Find the equivalent decimal value of the following floating-point representation using IEEE 754 standard single-precision (32-bit floating-point number with bias = 127)1 0111 1100 1000 0000 0000 0000 0000 000

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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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Find the equivalent decimal value of the following floating-point representation using IEEE 754 standard single-
precision (32-bit floating-point number with bias = 127)
1 0111 1100 1000 0000 0000 0000 0000 000

Expert Solution

Step 1

The value in binary representation is: 1 0111 1100 10000000000000000000000

In IEEE 754 single-precision representation, the first bit is used as a sign bit, the next eight bits are used for the exponent, and the remaining 23 bits of mantissa.

The first bit is 1, which means this is a negative number.

The exponent is = 01111100

The decimal value of the exponent is = 124

Now, we will decrease 127 from the above value to get the exponent.

= 2^{124 - 127} = 2^-3

The mantissa is = 10000000000000000000000

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