P1. We wish to store the following numbers in a hypothetical 9-bit decimal (base-10) computer that uses 6 bits for the magnitude of mantissa and 1 bit for the magnitude of exponent (note that 1 bit is always used for sign of mantissa and 1 bit is always used for sign of exponent). The computer rounds half to even. For each of the numbers below, answer the following questions: i. What will the number be stored as in the computer (don't forget the special numbers +Inf, 0)? ii. If the number can be stored as a regular number (NOT a special number), what is the round-off error Axl in its representation and the relative error in AXI round-off 1x1 iii. If the number can be stored as a regular number (NOT a special number), is it AX true that !s where 5 is the machine epsilon? |x 2 (a)-258.7500300x107 (b)-258.750400x106 (c)-258.7985x10-5 (d) 258.75962 (e) 258.7900000000x10-5 (f) 258.7x10-15 P2. For the hypothetical computer specified in P1, what is (a) The maximum spacing between any two consecutive numbers that can be represented exactly? Give an example. (b) The minimum spacing between any two consecutive numbers that can be represented exactly? Give an example. P3. If we had used fixed point representation (instead of floating point representation) to store numbers in a 9-bit decimal (base-10) computer that uses 1 bit for the sign with 4 bits before/after the decimal point, what is (a) The range of numbers that can be stored (min-max)? (b) The magnitude (neglecting sign) of the largest and smallest non-zero numbers that can be stored? (C) The maximum and minimum spacing between any two consecutive numbers that can be represented exactly? (d) The maximum relative error in round-off AX 1x1