关于中国佛教的英文讲稿

第一篇：关于中国佛教的英文讲稿

Writing I’m going to talk about Buddhism in China.This is my outline.1.Sorts of Chinese Buddhism 2.Famous mountains of Buddhism in China 3.Famous architecture of Buddhism in China 4.The Buddhist influence on China 5.Conclusion Firstly, I want to show you the sorts of Chinese Buddhism.In China, both women and men can participate in the Buddhism.In the middle of China, There is Chinese traditional Buddhism.And in the North-west and South-west of China, there is Tibetan Buddhism.People in different place believe different sorts of Buddhism.But they came from one place—India.So they all have special expression.And Buddhism mainly expressed by the architecture.Secondly, let me tell you about famous mountains of Buddhism in China.Buddhism in China has the most famous four mountains.They are mount Wutai, Putuo, e’mei, Jiuhua.They are respectively located in Shanxi, Zhejiang, Sichuan, Anhui province.At the same time, many famous places such as Shaolin temple in Songshan, Leshan Buddha, the Potala Palace in Tibet are deeply remembered by people in China even all over the world.Thirdly, I will show you the famous architecture of Buddhism in China.Such as Luoyang Baima temple, Pagoda forest, Pagoda Tianning and Dayan, Grotto Mogao and Longmen, The Potala Palace and Labrang Lamasery.And then, I want to talk about the Buddhist influence on China.The population with Buddhist Belief in China is more than one hundred million.That’s a big figure because China is a no-belief country.In the middle of China, people believe Buddhism because they just want to pray for the health and peace.Only few people are real believers.Most people participate in the Buddhist activity in order to pray for something.But Tibetan Buddhism is different.People in Northwest and Southwest are real believers.They go to worship by their knees and hands.They use all of their money for Buddhism.Buddhism’s main idea—kind is the same as Chinese traditional culture.So people would like to combine them with their peaceful and kind wishes to pray for a better life.That’s why only can Buddhism believed in China.Finally, I get a conclusion.The research on Buddhism in China shows the influence on each other between Chinese culture and Buddhism.Maybe we don’t believe it but we must have prayed for something.Maybe we are touched by the Buddhist mountain and architecture.I believe that Buddhism has its special charm to attract us.Today we think Buddhism as a kind of culture.The mount and building reflect the characteristic of Buddhism and Chinese culture.And the influence on Chinese is positive.So Buddhism should exist and be believed by those who have the hearts of love and kind.The specific treasure that Buddhism left for us is the mount and architecture.They are the treasure of us Chinese and the world.That’s all my presentation, thank you.

第二篇：中国佛教发展史

中国佛教发展史

公历纪元前后，佛教开传人中国，经长期始由印度传播发展，而形成具有中华民族特色的中国佛教。由于传入的时间、途径、地区和民族文化、社会历史背景的不同，中国佛教形成三大系，即汉地佛教(汉语系)、藏传佛教(藏语系)和云南地区上座部佛教(巴利语系)。

中国汉族地区的佛教，经过长期的经典传译、讲习、融化，与中国传统文化相结合，从而形成具有民族特点的各种学派和宗派；并外传朝鲜、日本和越南。三国时期，汉地佛教开始有戒律、受戒之始。到了南北朝，南朝宋、齐、梁、陈各代帝王大都崇信佛教。有大批外国僧人到中国弘法，中国也有一批信徒去印度游学，隋文帝统一南北方朝后恢复了在北周禁佛时期所破坏的寺院、佛像。唐代是中国佛教臻于鼎盛时期。终唐之世，佛教僧入备受礼遇，赏赐有加。唐时中国名僧辈出，对佛学义理上的阐发无论在深度和广度上都超过前代，因此为建立具有民族特点的很多宗派奠定了理论基础，而且佛教信仰深入民间，创造了通俗的俗讲、变文等等文艺形式。北宋初期，朝廷对佛教采取保护政策，恢复译经。南宋偏安时期，江南的佛教仍保持一定盛况，但由于官方限制佛教的发展，除禅、净两宗外，其他各宗已日益衰微，远非昔比。

