Chapter 2.6, Problem 13Q

The decimal number corresponding to a sequence of n binary digits $a_0,a_1,\mathrm{.......},a_{n-1}$, where each $a_i$ is either 0 or 1, is defined to be $a_0{2}^0+a_1{2}^1+\mathrm{.......}+a_{n-1}{2}^{n-1}$

For example, the sequence 0 1 1 0 is equal to 6 (= 0·2⁰ + 1·2¹ + 1·2² + 0·2³). Suppose a fair coin is tossed nine times. Replace the resulting sequence of H’s and T’s with a binary sequence of 1’s and 0’s (1 for H, 0 for T). For how many sequences of tosses will the decimal corresponding to the observed set of heads and tails exceed 256?