Please answer question c d e

Answer for part a and b

Question 3: An Imaginary Floating Point number representation system (16 points) Suppose you are asked to design a 16-bit floating point number system that works in a similar way as the IEEE754 standard. Assume the system uses 1 bit for the sign, x bit(s) for the exponent and all the remaining bits (out of the 16 bits) for the significand. Note 1. This representation has normalized, de-normalized and special cases as you have seen in IEEE754 standard. 2. The representable range of the system should be big enough to cover the interval [-65504.00, +32800.00). Answer the questions below: a) What is the minimum number of bits needed for the exponent? What is the value of the corresponding bias? Show your steps clearly otherwise no mark will be given. (6 points) b) Show the representation of +1376(10) with this system. Show your steps clearly, otherwise marks will be deducted. (2 points) c) Show the representation of the negative infinity with this system. Show your steps clearly, otherwise marks will be deducted. (2 points) d) Calculate the least positive number that can be represented, show the value in decimal format. Show your steps clearly, otherwise marks will be deducted. (4 points) e) Can the number -832.375(10) be represented precisely by the system? The answer "Yes" or "No" alone will get you no mark. You need to justify your answer with clear calculation steps. (2 points) ANSWER: The binary representation of 65504 = 1111111111100000 which can also be written as 1.1111111111* 215. The binary representation of 32800 = 1000000000100000 which can also be written as 1.0000000001* 215. 1) Number of bits required to store decimal value (unbiased exponent value) 16 is 4. The bias value is 15. Hence, the total number of bits required = 5. 2) Binary representation of 1376 = 10101100000 Sign bit = 0 since the number is positive. Normalizing 10101100000, we get 10101100000 = 1.01011 * 210 Biased exponent value = 10 + 15 = 25 = 110012 And the significand bits are 0101100000. Hence, the floating point number is: 0 11001 0101100000