19th Ave New York, NY 95822, USA

数学代写|数值分析代写Numerical analysis代考|MAT12004 Floating point formats

my-assignmentexpert™提供最专业的一站式服务：Essay代写，Dissertation代写，Assignment代写，Paper代写，Proposal代写，Proposal代写，Literature Review代写，Online Course，Exam代考等等。my-assignmentexpert™专注为留学生提供Essay代写服务，拥有各个专业的博硕教师团队帮您代写，免费修改及辅导，保证成果完成的效率和质量。同时有多家检测平台帐号，包括Turnitin高级账户，检测论文不会留痕，写好后检测修改，放心可靠，经得起任何考验！

数学代写|数值分析代写Numerical analysis代考|Floating point formats

The IEEE standard consists of a set of binary representations of real numbers. A floating point number consists of three parts: the sign $(+$ or -$)$, a mantissa, which contains the string of significant bits, and an exponent. The three parts are stored together in a single computer word.

There are three commonly used levels of precision for floating point numbers: single precision, double precision, and extended precision, also known as long-double precision. The number of bits allocated for each floating point number in the three formats is 32,64 , and 80 , respectively. The bits are divided among the parts as follows:
\begin{tabular}{|l|c|c|c|}
\hline precision & sign & exponent & mantissa \
\hline \hline single & 1 & 8 & 23 \
\hline double & 1 & 11 & 52 \
\hline long double & 1 & 15 & 64 \
\hline
\end{tabular}
All three types of precision work essentially the same way. The form of a normalized IEEE floating point number is
$$\pm 1 . b b b \ldots b \times 2^p$$
where each of the $N b$ ‘s is 0 or 1 , and $p$ is an $M$-bit binary number representing the exponent. Normalization means that, as shown in (0.6), the leading (leftmost) bit must be 1.

When a binary number is stored as a normalized floating point number, it is “leftjustified,” meaning that the leftmost 1 is shifted just to the left of the radix point. The shift is compensated by a change in the exponent. For example, the decimal number 9 , which is 1001 in binary, would be stored as
$$+1.001 \times 2^3$$
because a shift of 3 bits, or multiplication by $2^3$, is necessary to move the leftmost one to the correct position.

数学代写|数值分析代写Numerical analysis代考|IEEE Rounding to Nearest Rule

For double precision, if the $53 \mathrm{rd}$ bit to the right of the binary point is 0 , then round down (truncate after the $52 \mathrm{nd}$ bit). If the $53 \mathrm{rd}$ bit is 1 , then round up (add 1 to the 52 bit), unless all known bits to the right of the 1 are 0 ‘s, in which case 1 is added to bit 52 if and only if bit 52 is 1.

For the number 9.4 discussed previously, the 53 rd bit to the right of the binary point is a 1 and is followed by other nonzero bits. The Rounding to Nearest Rule says to round up, or add 1 to bit 52 . Therefore, the floating point number that represents 9.4 is
$$+1.0010110011001100110011001100110011001100110011001101 \times 2^3 .$$
Denote the IEEE double precision floating point number associated to $x$, using the Rounding to Nearest Rule, by $\mathbf{f l}(\mathbf{x})$.

Representation of floating point number
To represent a real number as a double precision floating point number, convert the number to binary, and carry out two steps:

1. Justify. Shift radix point to the right of the leftmost 1 , and compensate with the exponent.
2. Round. Apply a rounding rule, such as the IEEE Rounding to Nearest Rule, to reduce the mantissa to 52 bits.
To find $\mathrm{fl}(1 / 6)$, note that $1 / 6$ is equal to $0.0 \overline{01}=0.001010101 \ldots$ in binary.

数学代写|数值分析代写NUMERICAL ANALYSIS代 考|FLOATING POINT FORMATS

IEEE 标准由一组实数的二进制表示组成。一个浮点数由三部分组成: 符号 $(+$ 或者- ）个尾数，其中包含有效位串和一个指数。这 三个部分一起存储在一个计算机字中。

$\backslash$ begin ${$ tabular $}|||c| c|c|} \backslash h l i n e$ 精庶 \& 符号 \& 指数 \& 尾数 $\backslash \backslash$ hline $\backslash$ hline single \& $1 \& 8$ \& $23 \backslash \backslash h l i n e$ double \& $1 \& 11 \& 52 \backslash \backslash h l i n e$ long double \& 1 \& $15 \& 64 \backslash \backslash h l i r$

$$\pm 1 . b b b \ldots b \times 2^p$$

$$+1.001 \times 2^3$$

数学代写|数值分析代写NUMERICAL ANALYSIS代 考|IEEE ROUNDING TO NEAREST RULE

$+1.0010110011001100110011001100110011001100110011001101 \times 2^3$.

1. 证明合法。将最左边的 1 的小数点向右移动，并用指数进行补偿
2. 圆形的。应用舍入规则，例如 IEEE 舍入到最近规则，将尾数减少到 52 位。
寻找fl $(1 / 6)$ ，注意 $1 / 6$ 等于 $0.0 \overline{01}=0.001010101 \ldots$ 以二进制形式

Matlab代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。