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(7) Determine the machine representation in single precision on a 32-bit word-length computer for the decimal number -8 x 2 24.

(7) Determine the machine representation in single precision on a 32-bit word-length computer for the decimal number -8 x 2 24.

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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**Problem Statement:** Determine the machine representation in single precision on a 32-bit word-length computer for the decimal number \(-8 \times 2^{-24}\). **Explanation:** This problem involves converting the given decimal number into its IEEE 754 single-precision floating-point representation. Single-precision format uses 32 bits divided as follows: - 1 bit for the sign - 8 bits for the exponent - 23 bits for the fraction (mantissa) To solve this, you will need to: 1. Determine the sign bit (0 for positive, 1 for negative). 2. Normalize the number to find the exponent and mantissa. 3. Adjust the exponent using the bias (127 in this format). This procedure allows computers to handle a wide range of decimal values efficiently.
Transcribed Image Text:**Problem Statement:** Determine the machine representation in single precision on a 32-bit word-length computer for the decimal number \(-8 \times 2^{-24}\). **Explanation:** This problem involves converting the given decimal number into its IEEE 754 single-precision floating-point representation. Single-precision format uses 32 bits divided as follows: - 1 bit for the sign - 8 bits for the exponent - 23 bits for the fraction (mantissa) To solve this, you will need to: 1. Determine the sign bit (0 for positive, 1 for negative). 2. Normalize the number to find the exponent and mantissa. 3. Adjust the exponent using the bias (127 in this format). This procedure allows computers to handle a wide range of decimal values efficiently.
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