GATE CS 2017 Set 2 Q28 — Minimization (K-Maps etc.)

To find the minimum Product-of-Sums (POS) form of $f(w, x, y, z)$, we map the maxterms (where $f = 0$) and the don't-care conditions ($d$) on a Karnaugh map.

The maxterms (0s) are the minterms not present in $f$ or $d$:

• Maxterms (0s): $M = \{4, 9, 12, 13, 14\}$
• Don't-cares (Xs): $d = \{5, 6, 11, 15\}$

We group the 0s and Xs to find the simplified POS expression:

1. First Quad: Combining cells $\{9, 11, 13, 15\}$ gives the term $wz$ in the complement form, which corresponds to the POS sum term: $$(\bar{w} + \bar{z})$$
2. Second Quad: Combining cells $\{4, 6, 12, 14\}$ gives the term $x\bar{z}$ in the complement form, which corresponds to the POS sum term: $$(\bar{x} + z)$$

These two quads cover all the 0s (maxterms) of the function. Multiplying these sum terms yields the minimum POS expression:

Thus, the correct option is A.