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76.)

[ 10 pts ] Consider the two S-boxes S1 and S2 of DES shown. Three hex digits (12 bits) are provided to these two S boxes. The higher order six bits are fed to S1 and the lower order six bits are fed to S2. For the six bits input to S1, the first and last bits are used to select the row, and the middle four bits are used to select the column. Note that each S box has four rows numbered 0, 1, 2, and 3 and sixteen columns numbered 0 to 15. So, two bits are sufficient to select a row, as 2² = 4 and four bits are sufficient to select a column, as 2⁴ = 16. The output from each S box is a four bit binary number, which means that the output from each S box ranges from 0 to 15. You must express the output of the S-boxes in hexadecimal, even though the table values are in decimal.

S1	C0	C1	C2	C3	C4	C5	C6	C7	C8	C9	C10	C11	C12	C13	C14	C15
R0	0	15	7	4	14	2	13	1	10	6	12	11	9	5	3	8
R1	4	1	14	8	13	6	2	11	15	12	9	7	3	10	5	0
R2	14	4	13	1	2	15	11	8	3	10	6	12	5	9	0	7
R3	15	12	8	2	4	9	1	7	5	11	3	14	10	0	6	13

S2	C0	C1	C2	C3	C4	C5	C6	C7	C8	C9	C10	C11	C12	C13	C14	C15
R0	15	1	8	14	6	11	3	4	9	7	2	13	12	0	5	10
R1	13	8	10	1	3	15	4	2	11	6	7	12	0	5	14	9
R2	3	13	4	7	15	2	8	14	12	0	1	10	6	9	11	5
R3	0	14	7	11	10	4	13	1	5	8	12	6	9	3	2	15

Determine the hexadecimal output for the following input: AF7₁₆

            AF7₁₆ = ______________________ ₂

            Input to S1 = __________________ ₂

            So, the row selector = row no. ____________₁₀

            And the column selector = column no. ____________₁₀

            Thus, the output from S1 = ____________₁₆

            Input to S2 = _________________₂

            So, the row selector = row no. ____________₁₀

            And the column selector = column no. ____________₁₀

            Output from S2 = ____________₁₆

            Hence, the output is ____________₁₆

Answer 1