Answered: Convert -0.6 to a 16 bit floating point…

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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Convert -0.6 to a 16 bit floating point number.
(Sign:1-bit Exp:5-bit Mant:10-bit excess-15)
Convert -0.6 to a 16 bit floating number. Express your answer as hexadecimal.
(Sign:1-bit Exp:5-bit Mant:10-bit excess-15)

Expert Solution

Step 1

16 bit floating point number is called Half.

The Half type is more precisely described as a base-2 16-bit interchange format designed to facilitate the transfer of floating-point data between implementations.

Sign bit: 1 bit
Exponent bits: 5 bits
Significand bits: 10 bits (with 1 implicit bit that is not stored)
The true exponent is derived by subtracting 15 from the stored exponent. That's why it's called excess-15.

So the 16 bit floating representation generalized form is

-1^(sign bit) * 2^(storedExponent - 15) * (implicitBit + (significand/1024))

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