The following is a scheme for floating point number representations using 16 bits: s (1) e (6) m (9) Let s, e, and m be the numbers represented in binary in the sign, exponent, and mantissa fields respectively. Then the floating point number represented is (- 1)° (1 + m × 2 °) 2ª 31, if the exponent # 111111. 0, otherwise What is the maximum difference between two successive real numbers representable in this system?

The following is a scheme for floating point number representations using 16 bits: s (1) e (6) m (9) Let s, e, and m be the numbers represented in binary in the sign, exponent, and mantissa fields respectively. Then the floating point number represented is (- 1)° (1 + m × 2 °) 2ª 31, if the exponent # 111111. 0, otherwise What is the maximum difference between two successive real numbers representable in this system?

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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In a given 32-bit floating-point representation of numbers, if the number of bits of the mantissa is reduced to accommodate an increase in the number of bits of the exponent, this will result in the following: (select the best answer) Increased range of the numbers at the expense of the precision Increased precision of the numbers at the expense of the range Both range and precision increase Both range and precision decrease
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Implement the following error detection and error correction algorithms using C programming for Hamming code. For Hamming codes, flip a bit in the data and implement the algorithm to correct the same on the receiver side.
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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.) When you use this format to represent a real number, in which scenario an overflow will occur and in which scenarios an underflow may occur?
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