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3. Compute the decimal equivalent of the following IEEE single precision floating point numbers. Show your work. A. OXC2874000 B. Ox43960000

3. Compute the decimal equivalent of the following IEEE single precision floating point numbers. Show your work. A. OXC2874000 B. Ox43960000

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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**Exercise: Converting IEEE Single Precision Floating Point Numbers** **Problem Statement:** Compute the decimal equivalent of the following IEEE single precision floating point numbers. Show your work. **Given Numbers:** - A. 0xC2874000 - B. 0x43960000 **Instructions:** To solve for the decimal equivalent, follow these steps for each hexadecimal number: 1. **Convert Hexadecimal to Binary:** - Each hexadecimal digit converts to a 4-bit binary sequence. 2. **Identify Components in IEEE 754 Format:** - **Sign Bit**: 1 bit - **Exponent**: 8 bits - **Mantissa (Fraction)**: 23 bits 3. **Calculate Decimal Value:** - Determine the sign, exponent, and mantissa. - Adjust the exponent by the bias (127 for single precision). - Calculate the normalized real number using the formula: \((-1)^{\text{sign}} \times 1.\text{mantissa} \times 2^{\text{exponent} - 127}\). 4. **Perform Calculation:** - Substitute values into the formula to find the decimal equivalent. **Solution:** Show all steps and calculations clearly for each hexadecimal value.
Transcribed Image Text:**Exercise: Converting IEEE Single Precision Floating Point Numbers** **Problem Statement:** Compute the decimal equivalent of the following IEEE single precision floating point numbers. Show your work. **Given Numbers:** - A. 0xC2874000 - B. 0x43960000 **Instructions:** To solve for the decimal equivalent, follow these steps for each hexadecimal number: 1. **Convert Hexadecimal to Binary:** - Each hexadecimal digit converts to a 4-bit binary sequence. 2. **Identify Components in IEEE 754 Format:** - **Sign Bit**: 1 bit - **Exponent**: 8 bits - **Mantissa (Fraction)**: 23 bits 3. **Calculate Decimal Value:** - Determine the sign, exponent, and mantissa. - Adjust the exponent by the bias (127 for single precision). - Calculate the normalized real number using the formula: \((-1)^{\text{sign}} \times 1.\text{mantissa} \times 2^{\text{exponent} - 127}\). 4. **Perform Calculation:** - Substitute values into the formula to find the decimal equivalent. **Solution:** Show all steps and calculations clearly for each hexadecimal value.
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Here in this question question we have given two floating point number and we have asked to convert it into decimal equivalent.

A)  0xC2874000

B)  0x43960000

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