Answer most of 15.4

_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}