Q3. In Floating Point representations, answer the following questions showing all the steps: (Use the IEEE 754 standard for all) (showing all the steps used): (35 points) a) Write down the binary representation of the decimal number - 19.625. b) What decimal number does the bit pattern Ox0C000000 represent if it is a floating-point number? c) What number is represented by the following single precision float (single Precision): 11000000101000...0000 d) What number is represented by the following single precision float (single Precision):11000001110000000000000000...0000

Q3. In Floating Point representations, answer the following questions showing all the steps: (Use the IEEE 754 standard for all) (showing all the steps used): (35 points) a) Write down the binary representation of the decimal number - 19.625. b) What decimal number does the bit pattern Ox0C000000 represent if it is a floating-point number? c) What number is represented by the following single precision float (single Precision): 11000000101000...0000 d) What number is represented by the following single precision float (single Precision):11000001110000000000000000...0000

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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Q3. In Floating Point representations, answer the following questions showing all the steps: (Use the IEEE 754 standard for all) (showing all the steps used): a) Write down the binary representation of the decimal number 31.625 b) Write down the binary representation of the decimal number 31.625 assuming the IEEE 754 double precision format. c) Write down the binary representation of the decimal number 45.45. d) Write down the binary representation of the decimal number -19.625. e) What decimal number does the bit pattern Ox0C000000 represent if it is a floating-point number? f) What number is represented by the following single precision float (single Precision): 11000000101000...0000 g) What number is represented by the following single precision float (single Precision) :11000001110000000000000000...0000
Floating point calculation: a Show the IEEE 754 representation for the decimal value -0.375 in single precision b. Find the decimal representation for the following single precision floating point number 1011,1111,0111,0000,0000,0000,0000,0000 c. Perform the addition and multiplication of the two floating point numbers in (a) and (b) in binary scientific notation, and represent the sum and product in single precision.
47 by -18 (integers in decimal (base 10)). Q1 : What is the remainder of the division in FP decimal representation (i.e., if rem=53 then its FP decimal representation is 53.0)? What is the resulting number if you shift it three digits to the right of the decimal point? Express your shifted result as a single precision FP number using the IEEE 754 standard for single precision. YOU MUST FIRST CONVERT THE NUMBER FROM BASE 10 to BASE 2 and then do normalization etc. Do not calculate more than the first 8 fraction bits.
Perform the multiplication of the following two floating point numbers using the simple floating point format :(-0.75*23)*(-0.625*22) . Do the calculation in base 10 and comment on the accuracy of your calculation.
Perform the following additions. The numbers are in binary: 1) 1011 +0001 2) 00101110 +10010010 Repeat problem, this time convert the binary numbers to decimal, then perform the addition of the two decimal numbers. Convert the sum into binary representation and compare the results.
VI. Floating point representation Consider a 12-bit variant of the IEEE floating point format as follows: • Sign bit 5-bit exponent with a bias of 15. • 6-bit significand All of the rules for IEEE 754 Standard apply. Fill in the numeric value represented by the following bit patterns. You must write your number in decimal form (e.g. 0.0146485375, -0.0146485375). Bit Pattern 010011101110 111011101011 100101001111 001010111010 Numerical Value
lb. Floating point addition/subtraction Take the last 5 digits of your student number (example, A,A‚A‚A,A, in 2021-4,4‚A‚A„A,) and divide it by 4, taking note of the remainder. The value of the remainder will determine which set below is assigned to you. The given values below are written in 32-bit Single-precision Floating-point number representation (IEEE-754) in normalized form. Perform the floating-point operation assigned to you. Express the final answers in IEEE-754. Show your complete solution. Make sure to perform the arithmetic in binary (i.e. not in decimal, but you can do this to double-check your answer). Only solutions that show the binary arithmetic will be given full marks. (Please write down which set is assigned to you above your solution/answer) Given values: A: 11000000010110100101010000000000 B: 11000001110110111010000000000000 C: 01000001100111001000101010000000 D: 01000000010010011000100101000000 Set I (Remainder = 0): A+C Set III (Remainder= 2): B + C Set II…
4. The bfloat16 "brain floating point" format is a 16 bit format used in Google's machine learning and AI software. It is a binary floating point format which is very similar to the single precision IEEE-754 format: 1 bit is allocated for the sign, 8 bits for the exponent with a bias of 127, but only 7 bits are allocated for the fraction (the exponent is always chosen so that the first digit of the mantissa is 1, and then only the fraction is stored in memory). (a) What is the approximate decimal precision of a brain floating point? (b) If the bits are stored in the order: sign, exponent, fraction, and 0 corresponds to a positive sign, then calculate the decimal representation of the number stored as 1 00000110 0100010 (c) Given that the largest exponent actually used for numbers is 11111110, what is the largest number that can be expressed as a bfloat 16? (d) Supposing that numbers are truncated (rounded down), what is the maximum absolute rounding error in bfloat16?
3. Represent each of the following numbers as nor- malized base 2 floating-point numbers using 4 digits to represent the fractional part of the man- tissa; that is, represent the numbers in the form ±(1.b₁b₂b3b4)2 × 2k. (a) 21 (c) 9.872 (b) (d) -0.1
1- Given the value "OX40F40000" represents a single-precision IEEE floating-point number. Answer the following questions: (a) Represent the number in the format + 1.M × 2x (b) Find the decimal value for this number. Show your work by showing all steps needed to reach the final answer.
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 12.345 to the floating-point binary representation. (Remember we learned "implied one" format in the lecture) You need to type in the calculation steps or insert the picture of your handwriting using "insert" menu above.
3. floating point Convert the following decimal fixed point number to an IEEE single precision floating point format. Please show your intermediate calculations: 10.875 = Give the decimal fixed point equivalent of the following IEEE single precision floating point format number. Again, please show your intermediate calculations: 10000110 10101011000000000000000 (decimal)