How was PC2 designed?
They are the output of PC2s during the key schedule. PC2 table;

\begin{array}{|c|c|c|c|c|c|}\hline 
14 &amp; 17 &amp; 11 &amp; 24 &amp; 1 &amp; 5\\ \hline 
3 &amp; 28 &amp; 15 &amp; 6 &amp; 21 &amp; 10\\\hline 
23 &amp; 19 &amp; 12 &amp; 4 &amp; 26 &amp; 8\\\hline 
16 &amp; 7 &amp; 27 &amp; 20 &amp; 13 &amp; 2\\\hline 
41 &amp; 52 &amp; 31 &amp; 37 &amp; 47 &amp; 55\\\hline 
30 &amp; 40 &amp; 51 &amp; 45 &amp; 33 &amp; 48\\\hline 
44 &amp; 49 &amp; 39 &amp; 56 &amp; 34 &amp; 53\\\hline 
46 &amp; 42 &amp; 50 &amp; 36 &amp; 29 &amp; 32\\ \hline 
\end{array}

Let's look at only the  $C$ register map. The $D$ register map will be similar.

Let number the output of PC1's first half as;

   1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24


Now the outputs can be calculated as;

   1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 - index

   2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24  1 - rotate 1 PC1's first half to left
  14 17 11 24  1  5  3 28 15  6 21 10 23 19 12  4 26  8 16  7 27 20 13  2 - apply PC2 left half 
  15 18 12 25  2  6  4  1 16  7 22 11 24 20 13  5 27  9 17  8 28 21 14  3 - get this

   3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24  1  3 - rotate 1 to PC1's first half left
  14 17 11 24  1  5  3 28 15  6 21 10 23 19 12  4 26  8 16  7 27 20 13  2 - apply PC2 left half
  16 19 13 26  3  7  5  2 17  8 23 12 25 21 14  6 28 10 18  9  1 22 15  4 - get this


Note that sometimes you will see rotate left 2 since the rotate amount is defined in the key schedule according to round number as;

\begin{array}{|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|}\hline
\text{Number of Round  } &amp; 1&amp;2&amp;3&amp;4&amp;5&amp;6&amp;7&amp;8&amp;9&amp;10&amp;11&amp;12&amp;13&amp;14&amp;15&amp;16\\ \hline
\text{Number of Left rotations} &amp; 1&amp;1&amp;2&amp;2&amp;2&amp;2&amp;2&amp;2&amp;1&amp;2&amp;2&amp;2&amp;2&amp;2&amp;2&amp;1\\ \hline
\end{array}