Homework05_key - CS/ECE 3810 Solutions Homework #5 Fall...

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CS/ECE 3810 Solutions Homework #5 Fall 2009 1. Exercise 3.10: 3.10.3 (1 point each) : Convert to binary and extract the sign, exponent, and mantissa. 0x24A60004 = 00100100101001100000000000000100 Sign: Positive Exponent: 01001001 = 73 (with bias) = -54 (without bias, subtract 127) Mantissa: 1 + 0. 01001100000000000000100 = 1 + 2 -2 + 2 -5 + 2 -6 + 2 -21 = 1.296875476 1.296875476 * 2 -54 = 7.1991 * 10 -17 0xAFBF0000= 10101111101111110000000000000000 Sign: Negative Exponent: 01011111 = 95 (with bias) = -32 (without bias, subtract 127) Mantissa: 1 .01111110000000000000000 = 1 + 2 -2 + 2 -3 + 2 -4 + 2 -5 + 2 -6 + 2 -7 = 1.4921875 -1.4921875 * 2 -32 = -3.4742697 * 10 -10 3.10.4 (1 point each) : Convert to binary scientific notation, then extract fractional portion and exponent. Binary: -1609.5 = -11001001001 . 1 Normalize: -1. 10010010011 * 2 10 Add bias: 10 + 127 = 137 = 10001001 Result: 11000100110010010011000000000000 Binary: -938.8125 = -1110101010.1101 Normalize: -1. 1101010101101 * 2 9 Add bias: 9 + 127 = 136 = 10001000 Result: 11000100011010101011010000000000 3.10.5 (1 point each) : This is nearly the same as 3.10.4. Simply recompute the exponent and represent the mantissa with more bits. Binary: -1609.5 = -11001001001 . 1 Normalize: -1. 10010010011 * 2 10 Add bias: 10 + 1023 = 1033 = 10000001001 Result: 1100000010011001001001100000000000000000000000000000000000000000 Binary: -938.8125 = -1110101010.1101 Normalize: -1. 1101010101101 * 2 9 Add bias: 9 + 1023 = 1032 = 10000001000 Result: 1100000010001101010101101000000000000000000000000000000000000000
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2. Exercise 3.14: 3.14.4 (5 points) : Convert to binary scientific notation, then extract fractional portion and exponent.
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Homework05_key - CS/ECE 3810 Solutions Homework #5 Fall...

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