宋元明清时期，元代的统治者崇尚藏传佛教，但对汉地佛教也采取保护政策。佛教中的禅、律宗等继续流传、发展，寺院林立，僧尼众多。明万历以后，祩宏、真可、德清、智旭四大家出，进一步发展了对内融会禅、教、律等宗学说，对外融通儒、释、道三家的风气，所以深受士大夫的欢迎和一般平民的信仰，并使佛教更加具有中国的特色。清初皇室崇奉藏传佛教，对汉地沸教采取限制政策。康熙时禁令稍弛，迎请明末隐居山林的高僧重返京师，使已经衰微的佛教一时又呈现出活跃的气象。雍正虽重视体系的思想渊源之一。此外，一批名僧如月霞、谛闹、圆瑛、太虚、弘一等也都奋起从事振兴、弘扬佛教的工作，使佛教产生了新的气象。

藏传佛教，10世纪后半期形成。13世纪中开始流传于蒙古地区，至今，蒙古、土、裕固等民族，仍多信奉藏传佛教。藏传佛教正式形成。这一时期中藏传佛教的特点，一为大量传译印度波罗王朝时期盛行起来的密教无上瑜伽部的经典和法门，一为以密教传承为主形成各种教派。藏传佛教的各派也是在后弘期中逐渐形成的。藏传佛教奉行说一切有部戒律，各派对大乘菩萨戒及密宗根本戒等也都通行。但在后弘期中戒律也有所松弛。

佛教开始自汉地传入西藏，以后又直接自印度传入。在前弘期中，汉、印两系佛教在西藏都有影响。汉、印两地高度发展的工艺美术也一并传人，故莲花生主持兴建的桑耶寺即采用印、汉、藏三式，这种兼收并蓄，搏系众长，取精用宏的作风在西藏民族文化中随处可见。

云南傣族等少数民族佛教，属巴利语系，亦即南传的上座部佛教，它和北传的小乘佛教在教义、学说上都有不同的发展而各具特色。

现在云南地区上座部佛教摈其名称可分为润、摆庄、多列、左抵四派，又可细分为八个支派。

第三篇：中美关系英文讲稿

英语国家社会与文化入门——中美关系解说稿（周长专用）

Good morning, I have been fortunate enough today to show you, because of time constraints, and I can only show some general content of the Sino-US relations,if you find something is not good,please forgive me.if you are interested in this topic ,welcome to talk about it with me after the class.As we all know,China is the world's largest developing country, the United States is the world's most developed countries, China is the world's largest exporter, the United States is the world's largest importer, so, Sino-US relations are very important.First, we take a look at the stage characteristics of the Sino-US relations, Sino-US relations is divided into three stages.First stage: the founding of New China to the early 1970s, and china and america have a full-scale confrontation in this period, this a hostility period.Phase II: In the early 1970s to the 1980s, during this period ,due to various reasons, the Sino-US relations achieved normalization,and china and america established diplomatic relations.Phase III: Since the reform and opening up, during this period China and the United States formed a strategic partnership, cooperation and friction is the topic in this period.let us take a concern about the first period, the period of hostilities, the founding of New China, the Communist Party defeated the Kuomintang which supported by the United States, China confirmed “one-sided” strategy.So,The next 20 years China has been treated with political hostility and diplomatic isolation, military threats by america.The most typical manifestation is the Korean War，here we see the video of the Korean War,in this video, Chairman Mao made ainspiring speech in the the last,from this video,not only we can get the history, but also can experience the indomitable spirit with china’s leader.But this period end of China coming back to the United Nations,this case also mean U.S.policy of isolating china failed，英语国家社会与文化入门——中美关系解说稿（周长专用）

