Reason for DES table representation
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.