1. Consider a fictitious floating-point number system composed of the following numbers: S = {b.b2b3 2ty : b2, b3, y = 0 or 1, and b = 1 unless b = b2 = b3 = y = 0}. (a) Draw a portion of the real axis and plot the elements of S. (You first need to convert the elements of S to base 10.) Comment on the distribution of the elements. In particular, is the distribution uniform? (b) S contains twenty-five elements. What are the largest and smallest (in absolute value, nonzero) floating-point numbers? What is machine epsilon? Give your answers in base 2 and base 10.