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Basic points require to solve this question are

1) Ex-or gate behavior

       A⊕0 = A and A⊕1=A'

2) D FlipFlop

   after applying clock, i/p is o/p

3) Binary to gray code conversion for n-bit

          Gn-1=Bn-1

         Gn-2= Bn-2 ⊕  Bn-2

        Gn-3 = Bn-3 ⊕ Bn-2 ............................... G0=B0 ⊕ B1

Let come to question,

1st i/p of z can be represented by w and 2nd i/p of z can be represented as v for better understanding..

therefore w=0 because of given Q=0 initially by the statement D-flipflop is cleared initially. and note the i/p of D flipflop is b7 for first clock and v=b7.and from the result of Ex-OR operation z=b7

there are 8-bits therefore clk apply 8 times only to get result

at 1st time clock applying, following all operations done at the same time

                D send i/p as o/p ==> w=b7

                shift register shift the z in to the register then register look like as 

 b6 b5 b4 b3 b2 b1 b0 G7

                D i/p is b6 ==> v=b6 ==> z= b6 ⊕ b7 = G6

at 2nd time clock applying, following all operations done at the same time

                D send i/p as o/p ==> w=b6

                shift register shift the z in to the register then register look like as 

b5 b4 b3 b2 b1 b0 G7 G6

                D i/p is b5 ==> v=b5 ==> z= b5 ⊕ b6 = G5 .....

By continue the above process, after applying totally 8 clock pulses  then register  look like as

G7 G6 G5 G4 G3 G2 G1 G0

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