= Solution
Use <Karnaugh maps> with rows $wx$ and columns $yz$, both in <Gray code> order $00,01,11,10$. Juxtaposition means <Boolean conjunction>, $+$ means <Boolean disjunction>, and a bar means <Boolean negation>. The minimal <sum of products> forms are
$$
\boxed{c=\bar wx+\bar wz+\bar x\bar y,}
$$
and
$$
\boxed{d=w\bar x\bar y+\bar w\bar xy+\bar wy\bar z+\bar w\bar x\bar z+\bar wx\bar yz.}
$$
For $c$, the groups are $\{4,5,6,7\}$, $\{1,3,5,7\}$ and $\{0,1,8,9\}$. For $d$, take $\{8,9\}$, $\{2,3\}$, $\{2,6\}$, $\{0,2\}$ and the isolated minterm $\{5\}$. Every group contains only required ones. The last $c$ group wraps between the top and bottom map rows.
These covers are minimal: $c$ needs its three essential groups, forced by inputs 6, 3 and 8. For $d$, input 5 is isolated, while 9, 3 and 6 each force their respective pair; input 0 still needs a further group. These five groups also attain the minimum literal count of 16.
\Image[/past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2016/digital-resit-decoder-karnaugh.png]
{title=<Karnaugh maps> for the three decoder outputs used in the solution}
{description=Original maps in Gray order. Invalid inputs are fixed to zero for $c$ and $d$; only the $f$ map in part (d) treats them as X. Blue cells are required ones.}
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