Question

1. [20 marks) The following problems are about floating point sys- tem and floating point representation of a real number. as follows: A toy floating point system is given (B, t, L, U)= (4, 3,-1, 3) (1). [5 marks] Determine the number of distinct positive numbers can be represented by the system; (2). [4 marks] Determine the largest positive number and the small- est positive number the system can be represented by the system and give their decimal values; (3). [2 marks] Write down the rounding unit of the system; (4). [3 marks] Determine the decimal value of the number 2.0314 with e = 2; (5). (6 marks] Three real numbers in base 4 system are give as follows (the subscript 4 just indicate that it is the base 4 system): (a). 1 2.10332 (b). x2 3.311034 (c). x3 = 1.13232 - Write down their floating point representations with the round- ing strategy, i.e., fl(x1), fl(x2) and fl(x3).

Answer 1

t. The distinct bositive numaers tapres ents y he system The 3, 4 bositve number ts 4 QHe largesi 2,