Look at this picture ,this is a very famous picture, called qiao’s laughing,", Qiao Guanhua is the head of the Chinese delegation, the picture recorded after the victory

let's look at the second stage of normalization of the Sino-US relations in the 1970s to 1980s, and do you know why the two sides are seeking to improve relations during this period? The first should be the failure of U.S.policy of isolating China, Second, during this period, the United States on the defensive in US-Soviet hegemony, the Soviet hegemonism was a direct threat to our country in that age, from a strategic consideration, the normalization of Sino-US relations is the needs to against Soviet Union, which also gave the Soviet Union a big suprise indeed, of course, this decision is also out of the needs of the Taiwan issue.Look at this picture , Premier Zhou Enlai and President Nixon,you know, this handshake across the world's widest oceans.And This is in the state banquet,Premier Zhou Enlai take food for Nixon.Here we look at the video section of Nixon’s china visiting.I do not know did you notice the scene when Nixon took the coat for Zhou Enlai, it’s a famous detail,Premier Zhou Enlai has a very strong personality, foreign guests who have been in contact with Premier Zhou will be impressed by his sincerity, which is also worthy of our Chinese diplomat to learn.Let’s come to the final stage, period since the reform and opening up, i devid this period into three steps

The first step is the late 1970s to the late 1980s, this period is the first dacade after the normalization of Sino-US relations,the relations developed smoothly during this period, and vice-premier Deng Xiaoping visited the United States during this time.Here is a video of Deng Xiaoping's visiting to U.S..The second step of the late 1980s to the early 1990, United States began sanctions

英语国家社会与文化入门——中美关系解说稿（周长专用）

during this period, the collapse of the Soviet Union in Eastern Europe, China has also undergone a political storm, commonly known as the student movement.The United States believes that China's suppression of the counter-revolutionary rebellion is terrible, so america made sanctions against China.Incidentally, I personally do not agree with the student movement event, any historical event must have international and domestic background and underlying causes, and this incident precisely do not have.Ok,Return to the Sino-US relations, the third step, since the mid-1990s, the sanctions have no effect, the U.S.change the policy, cooperation accounted for the main line, such as China's accession to the WTO.Here is a video of China's accession to the WTO, Premier Zhu Rongji visited the United States.Actually,except these,i intended to show you Sino-US relations after U.S.President Barack Obama took office, such as trade friction, the United States to return to the Asia-Pacific strategy, but this problem is too complex to have the opportunity to be explained today.Why the Sino-US relations is so important and complex, only one word can describe,there is no permanent friends, no permanent enemies, only permanent interests!

Ok,This is the entire contents of the speech today ,Finally, I want to do a summary with Chinese to end the speech，中国的进步和发展奔腾向前，浩浩荡荡，势不可挡。我们坚信，勤劳勇敢智慧的中国人民，在全面建设小康社会这一前无古人的伟大实践中，一定能够万众一心，奋发图强，勇往直前地朝着宏伟目标阔步迈进，光荣完成时代赋予的崇高使命，把我国早日建设成为富强民主文明的社会主义现代化国家。最后愿我们的祖国在瞬息万变的世界大潮中屹立不倒！愿祖国繁荣昌盛！

第四篇：英文国际会议讲稿

PPT(1)大家上午好！今天我汇报的主题是：基于改进型LBP算法的运动目标检测系统。运动目标检测技术能降低视频监控的人力成本，提高监控效率，同时也是运动目标提取、跟踪及识别算法的基础。图像信号具有数据量大，实时性要求高等特征。随着算法的复杂度和图像清晰度的提高，需要的处理速度也越来越高。幸运的是，图像处理的固有特性是并行的，尤其是低层和中间层算法。这一特性使这些算法，比较容易在FPGA等并行运算器件上实现，今天汇报的主题就是关于改进型LBP算法在硬件上的实现。

good morning everyone.My report is about a Motion Detection System Based on Improved LBP Operator.Automatic motion detection can reduce the human cost of video surveillance and improve efficiency [ɪ'fɪʃ(ə)nsɪ]，it is also the fundament of object extraction, tracking and recognition [rekəg'nɪʃ(ə)n].In this work, efforts ['efəts] were made to establish the background model which is resistance to the variation of illumination.And our video surveillance system was realized on a FPGA based platform.PPT(2)

