We are using the m-sequence generator created according to the primitive polynomial x 10 +x 3 + 1. A

We are using the m-sequence generator created according to the primitive polynomial x 10 +x 3 + 1. A trial consists of initialization of the shift register with 10 bits, running the shift register with feedback according to the above connection polynomial for 500 steps, and the reading out the 500 bits of the LFSR. The following table shows some Initial Register Setting and Register Contents after 500 Steps. Table 2: Some pairs of register settings displaced by 500 steps Initial Register Setting Register Contents after 500 Steps 0100111010 1001000001 0111010010 1101000111 1011010110 1100101000 1000101101 1011011011 Using the above values can you figure out if the shift register was initialized with 1011000101, what would be the register contents after 500 steps? Can you say how many minimum such input and output pairs are needed to obtain the output for all possible non-zero inputs (i.e all inputs for which all input bits are not zero).