1. Fill in the following table to show how the given integers are represented, assuming that 16 bits are used to store values and the machine used two's complement notation. Integer 28 2216 -18675 -12 31456 Binary Hex 4 Byte Big Endian (hex value as seen in memory) 4 Byte Little Endian (hex value as seen in memory)

1. Fill in the following table to show how the given integers are represented, assuming that 16 bits are used to store values and the machine used two's complement notation. Integer 28 2216 -18675 -12 31456 Binary Hex 4 Byte Big Endian (hex value as seen in memory) 4 Byte Little Endian (hex value as seen in memory)

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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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.
1. Write down the mathematical notation for fixed point representationand floating representation and also explain each term. 2. Consider the following machine number in 64 bit and Precisely represent the above machine number in decimal digits. 0 10000000011 1011100100010000000000000000000000000000000000000000
Round the following binary numbers (rounding position is bolded – it is the bit at the 2-4 position) following the rounding rules of the IEEE floating point representation. I. 1.00111112 II. 1.10010012 III. 1.01111002 IV. 1.01101002 For each of the four (4) resulting rounded binary numbers, indicate - what type of rounding you performed and - compute the value that is either added to or subtracted from the initial binary number (listed above) as a result of the rounding process. In other words, compute the error introduced by the rounding (approximation) process. please note that the rounding is based on the bolded numbers!!! Not the 2s in the end those are just binary signs
Question 11 Not yet answered P Flag question A computer system uses 8 bits to represent floating-point values. The 8 bits are organised as follows: The first bit is a sign bit (0 for positive, 1 for negative). The middle 3 bits are the exponent, which uses bias of 3. The last 4 bits are the significand, which is normalised in the same way as the significand is normalised in IEEE-754 formats. The format does not reserve any special values. The following arithmetic operation is performed on this system: 00011000 x 11000110 The result is then stored in the same 8-bit floating-point format. What is the relative error of the stored result comapred to the value of the result of the arithmetic operation? Answer s are rounded to 5 decimal places. O a. None of the other answers. O b. 0.03030% O c. 0.03125% O d. 0.97865% O e. 0%
4. Fill in the empty slots in the table by converting numbers into different representations. All numbers are 8 bits in length. Use 2's complement representation in binary and hexadecimal numbers. Signed Decimal Binary 0010 0001 1010 0100 Hexadecimal Unsigned Decimal 6F 33 -25
3. Fractional Values Complete the following table. The first row is filled in to show the kind of values expect ed. For simplicity, the bits of the floating point numbers are shown in 3 groups - sign, exponent and significand. For the 8 bit floating point assume 1 bit for the sign bit, 4 for the exponent, and 3 bits for the significand. The bias is 7 for this type. Decimal Binary Fixed Point 8 bit floating point 0.25 0.01 0 0101 000 0.125 1.101 0 1101 100
3. Fill in the following table to show how the given integers are represented, assuming that 16 bits are used to store values and the machine uses two's complement notation. 4-Byte Big Endian (Hex 4-Byte Little Endian (Hex Integer Binary Hex value as seen in memory) |value as seen in memory) 28 2216 -18675 -12 31456
Perform the following number base conversions. (You are required to show your conversion steps clearly. If the question is illogical, state the reason.) (i) 145.3510 to binary number (ii) ABCDEF16 to octal mumber (1) 1235; to decimal number
True/False In Floating Point Addition, the exponents of the two numbers being added need to be made equal before the mantissa fields can be added, as this ensures that the bit positional values are now aligned
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
Convert IEEE Single-Precision Binary Format Real number 11000100101001000010101000000000 to decimal. Please show all the steps. a) [1] What is the sign? b) [1] What is the biased exponent value? c) [1] What is the unbiased exponent value? d) [2] What is the normalized representation of the number in BINARY? e) [1] What is the unnormalized representation of the number in BINARY? f) [1] What is the decimal value of the whole number part of the number? g) [2] What is the decimal value of the fractional part of the number? h) [1] What is the real number in base 10