No ai please, handwritten solutions preferred. Only d,e,f,g Suppose in the IEEE single format, the width of the exponent field is 4, not 8, and the width of the fraction field is 6, not 23.What should the exponent bias be?(b)What is the machine epsilon of this system?(c)What are the smallest and largest positive normal floating point numbers in this system?(d)Can any integer number between the smallest and largest positive normal floating point numbers be stored exactly inthis floating point system? Either prove it or give a counterexample.(e)What are the largest and smallest nonnegative subnormal floating point numbers in this system?(f)What are the two floating point numbers (neither is equal to 5) closest to 5?(g)Given number -(11.1001011) 2. Round it using the four rounding modes.

To answer the given questions on floating point systems, let's assume we are working with a specific…

Answered: Suppose in the IEEE single format, the…

Systems Architecture

7th Edition

ISBN:9781305080195

Author:Stephen D. Burd

Publisher:Stephen D. Burd

Chapter3: Data Representation

Section: Chapter Questions

Problem 5PE

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In a given 32-bit floating-point representation of numbers, if the number of bits of the mantissa is reduced to accommodate an increase in the number of bits of the exponent, this will result in the following: (select the best answer) Increased range of the numbers at the expense of the precision Increased precision of the numbers at the expense of the range Both range and precision increase Both range and precision decrease
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Suppose that we use the floating-point format with 12 decimal digits, SEEEMMMMMMMM, to rep- resent a real number, where S is the digit to represent the sign of the mantissa (use 0 for pos- itive and 5 for negative), EEE are the 3 digits to represent the exponent in excess-500 format, MMMMMMMM are the 8 digits to represent the magnitude of the mantissa, and the decimal point of the mantissa is right to the left of MMMMMMMM (i.e., SEEEMMMMMMMM representing the real number +0.MMMMMMMM × 10EEE-500) What are the smallest positive number and the largest positive number that can be represented in this format? Write them in exponential notation.
Suppose that we use the floating-point format with 12 decimal digits, SEEEMMMMMMMM, to rep- resent a real number, where S is the digit to represent the sign of the mantissa (use 0 for pos- itive and 5 for negative), EEE are the 3 digits to represent the exponent in excess-500 format, MMMMMMMM are the 8 digits to represent the magnitude of the mantissa, and the decimal point of the mantissa is right to the left of MMMMMMMM (i.e., SEEEMMMMMMMM representing the real number +0.MMMMMMMM × 10EEE-500.) When you use this format to represent a real number, in which scenario an overflow will occur and in which scenarios an underflow may occur?
X and Y are represented in IEEE single precision floating point notation. Let X = (41D00000)16, Y = (C0000000)16. The result of (x *y) in Decimal is
How many normalized numbers are represented by the floating point system F (β, t, L, U )? Provide a formula in terms of these parameters
B4
For IEEE 754 single-precision floating point, write the hexadecimal representation for positive zero, the smallest positive denormalized number and the largest positive normalized number
Computer Science Given the following 32-bit number in IEEE754 floating-point number format, B = OX4OBC000 b) Determine the hexadecimal representation in IEEE754 double-precision floating-point number format of the following two cases, i.
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).
In this question, you are provided with an IEEE-754 floating-point number in the form of 8 hexadecimal digits. You are asked to decode this value into its decimal representation. Do NOT use scientific notation. Do NOT round or truncate your answer. Do NOT add any spaces or commas to your answer. If the converted number is positive, do NOT add the plus sign. Your answer will consist of two parts, the integer value and the fraction value. Do not add any insignificant zeros to your answer. For the fraction part, you can start it by a decimal point or by a single 0, followed by a decimal point. Convert, i.e., decode, 0x48804008 from the 32-bit single-precision IEEE-754 FP representation into decimal representation. The integer part of the number is: D The fractional part of the number (including the decimal point) is: b
2. Convert the IEEE 754 single precision binary representation to a decimal number 1001 1001 1011 0000 0000 0000 0000 0000 Note: make sure that in final answer the fraction is in base 10 (at most 3 digits). You don't need to change the power of 2 in a power of 10.

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