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# CS代写|数字硬件系统代写Digital Hardware System代考|ECE622 TIMING, SYNCHRONIZATION AND MEMORY

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## CS代写|数字硬件系统代写Digital Hardware System代考|TIMING, SYNCHRONIZATION AND MEMORY

As well as the algorithms underlying the construction of a system, the timing of a computation will be an important topic in what follows. In many applications the time available to the computation is limited. The basic definitions and analysis do not depend on a particular technology but apply to all kinds of compute systems constructed from building blocks.
A system receiving an $n$-bit input code $\left(b_0, \ldots, b_{n-1}\right)$ does so by receiving every bit $b_i$ at a site $\mathrm{s}{\mathrm{i}}$ and during the time interval $\left[\mathrm{f}{\mathrm{i}}, \mathrm{t}{\mathrm{i}}\right]$. If two of them are input at the same site $\mathrm{s}{\mathrm{i}}=\mathrm{s}{\mathrm{j}}$, then the input intervals must not overlap; these bit are input serially. In general, the pattern of the $\mathrm{s}{\mathrm{i}}, \mathrm{f}{\mathrm{i}}, \mathrm{t}{\mathrm{i}}$ extends in space and time so that there is not a well-defined time reference for the entire input. The same applies to the outputting of multi-bit codes from a system. In order to simplify the subsequent discussion, the application of input data will be considered as an event that occurs at a specific time, assuming a n-bit input code to be applied simultaneously at $\mathrm{n}$ different sites.

Once a data processing machine has been put in place, it will not be used only once but many times for varying inputs. The machine responds to every input event with a corresponding output event (Figure 1.7). The time delay from the input event to the corresponding output event is called the processing time. For most machines, the time delay of the output event does not depend on the time of the input event (a property called time invariance) but it can depend on the input data. The maximum (worst case) processing time is an important characteristic of the machine.

## CS代写|数字硬件系统代写Digital Hardware System代考|Processing Time and Throughput of Composite Circuits

The building blocks of a complex system are themselves machines to which the definitions of worst case processing time and throughput apply. The processing time of the system actually results from the timing in which the building blocks perform the individual operations. If a building block B performs an operation on the result of another block A, then its input event occurs at the same time or later than the output event of $\mathrm{A}$. If it occurs later, then the intermediate data to be passed must be stored in some way until the later time.

We first consider the serial composition of two machines $\mathrm{m}_1$ and $\mathrm{m}_2$ computing functions $\mathrm{f}_1$ and $\mathrm{f}_2$ with worst case processing times $\mathrm{t}_1$ and $t_2$ (Figure 1.8) so that the output events of $\mathrm{m}_1$ are input events for $\mathrm{m}_2$. Then no time is needed to communicate a copy of the output data of $\mathrm{m}_1$ to the input of $\mathrm{m}_2$, and the composition computes the function $\mathrm{f}=\mathrm{f}_2{ }^{\circ} \mathrm{f}_1$ with a worst case processing time $t$ below $t_1+t_2$. Otherwise the process used to communicate the data can be considered as a third machine put in series with the others with a processing time $t_3$ that has to be added to the sum of the others. If we take into account that $t_1$ and $t_2$ are maximum execution times and that the actual execution times for any given input could be smaller at least for one of the circuits, then we can only conclude that:
$$\max \left(\mathrm{t}_1, \mathrm{t}_2\right) \leq \mathrm{t} \leq \mathrm{t}_1+\mathrm{t}_2$$
The serial composition does not use the components efficiently for an individual computation. Only after the processing time $t_1$ from applying a new input, does the machine $m_2$ get new valid input data. At this time, $\mathrm{m}_1$ has already completed its processing of the input data and is no longer used for the computation of the final result.

If $s_1$ and $s_2$, are the maximum throughputs of $m_1$ and $m_2$, their composition has the maximum throughput $s$ above satisfying:
$$s \geq \min \left(s_1, s_2\right)$$
i.e., the composite machine can process input events at the rate of its slowest building block. Again, this is a safe estimate; the input sequences to $\mathrm{m}_2$ are restricted and could permit a faster rate.

## CS代写数字硬件系统代写Digital Hardware System代考|Processing Time and Throughput of Composite Circuits

$$\max \left(\mathrm{t}_1, \mathrm{t}_2\right) \leq \mathrm{t} \leq \mathrm{t}_1+\mathrm{t}_2$$

$$s \geq \min \left(s_1, s_2\right)$$

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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。