6. e) Assume we are using a simple model for floating-point representation similar to the one used in Chapter 2 of the textbook which has a 14-bit format, 5 bits for the exponent with a bias of 15 (not 16 as in the textbook), a normalized mantissa of 8 bits, and a single sign bit. Show how the computer would represent the numbers 12.125 using this representation.
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- Scenario: In a biased N-bit binary number system with bias B, positive and negative numbers are represented as their value plus the bias B. For example, for 5-bit numbers with a bias of 15, the number 0 is represented as 01111, 1 as 10000, and so forth. Biased number systems are sometimes used in floating point mathematics. Consider a biased 8-bit binary number system with a bias of 12710 Question: What is the representation and value of the most negative number?Let a = 1.0 × 29 , b = −1.0 × 29 and c = 1.0 × 21 . Using thesimple floating-point model described in the text (therepresentation uses a 14-bit format, 5 bits for the exponent with abias of 15, a normalized mantissa of 8 bits, and a single sign bit forthe number), perform the following calculations, paying closeattention to the order of operations. What can you say about thealgebraic properties of floating-point arithmetic in our finitemodel? Do you think this algebraic anomaly holds undermultiplication as well as addition?1. b + (a + c) =2. (b + a) + c =1. 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?
- Please please don't copy Computer Science for BCH (16,12). when input is (0, 4, 14, 14, 4, 4, 15, 2, 4, 2, 15, 13), what are the check digits?1. Write down the mathematical notation for fixed point representationand floating representation and also explain each term. 2. Consider the following machine number in 64 bit and Precisely represent the above machine number in decimal digits. 0 10000000011 1011100100010000000000000000000000000000000000000000Explain 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).
- 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?a) A fixed-point binary number system has 5 whole bits and 3 fractional bits. What is the range of numbers in binary that can be represented in this format? What is the decimal value of the largest number that can be represented? b) A fixed-point binary number system has 4 whole bits and 12 fractional bits. Show the (4-hexit) hexadecimal representation of the following decimal numbers 0.375, - 1.33, and 1/40 in this finite format. Do not show recurring sequences. c) Assume a 16-bit floating point format designed as follows: 4-bit signed exponent and 12-bit fraction. Normalization is strictly enforced. What is the hexadecimal representation of the 16-bit floating point format for 1/40?The IEEE Standard 754 representation of a floating point numberis given as: 01101110110011010100000000000000. Determine thebinary value represented by this number. If a computer’s system clock is 2.4 GHz, calculate the period of thesystem clock. If an 8-bit binary number is used to represent an analog value inthe range from 200 ounces to 700 ounces, what is the resolution ofthe system?
- 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?Question 6 a) The IEEE Standard 754 representation of a floating point number is given as: 01101110110011010100000000000000. Determine the binary value represented by this number. b) Convert each of the following 8-bit two’s complement binary values to decimal. i) 10110111(base 2) ii) 01001101(base 2) iii) 11010111(base 2) iv) 01110111(base 2) c) Discuss the differences between static RAM and dynamic RAM