2. Assume we are using the simple model for floating-point representation as given in this book (the representation uses a 16-bit format, 5 bits for the exponent with a bias of excess-15, a normalized mantissa of 10 bits, and a single sign bit for the number): Show how the computer would represent the numbers a) +3.53125 and -3.34375 using this floating-point format. a) +3.53125 b)-0.09375
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- Data represented in ________ is transmitted accurately between computer equipment from different manufacturers if each computer’s CPU represents real numbers by using an IEEE standard notation.A(n) __________ is an integer stored in double the normal number of bit positions.Assume we are using the simple model for floating-point representation discussed in the class (the representation uses a 14-bit format, 5 bits for the exponent with an Excess-M, a significand of 8 bits, and a single sign bit for the number): Convert -43.0735 to the floating-point binary representation. (Remember we learned "implied one" format in the lecture)
- Show Steps Please 18. If the floating-point number representation on a certain system has a sign bit, a 3-bit exponent and a 4-bit significand: a) What is the largest positive and the smallest positive number that can be stored on this?system if the storage is normalized? (Assume no bits are implied, there is no biasing, exponents use two's complement notation, and exponents of all zeros and all ones are allowed.) b) What bias should be used in the exponent if we prefer all exponents to be non-negative? c) Why would you choose this bias?Assume we are using the simple model for floating-pointrepresentation as given in the text (the representation uses a 14-bitformat, 5 bits for the exponent with a bias of 15, a normalizedmantissa of 8 bits, and a single sign bit for the number):1. a) Show how the computer would represent the numbers100.0 and 0.25 using this floating-point format.2. b) Show how the computer would add the two floating-pointnumbers in Part a by changing one of the numbers so theyare both expressed using the same power of 2. c) Show how the computer would represent the sum in Partb using the given floating-point representation. Whatdecimal value for the sum is the computer actually storing?Explain.Please answer parts a, b, and c of this question. Assume we are using the simple model for floating-point representation as given in the text (the representation uses a 14-bit format, 5 bits for the exponent with a bias of 15, a normalized mantissa of 8 bits, and a single sign bit for the number): a) Show how the computer would represent the numbers 100.0 and 0.25 using this floating-point format. b) Show how the computer would add the two floating-point numbers in Part a by changing one of the numbers so they are both expressed using the same power of 2. c) Show how the computer would represent the sum in Part b using the given floating-point representation. What decimal value for the sum is the computer actually storing? Explain.
- Please answer both part a and b of this question. If the floating-point number representation on a certain system has a sign bit, a 3-bit exponent, and a 4-bit significand: a) What is the largest positive and the smallest positive number that can be stored on this system if the storage is normalized? (Assume that no bits are implied, there is no biasing, exponents use two’s complement notation, and exponents of all 0s and all 1s are allowed.) b) What bias should be used in the exponent if we prefer all exponents to be non-negative Why would you choose this bias?Explain the term masking. How is it useful for data representation? Explain the concept using an example For a floating-point format with a k -bit exponent and an n -bit fraction, give a formula for the smallest positive integer that cannot be represented exactly (because it would require an n + 1 –bit fraction to be exact).Assume we have a byte system for the fixed number representation (the whole number is presented with 8-bits (one byte) and the fractional part is presented with 2-bits), find the 2's complement of 0110 0010.01 The answer should be formatted as a fractional 2's complement binary number representation with the exact format of the answer that is required of this particular calculation
- Representing 7 bit floating -point Given that the: Sign: 1 bit (MSB)•Exponent: 3 bits•Mantissa: 3 bits (LSB) State/provide the representation in 1s and 0s of the value indicated for each of the following subquestions. Make certain you include all of the bits required for a complete 7-bit representation. Please show all the steps a- 5.2510 B: -2.75101. Assume we are using the simple model for floating-point representation discussed in the class (the representation uses a 14-bit format, 5 bits for the exponent with an Excess-M, a significand of 8 bits, and a single sign bit for the number) Convert -123.075 to the floating-point binary representation. 2. a) What is "Approximation Error" in floating-point representation? b) Why is it happening? c) How can we minimize it? d) How can the character codes be a solution for this?Consider a hypothetical 8 bit floating point machine representation with a sign bit, a 3 bit exponent, and a 4 bit mantissa (se1e2e3b1b2b3b4), where the exponent bias is 3 (add 3 to exponent of number to form machine representation). Recall that actual mantissa has 5 bits, since the leading 1 is not stored on the machine. (a) What is the number ?≈2.718 in this 8-bit format? (b) What is the number that (10100111)2 represents in this 8-bit format? (c) What is the upper bound of the relative error when representing a real number in this 8-bit format?