目前，常用的运动目标检测算法有背景差分法、帧间差分法等。帧间差分法的基本原理是将相邻两帧图像的对应像素点的灰度值进行减法运算，若得到的差值的绝对值大于阈值，则将该点判定为运动点。但是帧间差分检测的结果往往是运动物体的轮廓，无法获得目标的完整形态。

Currently, Optic Flow, Background Subtraction and Inter-frame difference are regard as the three mainstream algorithms to detect moving object.Inter-frame difference based method need not model ['mɒdl] the background.It detects moving objects based on the frame difference between two continuous frames.The method is easy to be implemented and can realize real-time detection, but it cannot extract the full shape of the moving objects [6].PPT(3)

在摄像头固定的情况下，背景差分法较为简单，且易于实现。若背景已知，并能提供完整的特征数据，该方法能较准确地检测出运动目标。但在实际的应用中，准确的背景模型很难建立。如果背景模型如果没有很好地适应场景的变化，将大大影响目标检测结果的准确性。像这副图中，背景模型没有及时更新，导致了检测的错误。

The basic principle of background removal method is building a background model and providing a classification of the pixels into either foreground or background [3-5].In a complex and dynamic environment, it is difficult to build a robust [rə(ʊ)'bʌst] background model.PPT(4)

上述的帧间差分法和背景差分法都是基于灰度的。基于灰度的算法在光照条件改变的情况下，性能会大大地降低，甚至失去作用。

The algorithms we have discussed above are all based on grayscale.In practical applications especially outdoor environment, the grayscales of each pixel are unpredictably shifty because of the variations in the intensity and angle of illumination.PPT(5)为了解决光照改变带来的基于灰度的算法失效的问题，我们考虑用纹理特征来检测运动目标。而LBP算法是目前最常用的表征纹理特征的算法之一。首先在图像中提取相邻9个像素点的灰度值。然后对9个像素中除中心像素以外的其他8个像素做二值化处理。大于等于中心点像素的，标记为1，小于的则标记为0。最后将中心像素点周围的标记值按统一的顺序排列，得到LBP值，图中计算出的LBP值为10001111。当某区域内所有像素的灰度都同时增大或减小一定的数值时，该区域内的LBP值是不会改变的，这就是LBP对灰度的平移不变特性。它能够很好地解决灰度受光照影响的问题。

In order to solve the above problems, we proposed an improved LBP algorithm which is resistance to the variations of illumination.Local binary pattern(LBP)is widely used in machine vision applications such as face detection, face recognition and moving object detection [9-11].LBP represents a relatively simple yet powerful texture descriptor which can describe the relationship of a pixel with its immediate neighborhood.The fundamental of LBP operator is showed in Fig 1.The basic version of LBP produces 256 texture patterns based on a 9 pixels neighborhood.The neighboring pixel is set to 1 or 0 according to the grayscale value of the pixel is larger than the value of centric pixel or not.For example, in Fig1 7 is larger than 6, so the pixel in first row first column is set to 1.Arranging the 8 binary numbers in certain order, we get an 8 bits binary number, which is the LBP pattern we need.For example in Fig.1, the LBP is 10001111.LBP is tolerant ['tɒl(ə)r(ə)nt] against illumination changing.When the grayscales of pixels in a 9 pixels window are shifted due to illumination changing, the LBP value will keep unchanged.PPT(6)

图中的一些常见的纹理，都能用一些简单的LBP向量表示，对于每个像素快，只需要用一个8比特的LBP值来表示。

There are some textures , and they can be represent by some simple 8bit LBP patterns.PPT(7)

