Fibonacci LFSR, recovering previous bits Suppose somewhere is Fibonacci LFSR, we know that it has 7 cells and feedback taps are cell 2 and 7.

We intercepted part of a stream, and part intercepted is 1010101.

Is it possible to recover (preceeding)previous bits from this stream using this information?
Yes. just run the lfsr backwards, so if you have $$s(t)=s(t-2)+s(t-7)$$ use $$s(t-7)=s(t-2)+s(t)$$ all mod 2 with $$(s(-6),\ldots,s(0))=(1,0,1,0,1,0,1)$$ your initial loading.