \end{aligned} \]
Four maxterms of three literals each give 4 × 3 = 12 literals. 4 counts the maxterms instead of the literals, and 8 would need some maxterms to shrink to two literals, which the checkerboard pattern of XOR does not allow.
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