(Solved): Consider a hypothetical floating point system in base-2 that uses 8-bit words. The system stores 1 ...

Consider a hypothetical floating point system in base-2 that uses 8-bit words. The system stores 1 digit for the sign, 3 digits for the exponent, and 4 digits for the mantissa. All floating point values are normalized, except for the special numbers, 0 and \( \infty \) ( 0 has exponent and mantissa of zeros; \( \infty \) has an exponent of ones and a mantissa of zeros). Answer the following questions about the hypothetical floating point system: (a) What are the lower and upper bounds, \( L \) and \( U \), on the exponent? (b) What is the approximate value of the largest positive number that can be represented by this floating point system? (report your answer in base-10 with three significant digits) (c) What is the machine precision? (report your answer in base-10 with three significant digits)