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You are asked to design a system of FP numbers representation (with your own design choices), labeled
Custom_FP_48, for which we have 48 bits at our disposal in order to represent a number, in analogy with
the IEEE 754 prototype. You are asked to provide:
a) The types for evaluating this number
b) The width of representation of these numbers (upper and lower)
c) The maximum precision (i.e., the minimum difference between two successive numbers).
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- You are asked to design a 16-bit floating point number system to store the lengths of various man-made objects. This system should work in a similar way as the IEEE754 standard. Assume a value stored in the system denotes the length of an object in centimeters, assume also that the maximum length to be stored is 45845.0 centimeters (i.e. length of the biggest man-made oil-tanker, the “Seawise Giant”). Note: This representation has normalized, de-normalized and special cases as you have seen in IEEE754 standard. Answer the questions below: a) Is sign bit needed in this system? Why yes or why not. b) What is the minimum number of bits needed for the exponent? What is the value of the corresponding bias? Show your steps clearly. If you write the values directly without showing the steps, you will not get any point. c) What is the maximum length the system can represent? Please show your steps clearly, otherwise no point will be given.Given the code segment below for r k to n do for s k to n do x[r,s] = 0.0; for r k to n do x[r,r] = 1.0; a) Generate intermediate code for the above coded And identify the basic blocks for the intermediate code generatedAs the IEEE 754 floating point standard only allows finite number of floating pointrepresentations in its format, the density of such representations may not be evenly distributed.Consider a region of (0,2) and (100,102). Which region do you think contains morerepresentations of floating points? Explain your logic.
- 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?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 =Answer the given question with a proper explanation and step-by-step solution. Consider a Hamming (7.4) code in which the parity bits are calculated according to the following equations: r0 = a0 + a1 + a2 r1 = a1 + a2 + a3 r2 = a0 + a1 + a3 The following dataword is to be coded with this scheme: format: a3 a2 a1 a0 0010 What is the parity code for the above dataword? Show it in decimal format for (r2,r1,r0); e.g. if the resulting bits are r2=1, r1=0, r0=0 (100), type the decimal equivalent of 100, which is 4.
- 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?Question 2(a). Consider the applications of the following number systems and explain why they are best suited for implementation of such systems.a) Binaryb) Octalc) Decimald) HexadecimalWrite in C++ program: Problem: Represent the binary representation of a float type to integer type. Single precision float (32-bit length) is represented in IEEE754 format: 1 bit of sign, 8 for exponent plus bias of 127, and 23 for the mantissa. Example: * 85.125 is [101 0101.001] in binary and this would be [1.0101 0100 1 x 2^6] in scientific notation of base 2. * Our sign bit will be [0] (positive), exponent+bias is [1000 0101] (6 + 127 = 133), and mantissa of [0 1010 1001000...] (whole is omitted and zeroes are added to the right until its length is 23). * Merging this will be [0100 0010 1010 1010 0100 0000 0000 0000] which is equivalent as 1118453760 in integer. * Therefore, binary of 85.125 in float is 1118453760 in integer. Input A single line containing a float type non-positive number. 85.125 Output A single line containing the integer representation of float type binary. 1118453760
- What does the Huffman code for a series of only two-character symbols look like? Give an example of a series of N characters with all of the characters coming from a two-character script to demonstrate the highest number of bits that could be used in a Huffman code.If an unsigned 8-bit integer were to be extended to a 16-bit one, the first 8 most significant bits (MSB) would be filled with ones, creating a signed 16-bit representation. Pick a solution from these two options: Is it true or false that...?Represent the binary representation of a float type to integer type. Single precision float (32-bit length) is represented in IEEE754 format: 1 bit of sign, 8 for exponent plus bias of 127, and 23 for the mantissa. Example: * 85.125 is [101 0101.001] in binary and this would be [1.0101 0100 1 x 2^6] in scientific notation of base 2. * Our sign bit will be [0] (positive), exponent+bias is [1000 0101] (6 + 127 = 133), and mantissa of [0 1010 1001000...] (whole is omitted and zeroes are added to the right until its length is 23). * Merging this will be [0100 0010 1010 1010 0100 0000 0000 0000] which is equivalent as 1118453760 in integer. * Therefore, binary of 85.125 in float is 1118453760 in integer. Input A single line containing a float type non-positive number. 85.125Output A single line containing the integer representation of float type binary. 1118453760