1 Suppose a computer company is developing a new floating point system for use with their...

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1 Suppose a computer company is developing a new floating point system for use with their machines. They need your help in answering a few questions regarding their system. The company's floating point system is specified by (B,t, L,U). Assume the following: All floating point values are normalized (except the floating point representation of zero). All digits in the mantissa (i.e., fraction) of a floating point value are explicitly stored. The number 0 is represented by a float with a mantissa and an exponent of zeros. (Don't worry about special bit patterns for too and NaN.) Answer the following: (a) How many different nonnegative floating point values can be represented by this floating point system? (b) Same question for the actual choice (B,t, L,U) = (7, 10, 20, 50) (in decimal) which the com- pany is contemplating in particular. (c) What is the approximate value (in decimal) of the largest and smallest positive numbers that can be represented by this floating point system? (d) What is the rounding unit? (e) The number 80/7 = 11.4285714285714... has no exact representation in any decimal floating- point system with finite precision. Can it be represented exactly in the proposed new system? What are the exponent and mantissa? 1 Suppose a computer company is developing a new floating point system for use with their machines. They need your help in answering a few questions regarding their system. The company's floating point system is specified by (B,t, L,U). Assume the following: All floating point values are normalized (except the floating point representation of zero). All digits in the mantissa (i.e., fraction) of a floating point value are explicitly stored. The number 0 is represented by a float with a mantissa and an exponent of zeros. (Don't worry about special bit patterns for too and NaN.) Answer the following: (a) How many different nonnegative floating point values can be represented by this floating point system? (b) Same question for the actual choice (B,t, L,U) = (7, 10, 20, 50) (in decimal) which the com- pany is contemplating in particular. (c) What is the approximate value (in decimal) of the largest and smallest positive numbers that can be represented by this floating point system? (d) What is the rounding unit? (e) The number 80/7 = 11.4285714285714... has no exact representation in any decimal floating- point system with finite precision. Can it be represented exactly in the proposed new system? What are the exponent and mantissa?