A B a) 3.264x10^3 6.52x10^2 b) -2.27734375x10^0 1.154375x10^2 Calculate by hand

Question

                           A                        B a)                3.264x10^3           6.52x10^2 b)         -2.27734375x10^0      1.154375x10^2 Calculate by hand A divided by B. Show all the steps necessaryto achieve your answer. Assume there is a guard, round, and stickybit, and use them if necessary. Write the final answer in both16-bit floating-point format and in decimal and compare thedecimal result to that which you get if you use acalculator.                            A                        B a)                3.264x10^3           6.52x10^2 b)         -2.27734375x10^0      1.154375x10^2 Calculate by hand A divided by B. Show all the steps necessaryto achieve your answer. Assume there is a guard, round, and stickybit, and use them if necessary. Write the final answer in both16-bit floating-point format and in decimal and compare thedecimal result to that which you get if you use acalculator.

Explanation / Answer

x.Xlor="red">please rate - thanks a) 3.264 × 103/6.525 × 102 3.264 × 103 = 3264 = 1.1001100000 × 211 6.525 × 102 = 652.5 = 1.0100011001 × 29 Exponent= 11 – 9 = 2, 2 + 16 = 18 (100102) Signs: both signs are positive so the answer will be positive Mantissa:                           1.0100000000100101 10100011001. | 11001100000.000000                         –10100011001.                                           101000111.0                             –101000110.01                                                 .11000000000                                               –.10100011001                                                 .00011100111000                                               –.00010100011001                                                 .0000100001111100                                               –.0000010100011001                                                 .0000001101100011 1.0100000000 10 0101 Guard = 1, Round = 0, Sticky = 1: Round up 1.0100000001 × 22 = 0100100100000001 = 101.00000001 = 5.00390625 calculator answer 5.002298850575 off by .001607399425 b) –2.27734375 × 100/1.154375 × 102 –2.27734375 × 100 = –2.27734375 = –1.0010001110 × 21 1.154375 × 102 = 115.4375 = 1.1100110111 × 26 Exponent = 1 – 5 = –5, –5 + 16 = 11 (010112) Signs: one is negative, the other is positive, so the answer will be negative Mantissa:                                               0.1010000110011101 11100110111. | 10010001110.0000000000000000                          – 1110011011.1                                                 11110010.100                              – 11100110.111                                         1011.10100000                                        – 111.00110111                                           100.011010010                                          – 11.100110111                                                 .110011011001                                               –.011100110111                                                 .0101101000010                                               –.0011100110111                                                 .00100000010110                                               –.00011100110111

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