diff --git a/_psets/12.md b/_psets/12.md index b4828d960949685239dfc205d6a13c2c0bac1037..ee34eaa37f2e271baa5460415bd2cabe1be1fe9a 100644 --- a/_psets/12.md +++ b/_psets/12.md @@ -179,12 +179,26 @@ corrupted by additive uncorrelated white noise. {:.question} For an order 4 maximal LFSR work out the bit sequence. +Table (13.1) indicates that a maximal LFSR of order 4 is $$x_n = x_{n-1} + x_{n-4}$$. The bit +sequence has to repeat in a cycle of length $$2^4 - 1 = 15$$. The bits are 1, 1, 1, 1, 0, 1, 0, 1, +1, 0, 0, 1, 0, 0, 0. + ### (b) {:.question} If an LFSR has a chip rate of 1GHz, how long must it be for the time between repeats to be the age of the universe? +The age of the universe is 13.7 billion years, which is about $$\num{43e16}$$ seconds. + +$$ +\begin{align*} +(2^N - 1) \cdot 10^{-9} \si{s} = \num{43e16} \si{s} \\ +(2^N - 1) = \num{43e25} +N = 88.5 +\end{align*} +$$ + ### (c) {:.question}