I am new to this concept so please show your work for parts a, b, and c. Please don't skip the steps for b or c because I don't understand how the navigation of the S box works and I need all 3 examples worked through in order to understand it. Also please be certain of your work as I hope to use this as a basis for my understanding of the concept. Please don't guess and I'll be sure to up vote.

An important property which makes DES secure is that the S-boxes are nonlinear. Verify the nonlinearity of the S-boxes by computing the output of box S1, for several pairs of inputs. Show that for a. x,-000000, x2 = 000001 c. X1=101010, x2 = 010101 The first S-Box is shown below: Input bits 1 and 6 Input bits 2 thru 5 0000 0001 0010 0011 0100 0101 0110 0111 1000 1001 1010 1011 1100 1101 1110 1111 01 10000 11110111 0100 1110 0010 1101 0001 1010 0110 1100 1011 1001 0101 0011 1000