QUESTION 2 A machine stores floating point number in a 9-bit word. The first bit is for the sign of the number, the second bit is for the sign of the exponent, the next 3 bits are for the exponent, and the final 4 bits are for the mantissa. The number that (101111011)2 represents in the above given 9-bit format is

QUESTION 2 A machine stores floating point number in a 9-bit word. The first bit is for the sign of the number, the second bit is for the sign of the exponent, the next 3 bits are for the exponent, and the final 4 bits are for the mantissa. The number that (101111011)2 represents in the above given 9-bit format is

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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Consider an 8-bit floating point format. In this representation 4 bits are reserved for the mantissa and 3 bits are reserved for the exponent and 1 bit is reserved for the sign of the number. The exponent of the number is stored with a bias = 3. Express the decimal number 4.75 in this 8 bit floating point format. Write down the next bigger representable number in decimal base. B If you would be conducting the following operation using this 8 bit floating point format what would the result of the following calculation be ? 4.75 + 0.05 - 4.75 Express the decimal number 4.75 in this 8 bit floating point format. [10] b) Write down the next bigger representable number in decimal base. [7.5] c) If you would be conducting the following operation using this 8 bit floating point format what would the result of the following calculation be ? 4.75 + 0.05 - 4.75
Assume a 24-bit word on a computer. In these 24 bits, wewish to represent the value 295.1. a) How would the computer represent the decimal value295?2. b) If our computer uses 8-bit ASCII and even parity, howwould the computer represent the string 295?3. c) If our computer uses packed BCD with zero padding, howwould the computer represent the number +295?
This problem covers floating-point IEEE format.(a) Assuming single precision IEEE 754 format, what is the binary pattern for decimal number -6.16?(b) Assuming single precision IEEE 754 format, what decimal number is represented by this word:0 01111100 01100000000000000000000(Hint: remember to use the biased form of the exponent.)
A, What is the Hex value for the ASCII bit pattern that represents the letter lower case 't' ? b, When interpreted using floating-point format in which the most significant bit is the sign bit, the next three bits represent the exponent field in excess notation, and the last four bits represent the mantissa, the bit pattern 01001100 represents the value _____________ .
J - For the IEEE 754 single-precision floating point, what is the number, as written in binary scientific notation, whose hexadecimal representation is the following? FF80 0000
In each of the following you are given a bit sequencecorresponding to the IEEE single precisionrepresentation of a floating-point number. In eachcase determine the base 2 floating-point representationof the number and also the base 10 decimalrepresentation of the number: 10111100010110000000000000000000
Suppose A = -14 and B = +6 (both in base 10) C=A*B What is the resulting product of your previous multiplication in FP decimal representation (simply use a decimal point)? Take the result you just produce and shift it by three digits to the right of the decimal point (e.g., if your number was 12.0 it now becomes 0.012). Now, express your shifted result as a single precision FP number using the IEEE 754 standard for single precision (of course you need to convert the number from decimal to binary). Please do not calculate more than the first 8 fraction bits.
a) A fixed-point binary number system has 5 whole bits and 3 fractional bits. What is the range of numbers in binary that can be represented in this format? What is the decimal value of the largest number that can be represented? b) A fixed-point binary number system has 4 whole bits and 12 fractional bits. Show the (4-hexit) hexadecimal representation of the following decimal numbers 0.375, - 1.33, and 1/40 in this finite format. Do not show recurring sequences. c) Assume a 16-bit floating point format designed as follows: 4-bit signed exponent and 12-bit fraction. Normalization is strictly enforced. What is the hexadecimal representation of the 16-bit floating point format for 1/40?
A random positive integer between 0 and 35767 is generated by the computer. Write aprogram which sets bits 3, 5, 8, 12 and 15 using logical operators only. You are onlyallowed to use 1 bitwise operator. Also, the bitwise operator you are choosing can only beused once. Show the originally generated number and the modified number using 16 bitrepresentation using showbits().
Write down the bit pattern in the fraction of value1/3 assuming a floating point format that uses Binary Coded Decimal (base 10) numbers in the fraction instead of base 2. Assume there are 24 bits, and you do not need to normalize. Is this representation exact?
What are the mantissa and exponent values if 6.75 is represented in 8-bit binary floating-point representation? a) Mantissa is 1011 and exponent is 101 b) Mantissa is 0011 and exponent is 100 c) Mantissa is 1011 and exponent is 100 d) Mantissa is 0011 and exponent is 101
1. Assume we are using the simple model for floating-point representation discussed in the class (the representation uses a 14-bit format, 5 bits for the exponent with an Excess-M, a significand of 8 bits, and a single sign bit for the number) Convert -123.075 to the floating-point binary representation. 2. a) What is "Approximation Error" in floating-point representation? b) Why is it happening? c) How can we minimize it? d) How can the character codes be a solution for this?