Listing first 8 bits generated by LFSR Consider the primitive polynomial P(x) = x^4 + x^3 + 1, initialized with the bit string (shifting occurs from left to right, were the right-most bit represents the LFSR output): 1101.
List the first 8-bits generated by the LFSR, starting with the bit 1 that is the right-most bit of the initialization sequence above.
This was my work to solve this:
          s1 s2 s3 s4  output (s4 xor s3)

         [[ 1  0  1   1    0 
          0  1  0]]   1    1
          1  0  1     0    1
          1  1  0     1    1
          1  1  1     0    1
          1  1  1     1    0 
          0  1  1     1    0 
          0  0  1     1    0
  

The answer is : 10110010. Is this because it is in result of what I have put in brackets?
A few things have gone wrong:

You've reversed the initial state, but continued to shift from left to right. If you do reverse then the shift is from right to left.
You've confused the output bit (the oldest bit in the register) with the feedback bit (the new value that is introduced after shifting)
The feedback rule for the polynomial $x^4+x^3+1$ is $s_{i+4}=s_{i+3}\oplus s_{i}$ and so in your notation would be $s_4$ xor $s_1$

With this borne in mind the first two rows of you table should read as follows:
s1  s2  s3  s4  feedback bit (s4 xor s1)  output bit (s1)
1   0   1   1   0                         1
0   1   1   0   0                         0...

and so on