= Solution
Only now may the invalid codes 10–15 be marked as <don't-care conditions>. The $f$ <Karnaugh map> gives
$$
\boxed{f=w+x\bar y+x\bar z+\bar y\bar z.}
$$
The groups are $\{8,\ldots,15\}$, $\{4,5,12,13\}$, $\{4,6,12,14\}$ and $\{0,4,8,12\}$. They cover all required ones, avoid valid-digit zeros, and may assign either output to invalid codes. The valid inputs 0, 5, 6 and 9 cannot share a valid implicant with each other, so at least four product terms are necessary. The displayed four-term cover uses only seven literals.
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