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# CS代写|数字硬件系统代写Digital Hardware System代考|ECE327 Code Conversions and More Codes

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## CS代写|数字硬件系统代写Digital Hardware System代考|Code Conversions and More Codes

If $\mathrm{c}: \mathrm{N}->\mathrm{B}^{\mathrm{n}}$ and $\mathrm{c}^{\prime}: \mathrm{N}^{\prime}->\mathrm{B}^{\mathrm{m}}$ are encodings on two sets $\mathrm{N}, \mathrm{N}^{\prime}$ of numbers, the numbers in the set $\mathrm{Q}=\mathrm{N} \cap \mathrm{N}^{\prime}$ are encoded both by $\mathrm{c}$ and $\mathrm{c}^{\prime}$. The code conversion function is defined on $\mathrm{c}(\mathrm{Q})$ $\subset \mathrm{B}^{\mathrm{n}}$ and maps a code $\mathrm{c}(\mathrm{q})$ to $\mathrm{c}^{\prime}(\mathrm{q})$. Often, code conversions are implemented as processing functions in the digital system and used to switch to the encodings that are most convenient for the desired processing steps (e.g. compact codes that can be communicated in a shorter time, or ones for which the implementation of the arithmetical operations is particularly simple).
The simplest conversions are those that transform an n-bit binary or twos-complement code into an m-bit one by appending or stripping zero or sign bits. Other common conversions are between integer and floating point formats, or floating point formats of different lengths. If real numbers are first approximated by numbers in a set $\mathrm{N}$ on which an encoding is defined (as in the case of fixed and floating point encodings), the notion of code conversion becomes relaxed. The conversion from an $\mathrm{m}$-bit to an $\mathrm{n}$-bit fixed point code (6) is by appending zero bits if $\mathrm{n}<\mathrm{m}$ or by performing a rounding operation otherwise, i.e. using the closest approximation by an n-bit fixed point number. A single precision (32-bit) floating point code can be exactly converted into a double precision (64-bit) code, but the conversion from double to single involves first performing a rounding operation to the closest number that can be represented in the shorter format. The conversion is defined on all double precision codes of numbers $p$ satisfying $-\mathrm{r} \leq \mathrm{p} \leq \mathrm{r}$ where $\mathrm{r}$ is the maximum single precision number. If a number is to be converted that is absolutely greater than the maximum representable one in a fixed or floating point target format, then sometimes saturation to the maximum representable number of the right sign is performed.

Conversions are also needed for input and output. For example, numeric input and output are most convenient in the multiple decimal digits format whereas the arithmetic operations are implemented more efficiently for the twos-complement codes. Or, the result of a computation performed with floating point numbers may be desired in a rational representation $\mathrm{p} / \mathrm{q}$. This conversion is achieved by means of Euclid’s algorithm to expand it into a continued fraction $[12]$

## CS代写|数字硬件系统代写Digital Hardware System代考|ALGORITHMS AND ALGORITHMIC NOTATIONS

Digital systems are constructed from building blocks of a few types that perform some simple transfer functions (called elementary). If the input and output signals of these are compatible, the output signals of a building block or copies of them can be used as input signals of another. For electronic building blocks using voltage signals between pairs of reference sites this is particularly simple. As already pointed out, the output signal sites are directly connected to the input sites by means of wires that force the potentials at the connected input and output reference sites to become the same after a short time. If an output value is required as an input later, it must be passed through an electronic storage device that conserves or delays it until that time.

For two building blocks with the (abstract or encoded) transfer functions $\mathrm{f}$ and $\mathrm{g}$, respectively, their connection in series computes the composition ‘ $\mathrm{g}{ }^{\circ} \mathrm{f}$ ‘, i. e. the function defined by:
$$\left(g^{\circ} f\right)(x)=g(f(x))$$

## CS代写|数字硬件系统代与Digital Hardware System代考|ALGORITHMS AND ALGORITHMIC NOTATIONS

$$\left(g^{\circ} f\right)(x)=g(f(x))$$

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## 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。