从这幅图也可以看出，虽然灰度发生了很大的变化，但是纹理特征并没有改变，LBP值也没有变化。

You can see, in these picture , although the grayscale change alot, but the LBP patterns keep it value.PPT(8)上述的算法是LBP算法的基本形式，但是这种基本算法不适合直接应用在视频监控系统中。主要有两个原因：第一，在常用的视频监控系统中，特别是在高清视频监控系统中，9个像素点覆盖的区域很小，在如此小的区域内，各个像素点的灰度值十分接近，甚至是相同的，纹理特征不明显，无法在LBP值上体现。第二，由于以像素为单位计算LBP值，像素噪声会造成LBP值的噪声。这两个原因导致计算出的LBP值存在较大的随机性，甚至在静止的图像中，相邻两帧对应位置的LBP值也可能存在差异，从而引起的误检测。

为了得到更好的检测性能，我们采用基于块均值的LBP算法。这种方法的基本原理是先计算出3×3个像素组成的的像素块的灰度均值，以灰度均值作为该像素块的灰度值。然后以3×3个像素块（即9×9个像素）为单位，计算LBP值。

The typical LBP cannot meet the need of practical application of video surveillance for two reasons: Firstly, a “window” which only contains 9 pixels is a small area in which the grayscales of pixels are similar or same to each other, and the texture feature in such a small area is too weak to be reflected by a LBP.Secondly, pixel noise will immediately cause the noise of LBP, which may lead to a large number of wrong detection.In order to obtain a better performance, we proposed an improved LBP based on the mean value of “block”.In our algorithm, one block contains 9 pixels.Compared with original LBP pattern calculated in a local 9 neighborhood between pixels, the improved LBP operator is defined by comparing the mean grayscale value of central block with those of its neighborhood blocks(see Fig.2).By replacing the grayscales of pixels with the mean value of blocks, the effect of the pixel noise is reduced.The texture feature in such a bigger area is more significant to be described by LBP pattern.PPT(9)

运用LBP描述背景，其本质上也是背景差分法的一种。背景差分法应用在复杂的视频监控场景中时，要解决建立健壮的背景模型的问题。驶入并停泊在监控画面中的汽车，被搬移出监控画面的箱子等，都会造成背景的改变。而正确的背景模型是正确检测出运动目标并提取完整目标轮廓的基础。如果系统能定时更新背景模型，将已经移动出监控画面的物体“剔除”出背景模型，将进入监控画面并且稳定停留在画面中的物体“添加”入背景模型，会减少很多由于背景改变而造成的误检测。

根据前一节的介绍，帧间差分法虽然无法提取完整的运动目标，但是它是一种不依赖背景模型就能进行运动目标检测的算法。因此，可以利用帧间差分法作为当前监控画面中是否有运动目标的依据。如果画面中没有运动目标，就定期对背景模型进行更新。如果画面中有运动目标，就推迟更新背景模型。这样就能避免把运动目标错误地“添加”到背景模型中。

In practical application, the background is changing randomly.For traditional background subtraction algorithm the incapability of updating background timely will cause wrong detection.In order to solve this problem, we propose an algorithm with dynamic self updating background model.As we know, Inter-frame difference method can detect moving object without a background model, but this method cannot extract the full shape.Background subtraction method can extract the full shape but needs a background model.The basic principle of our algorithm is running a frame difference moving object detection process concurrently [kən'kʌrəntli] with the background subtraction process.What’s time to update the background is according to the result of frame difference detection.PPT(10)

运动目标检测系统特别是嵌入式运动目标检测系统在实际应用中要解决实时性的问题。比如每秒60帧的1024×768的图像，对每个像素都运用求均值，求LBP等算法，那么它的运算量是十分巨大的，为此我们考虑在FPGA上用硬件的方式实现。

If LBP algorithm is implemented in a software way, it will be very slow.FPGA have features of concurrent computation, reconfiguration and large data throughput.It is suitable to be built an embedded surveillance system.The algorithm introduced above is implemented on a FPGA board.PPT(11)

