Sec $11\mathrm{.}5$: #$26$ You might think that n $1$ multiplications are needed to compute x n $,$ since x n $=$ x $$ x $$ x But observe that, for instance, since $6=4+2,$ x $6=$ x $4$x $2=($x $2)2$x $2.($Note: in binary, $6$ is $110)$ Thus x $6$ can be computed using three multiplications: one to compute x $2,$ one to compute $($x $2)2,$ and one to multiply $($x $2)2$ times x $2.$ Similarly, since $11=8+2+1,$ x $11=$ x $8$x $2$x $1=(($x $2)2)2$x $2$x $($Note: in binary, $11$ is $1011)$ So x $11$ can be computed using five multiplications. These potential patterns can be rewritten as: x $6=$ x $122$ x $121$ x $020$ x $11=$ x $123$ x $022$ x $121$ x $120$ a$.($Credit given for attempting only, please give it a try $-$ if you don$$t have a good idea where to start, please reach out to me for help$)$ Write an algorithm to take a real number x and a positive integer n and compute $5$ x n $.$ As you build the algorithm, note the relationship between the binary representation of n and the x $2$ i terms that are included in the product. Remember that we can $$shift$$ the binary digits of a number to the right by dividing by $2($truncating to keep the value an integer$)$ b$.$Analyze your algorithm in part $($a$)$ and determine the number of multiplications performed in terms of the value of n$.$ How does it compare with the optimal solution of $$log$2($n$)$