Assume we are using the simple model for floating-pointrepresentation discussed in the class (the representation uses a 14-bit format, 5 bits for the exponent with an Excess-M, a significand of8 bits, and a single sign bit for the number):Convert 22.375 to the floating-point binary representation.Your Answer:

Here in this question we have given a decimal number and we have asked to convert it into 14 bit…

Answered: Assume we are using the simple model…

Systems Architecture

7th Edition

ISBN:9781305080195

Author:Stephen D. Burd

Publisher:Stephen D. Burd

Chapter3: Data Representation

Section: Chapter Questions

Problem 4PE

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A(n) __________ is an integer stored in double the normal number of bit positions.
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 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)
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...?
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?
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?
Calculate (3.41700875 *10-3 + 6.34005625*10-3)* 1.25625* 102 by hand, assuming each of the values are stored in the 16-bit half precision format describedin in the textbook. Assume 1 guard, 1 round bit, and 1 sticky bit, and round to thenearest even. Show all the steps, and write your answer in both the 16-bit floating point format and in decimal.
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. I've gotten an answer of 1001 1110.00 but it says its wrong please help
Consider the following floating point representation where each number has 2exponent bits and 5 fraction bits. The exponent bias is 1. Round each number tohave 3 fraction bits. Apply round-to-even and round-toward-zero modes.a. 1 10 11100b. 0 00 00101c. 1 01 10101i. Can you see a pattern for rounding floating point numbers when thenumber of exponent bits are intact?
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.
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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 1011100100010000000000000000000000000000000000000000

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