1. (a) [6 points] Consider a base 5 normalized, floating-point number system. Assume that a hypothetical computer using this susytem has the following floating-point represen- tation: where sm is the sign of the mantissa, se is the sign of the exponent (1 for negative, 0 for positive), di are the digits of the mantissa, and e, are the digits of the exponent. i. Consider the base 5 number, given using the above representation, 02003004. What exact decicaml value does it represent? ii. What decimal value does 11004003 represent? iii. What is the smallest positive, non-zero, number that can be represented in this system? Give the answer in the above form (i.e. as 8 base-5 digits.) (b) [4 points] Determine the second order (n = 2) Taylor approximation for f(x) In (x -1), expanded about a 2, including the remainder term. Do not simplify the form of this polynomial: that is, do not multiply out any powers