这就是我们硬件实现的系统结构图。首先输入系统的RGB像素信号的滤波、灰度计算及LBP计算，得到各个像素块的LBP值。然后背景更新控制模块利用帧差模块的检测结果控制背景缓存的更新。区域判定模块根据背景差模块的输出结果，结合像素块的坐标信息，对前景像素块进行区域判定。

The structure of the system is showed in this figure.In this system, a VGA signal is input to the development board.and the LBP pattern is calculated , Frame difference module also compares the current frame and the previous frame to determine whether there is a moving object in the surveillance vision.If the surveillance vision is static for a certain amount of frame, the background model will be updated.PPT(12)图中是LBP计算模块。图中所示的窗口提取结构可以实现3×3像素块窗口的提取。像素信号按顺序输入该结构，窗口中的数据就会按顺序出现在Pixel1-Pixel9这9个寄存器中，从而在最短的延时内提取出相邻9个像素点的灰度值。行缓存的大小等于每一行图像包含的像素个数减1。将9个像素点的灰度值通过求均值模块，可以求出一个像素块的像素均值。

将像素块均值作为输入再次通过类似的结构，可以提取出3×3个相邻像素块的灰度值。这时行缓存的大小为每一行包含的像素块的个数减1。再用9个窗口的灰度值作为输入，用比较器阵列计算出最终的LBP值。

To achieve real time computation of the LBP, a circuit structure is put forward as showed in Fig.5.Two line buffers and nine resisters are connected in the way showed in the figure.Nine neighbor pixels are extracted with minimum ['mɪnɪməm] delay, and the mean value of this block is calculated by the mean value calculate module which contains some adders and shifters.The mean values of the blocks are inputted to a similar structure and extracted in a similar way, and the LBP is calculated by the consequence LBP calculate module.PPT(13)求均值模块采用如图3-12所示的四级流水方式实现。在算法的设计过程中，需要求出的是3×3像素块中9个像素的均值。但是在硬件实现时，为了更合理地利用硬件资源，只计算剔除中心像素后的8个像素的均值。这样做可以在不对计算结果造成太大影响的情况下减少加法器的使用。而且在求均值的最后一级流水，除8运算比除9运算更容易实现。因为8是2的整数幂，除8运算只需要将各个像素的和右移3位。而除9运算在FPGA中需要专用的DSP模块来完成。PPT(14)如图所示，块均值计算模块计算出的8个块均值被图3-11中的窗口提取模块提取出来，并作为比较器阵列的输入，比较器的输出结果用0和1表示。最终的比较结果按一定的顺序排列，重新拼接成一个8位的二进制数，即LBP值。LBP计算电路没有采用流水结构，在一个时钟周期内就能得到计算结果。

PPT(15)

这个是在系统测试中，实现对多个目标的检测。

In this system test ,we achieve a multi-object detection.PPT(16)

这个图是对动态背景更新的测试，在监控区域中划定一个目标区域，把一个静止的物体放置到目标区域中。在前3分钟内，系统会将其当做前景目标，矩形窗口会以闪烁的形式发出报警信号。3分钟过后，由于物体一直处于静止状态，系统检测到了10800个静止帧，于是更新背景模型。静止的物体被当做背景的一部分，此后窗口不再闪烁。经验证，该系统能够正确实现背景模型更新算法。

This is the test for the auto background update.We put a statics object in the surveillance area，at the beginning this is trusted as a moving object.after 3 minutes , the system receive ten thousand static frames ,and then update the background model.Then this object is regard as a part of the background.PPT(17)

此外为了验证系统对室外光照变化抑制能力，我们选取了大量有光照变化，并且有运动目标的视频对系统进行了测试。

In order to verify the resistance to the varation of illumination , a certification experiment is designed, and the ROC curves of the two algorithms based on LBP and grayscale are plotted and compared.A number of short video clips with shifty and fixed illumination, including positive samples with moving objects and negative samples without moving objects.PPT(18)

