quiz1_sol - (2 6 2 4 2 2 2 1 =-86 10(d(4 points 8-bit...

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CDA3101 Quiz 1 (Solution) Last Name ________________________ Fall 2009 First Name ________________________ Time: 15 minutes Show all your work to get full credits. You can leave your answer in powers of 2. No calculators allowed. 1. Convert 11010110 2 to decimal assuming it is an (a). (2 points) 8-bit unsigned representation 2 7 + 2 6 + 2 4 + 2 2 + 2 1 = 214 10 (b). (2 points) 8-bit 2’s complement representation -2 7 + 2 6 + 2 4 + 2 2 + 2 1 = -42 10 (c). (2 points) 8-bit sign and magnitude representation Sign: Negative
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Unformatted text preview: -(2 6 + 2 4 + 2 2 + 2 1) = -86 10 (d). (4 points) 8-bit floating point number representation that uses 1 bit for the sign, 3 bits for the biased exponent and 4 bits for the fraction (f). Other than the numbers of bits, the representation is similar to the IEEE 754 standard. Sign: Negative Exponent: 101 2 = 5 10 ; 5 – 3 = 2 Fraction: 0110 As a result, -1 * (1.0110) * 2 2 = -1 * (1 + 2-2 + 2-3 ) * 4 = -1 * (1 + 0.25 + 0.125) * 4 = -5.5 10...
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