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 ofthe 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 canbe represented in this format? Write them in exponential notation.

Answered: Suppose that we use the 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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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.

Expert Solution

Step 1

Introduction

In the IEEE 754 floating-point standard, the smallest positive number is referred to as the "positive denormalized number" or just "denormalized number". This number is the smallest positive number that can be represented in the standard, and its value is determined by the number of exponent and significand bits used in the format. The smallest positive number in the single-precision format is typically around 2^(-126), while in the double-precision format it is around 2^(-1022).

The largest positive number that can be represented in the IEEE 754 standard is "Infinity", which is represented as a special value. The value of Infinity is greater than any representable finite number, and it is used to represent overflow conditions.

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