(a) Consider a base 5 normalized, floating-point number system. Assume that a hypothetical computer using this susytem has the following floating-point representation:

Where S _m is the sign of the mantissa, s _e is the sign of the exponent (1 for negative, 0 for positive), d _i are the digits of the mantissa, and e _j are the digits of the exponent.

i. Consider the base 5 number, given using the above representation, 02003004. What exact decimal value does it represent? ii. What decimal value does 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) Determine the second order (n = 2) Taylor approximation f(x) = ln(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.

Smdd d3 d4 Se e2