I designed 8 bit lfsr in vhdl. According to mathematical theory, I xor processed the outputs of registers 1, 4, 5, 6 and 8 and connected them to the input of register 1. theory says that if I give the inputs the polynomial "10111000", I get the repetition of (2^8)-1.
I tried some more. And I tried the circuit without connecting the output of the 1st register to the xor gate. interestingly I got the same (2^8)-1 repetition again. however, this time every 8-bit polynomial containing a 1-bit "1" signal produced the same signal. For example, when I gave "00100000" to the inputs, I got the same signal again.
What I'm wondering is why when I bind the output of register 1 to the xor gate I only get the repeat (2^8)-1 with 1 polynomial, while I get it with every polynomial when I don't?