PYTHON

What we think of as real numbers in an algorithm, we approximate for computing purposes as floating-point numbers of the form: (-1)S (do d1d2... dp-1 Be where s E 0,1 indicates the sign p is the number of digits or precision each digit di [0, 1,...,B - 1] B is the base and e is the exponent. While we, as humans, tend toward base B = 10 , computers almost universally use a binary representation with B= 2. The floating-point representation corresponds to a unique real number: x = (-1)$(do + 8 + ... B + 4 "Alpe Some real numbers have an exact (but not unique) floating-point representation; e.g. x = 0.5 has the following representations: * = (-1)0 (1.0) 2-1=(-1)0(1 + ) 2-1= and i =(-1) (0.1) 2 = (-1 For uniqueness, choose the normalized (first) version with do + 0. A floating point number system is defined by base B, precision (number of digits) p, and range of exponents [eminemax. . Let's take a look at an example: B = 2, p = 2, e (-2,3] Positive normalized numbers: x = (-1)(1.0) 2-2 = 1 = (-1) (1.1) 2-2 1 # =(-1)(1.0) 2-1= 1 * =(-1) (1.1) 2-1= 3 x = (-1) (1.0) 20 = 1 * =(-1) (1.1) 20 = # =(-1) (1.0) 2+ = 2 =(-1) (1.1) 21 x= (-1)^(1.0) 22 = 4 x = (-10 (1.1) 22 = 6 = (-1) (1.0) 23 = 8 = (-1) (1.1) 23 = 12 xe X = {{1/4, 3/8, 1/2, 3/4, 1, 3/2, 2, 3, 4, 6, 8, 12} Here we embellish slightly by adding 1 digit of precision to get: = 2, p = 3, e -1,0,1,2,3 2a) Write a function (by completing the template below) to compute the number of entries in the array of all normalized representable values in a floating point system. Remember that the first digit in a normalized number must be non-zero. The other digits are integers satisfying 0