1 8 23 EXPONENT FRACTION N = (-1)5 × 1.fraction x 2@xponent– 127 Here the exponent has the limits: 1 < exponent < 254 For example, is given by the bit pattern: O 01111111 10000000000000000000000 while is given by 2 O 01111110 00000000000000000000000 Decimal to Floating Point and Back Again Convert the following float-point binary numbers to decimal. a) binary: 1 10000000 10000000000000000000000 decimal: b) binary: 1 10000001 11000000000000000000000 decimal: Convert the following numbers to the floating-point binary format. c) a fraction: binary: d) an integer: 1 binary: e) an integer: 2 binary:

1 8 23 EXPONENT FRACTION N = (-1)5 × 1.fraction x 2@xponent– 127 Here the exponent has the limits: 1 < exponent < 254 For example, is given by the bit pattern: O 01111111 10000000000000000000000 while is given by 2 O 01111110 00000000000000000000000 Decimal to Floating Point and Back Again Convert the following float-point binary numbers to decimal. a) binary: 1 10000000 10000000000000000000000 decimal: b) binary: 1 10000001 11000000000000000000000 decimal: Convert the following numbers to the floating-point binary format. c) a fraction: binary: d) an integer: 1 binary: e) an integer: 2 binary:

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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CPU contains a special bit called the overflow bit , denoted by V. When CPU adds two binary integers, if their sum is out of range when interpreted in 2's complement representation, then V is set to _____, otherwise V is set to _______. Question 4 options: A. 0 : 0 B. 1 : 0 C. 0 : 1 D. 1 : 1 2 X = 0 0000 0000 1000 0000 0000 0000 0000 000 is an IEEE 754 single precision floating point number, what is the decimal value of X? Question 5 options: 1.5 × 2–127 0.5 × 2–127 1.5 × 2–126 0.5 × 2–126 None of the above
n alternative to hexadecimal notation for representing bit patterns is dotted decimal notation in which each byte in the pattern is represented by its base ten equivalent. In turn, these byte representations are separated by periods. For example, 12.5 represents the pattern 0000110000000101 (the byte 00001100 is represented by 12, and 00000101 is represented by 5), and the pattern 100010000001000000000111 is represented by 136.16.7. Represent each of the following bit patterns in dotted decimal notation. 0000111100001111 001100110000000010000000 0000101010100000
Consider the following floating point representation where each number has 2exponent bits and 5 fraction bits. The exponent bias is 1. Round each number tohave 3 fraction bits. Apply round-to-even and round-toward-zero modes.a. 1 10 11100b. 0 00 00101c. 1 01 10101i. Can you see a pattern for rounding floating point numbers when thenumber of exponent bits are intact?
A binary code is a string of 0's and 1's. In particular, an n-bit binary code is a string of "n" 0's and 1's. For example, the code "01001" is a 5-bit binary code. How many 5-bit binary codes can be formed?
In a Digital Logic examination, you are given two signed integers in different number systems. A= (64)16 B= -(103)8Determine their values in the decimal system AN, b) Find the value of n, the shortest word-length of a computer using two’s complement representation which can represent all these numbers. Find the largest and thesmallest numbers that can be represented. c) Give the n-bit two’s complement representations of the two numbers, where n isvalue determined in b.
Write it in a Basic C Program Represent the binary representation of a float type to integer type. Single precision float (32-bit length) is represented in IEEE754 format: 1 bit of sign, 8 for exponent plus bias of 127, and 23 for the mantissa. Example: * 85.125 is [101 0101.001] in binary and this would be [1.0101 0100 1 x 2^6] in scientific notation of base 2. * Our sign bit will be [0] (positive), exponent+bias is [1000 0101] (6 + 127 = 133), and mantissa of [0 1010 1001000...] (whole is omitted and zeroes are added to the right until its length is 23). * Merging this will be [0100 0010 1010 1010 0100 0000 0000 0000] which is equivalent as 1118453760 in integer. * Therefore, binary of 85.125 in float is 1118453760 in integer. Input A single line containing a float type non-positive number. 85.125 Output A single line containing the integer representation of float type binary. 1118453760
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?
Given that a computer uses 4-bit ones’s complement numbers, what value will be stored in the variable j after the following code segment terminates? j = 1 k = -2 while(k != 0) { j = j + 1; k = k + 1; }
Consider a 6-bit two’s complement representation. Fill in the box with question mark "?" in the following table. You don't need to care about "n/a." Number Binary Representation TMin + TMin ? Please input the binary representation in this format xxxxxx. For example, if the answer is 010010, please input 010010.
Please help me solve this problem with kind explanations :) We are running programs on a machine where values of type int have a 32-bit two's complement representation. Values of type float use the 32-bit IEEE format, and values of type double use the 64-bit IEEE format. We generate arbitrary integer values x, y, and z, and convert them to values of type double as follow: /* Create some arbitrary values */ int x = random(); int y = random(); int z = random(); /* Convert to double */ double dx = (double) x; double dy = (double) y; double dz = (double) z; For each of the following C expressions, you are to indicate whether or not the expression always yields 1. If it always yields 1, describe the underlying mathematical principles. Otherwise, give an example of arguments that make it yield 0. Note that you cannot use an IA32 machine running GCC to test your answers, since it would use the 80-bit extended-precision representation for both float and double. A. (double)(float) x == dx B. dx…
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?