Reason for DES table representation Currently in college I'm learning about DES, and everywhere I look the table S-boxes are represented as follows:


S1  x0000x  x0001x  x0010x  x0011x  x0100x  x0101x  x0110x  x0111x  x1000x  x1001x  x1010x  x1011x  x1100x  x1101x  x1110x  x1111x
0yyyy0  14  4   13  1   2   15  11  8   3   10  6   12  5   9   0   7
0yyyy1  0   15  7   4   14  2   13  1   10  6   12  11  9   5   3   8
1yyyy0  4   1   14  8   13  6   2   11  15  12  9   7   3   10  5   0
1yyyy1  15  12  8   2   4   9   1   7   5   11  3   14  10  0   6   13


Is there any reason at all why this table is set up like this? Why not with the last two bits as row and the first 4 as column? Or even as a single row with the number as identifier, as I seem to have managed to do in a spreadsheet here (see A39:D103 for a single-index list)?
It demonstrates that for any fixed value $(x_1,x_6)=(a_1,a_6)$ of the first and last input bits, $$S(a_1,x_2,x_3,x_4,x_5,a_6)$$ forms a permutation as $(x_2,x_3,x_4,x_5)$ ranges over
 $\{0,1\}^4$ thus giving structural information about the DES 
S boxes.