测试平台如图所示。用一台PC机作为测试信号的输出源，然后在PC机中播放视频，并将视频VGA信号发送给运动目标检测系统，模拟真实的监控环境。FPGA将输入信号和区域边框图形相叠加后在LCD上显示。

The picture of the certification experiment is showed in this picture.A PC acts as the source of the test signal which is input to the FPGA in the form of VGA.Passing through the FPGA board, video signal is displayed on a LCD screen.PPT(19)

并最终描绘了系统的ROC特性曲线。在没有光照强度变化的情况下，采用基于灰度的运动目标检测算法的性能略优于基于LBP值的运动目标检测算法，两种算法都能取得较好的检测效果。但是在图5-15中（测试集2），也就是在光照强度变化的情况下，画面整体灰度发生较大的改变，基于灰度的检测算法的性能大幅度下降，接近于失效。而采用LBP值的检测算法却能维持较好的性能。可见基于LBP的检测算法对抑制光照强度变化造成的误检测有较好的效果。

This two figure are the ROC curves of the experiments using our

algorithm and traditional grayscale-based algorithm.We can see in the Fig.1 which corresponds to the condition with fixed illumination, the performance of the grayscale-based algorithm is slightly better than these of LBP-based algorithm, they can both detect moving object effectively.But in Fig.2 which corresponds to the condition with shifty illumination, grayscale based algorithm deteriorates drastically and nearly lose efficacy ɪkəsɪ].But the improved LBP algorithm still keeps a good performance.PPT(20)

谢谢大家！

Thanks for your attention

第五篇：英文试讲稿[范文模版]

