Problem 13
The following is a system diagram for 3 bit linear feedback shift register:
a2
a1
ao
? output
a. If you were to start with 100 ($a_0a_1a_2$, $a_0$ = 1, $a_1$ = $a_2$ = 0), show that linear feedback
shift register returns to the same value (100). Show the values of taps ($a_0$, $a_1$, $a_2$) for every
shift step. What is the period (number of shifts required to return to same value)?
b. Find value of autocorrelation, R(n), for shift (n) in one period of the output stream emerging
from the shift register for n = 0, 1, and 3. N denotes the period of linear feedback shift
register.
N
1
R(n) = \frac{1}{N} \sum_{m=1}^{N} s[m]s[m + n]
