(a)

Refer the block cipher in Figure 8.5 in the texbook.

With n = 3 and the original 64-bit input equal to 10100000 repeated eight times, let's calculate the value of the output:

The block cipher Ti simply reverses the order of the eight input bits, so the 64-bit input sequence after applying the block cipher would be: 00000101 00000101 00000101 00000101 00000101 00000101 00000101 00000101

The 64-bit scrambler does not modify any bits, so the output remains the same: 00000101 00000101 00000101 00000101 00000101 00000101 00000101 00000101

(b)

Now, let's change the last bit of the original 64-bit input from a 0 to a 1:

The original 64-bit input with the last bit changed would be: 10100001 repeated eight times

After applying the block cipher Ti, the 64-bit input sequence becomes: 10000101 10000101 10000101 10000101 10000101 10000101 10000101 10000101

Since the 64-bit scrambler does not modify any bits, the output remains the same: 10000101 10000101 10000101 10000101 10000101 10000101 10000101 10000101

(c)

Now, let's consider the 64-bit scrambler that inverses the order of the 64 bits:

For both parts (a) and (b), the original 64-bit input remains the same: 10100000 repeated eight times

After applying the block cipher Ti, the 64-bit input sequence becomes: 00000101 00000101 00000101 00000101 00000101 00000101 00000101 00000101

With the 64-bit scrambler inversing the order of the 64 bits, the output would be: 10100000 10100000 10100000 10100000 10100000 10100000 10100000 10100000