F(10,3,-54) be the system of normalized floating point system with Problem 1, Let F b= 10, 3 significant digits, and L =-5 and U = 4, One denotes FP = {x EF ; x > 0} lal amax, one denotes fl(x) E F the round- If z is a real number such that zmin ing floating point. An approximate addition is denoted by and is defined as follows. For (z, y) in FP x FP such that if x +xmaz, xy = fl (x + y). a) Are there numbers x E FP such that x 1 = x ? If yes, what the smallest of these numbers? b) Let zk = fl() for and integer k, k 1 . One sets S1 = x1 and Sk = Sk-1 e xk for k > 2. Determine S10. Compare with , 1/k