1. Consider the following algorithm.

// Assume n is a given integer being power of 2 count 0 xn while x > 1 do

begin

x x/2

count count + 1 end

output count

(a) Give the trace table and the output of the above algorithm when n = 32.

(b) In general, how many times the while loop is executed for input n being a positive power of 2 (e.g., when n = 2,4,8,16,32,64,...)?