We have discussed how to simplify a logic function using logic algebra.This method relies on the skill of the individual in applying the appropriate rules.Sometimes it is hard to be sure whether the logical function is already simplest form or not.Now we will introduce a new method, which is graphical, known as the Karnaugh map.It’s a tool for performing the simplification of logic function.2 first, we must know what is the K-map, and how to design it!Usually, the K-map is made up of 3 parts, and the 3 parts are variables, cells and binary numbers.Ok, we can get 2 k-maps, you should note each map includes 3 parts.Please remember the 3 parts, when you design k-maps, each of the parts is essential.we note the first map has 2 variables, it has 4cells, and the second map has 3 variables, it has 8 cells.So in an n-variable k-map, there are 2 to power n cells.4 then please observe the binary numbers on the upper and left side of the k-map.What do you discover from the changed values? Take the numbers on the upper side as example, look at the first map, the numbers is changed from 0 to 1 between adjacent cells, only one-bit is changed, of course, the number just has one-bit.On the second map, each number has 2 bits, the number is changed from 00 to 01, from 01 to 11, from 11 to 10, between the adjacent cells, there is only one-bit in the number changed.If we change the position of the 2 binary numbers, do you think this sequence is right? No!It’s not right, because the number is changed from 01 to 10, two bits are changed.So you should know there is only a single-variable value changed between adjacent cells.This is one of the K-map’s features.5 we look at other features.On the fist map, Cell 1’s adjacent cells are cell 2 and 3, it’s easy to understand.What are the cell 4’s adjacent cells? They are also cell 2 and 3.But on the second map, cell 3’s adjacent cells are cell 1, 4 and 7.This is easy to understand.Now please give the cell 1’s adjacent cells!You may list cell 2 and 3, it’s right, but it’s not all right, because you ignore the cell 5.Do you know what that is on the left side of cell 1? In fact, cell 5 is on the left side of cell 1, of course, cell 6 is on the left side of cell 2.In this case, adjacent cell include the cells located in the symmetric place.I hope everyone should note this.6 this is a 4-variable K-map.Please give the cell 11’s adjacent cells!Now you should know except cell 12 and 15, cell 3 and 9 are cell 11’s adjacent cells.Cell 3 is on the right side of the cell 11, and cell 9 is on the lower side.7 Ok, let’s summarize the feature of K-map.Fist, if a k-map has n variables, it must possess 2 to power n cells.Second, when you design a k-map, please note how to change the binary number on the upper and left side, there is only a single-variable value changed between adjacent cells.Third, it’s easy to find a cell’s adjacent cells, but I must emphasize that you don’t ignore these cells located in the symmetric place.Please care about these, it will easy for you to make use of K-map.8 after discussing K-map, let’s learn how to represent a truth table on k-map.Here is an example.This is a truth table of a 3-variable function, the knowledge about the truth table has been discussed earlier.The key step is to design a K-map, we know the function has 3 variables, the k-map also has 3-varibales, according to the features of k-map, there are 2 to power 3 cells in the K-map, they are 8 cells.Then the binary numbers will be written, you seem to note there is only single-variable value changed between adjacent cells, we have drawn a K-map.The second step is to mapping the logic function.It is an easy work for you to enter the value of the output variable Y in each cell.On the K-map, cell 0 corresponds to row 0, because the variables’ value are same, a is equal to 0, b is equal to 0, c is equal to 0, so we should enter 0 in cell 0.Cell 1 corresponds to row 1, a is equal to 0, b is equal to 0, c is equal to 0, enter 1 in cell 1.so we can draw a conclusion if all variables’ value on the map is same as those in the table, enter output value in corresponding cell.Ok, fig.5.3 gives the complete K-map of the truth table.Look at this example 2, this equation is in SOP form, first we should convert it into standard SOP, and then it can be represented on K-map.Observe this equation, this term and this term are not minterm.Although minterm and SOP form are discussed early, I think it’s necessary to review this knowledge.Minterm is also called standard product form, we look at example 2, the 3 terms are product form.This and this terms are only product form, they are not standard product form.But this term is standard product form.What’s minterm? A function has n variables, if the product term contains n variables, each variable may be in complemented form or in uncomplemented form.The product term is called a minterm or standard product form.11 of course, it’s easy to understand that if a function has n variables, there must be 2 to power n minterms.There are 3 variables A,B,C, so we can write 8 minterms.12 if the logical function is represented as a sum of minterms only, the function is said to be in standard sum of products form.This expression is not in standard SOP form, because this and this term are not minterms, and this expression is in standard SOP form.13 In fact, the logical function can be converted into standard SOP form.We know the C plus the complement of c equal 1, any term multiply 1 equal itself.So if the fist term multiplies this expression, it can be converted into two minterms, the two sides of the equal mark are equivalent.The second term can be converted into two minterms by the same way.We can get a standard SOP form.14 the represent the SOP form on K-map.15 According to minterm’s features, logical 1 corresponds to the original variable, logical 0 corresponds to complement of variable.When a equal 0, b equal 0, c equal 0, we can get this minterm, this term corresponds to this cell.In fact, the K-Map includes all minterms.16 the first term corresponds to this cell, so we enter 1 in this cell.the second term corresponds to this cell, so we enter 1 in this cell.the third term corresponds to this cell, so we enter 1 in this cell.the forth term corresponds to this cell, so we enter 1 in this cell.the fifth term corresponds to this cell, so we enter 1 in this cell.17 Ok.The equation in standard SOP form is represented on K-Map.18 this section is very important.It is well-known that K-map is perhaps the most extensively used tool for simplification of logical function.Ok, let’s look at how to simplify logical function using K-map.We will illustrate every step through a example so that you can understand this method easily.Let’s look at the fist step, Mark those cells with a 1 that correspond to the terms in expression.Here is an equation in standard SOP form.After designing a k K-map, enter 1s in corresponding cells.So we get fig 5.6.19 Form the 1s into the largest valid group.Some conditions limit the largest group.The group must be a rectangle, and must contain 2 to power i cells, i is equal 0, 1, 2, n.n is the number of variables.When you face this K-map, how to make valid group, on the left side, there are 3 ones, on the right side, there are 2 ones.The 3 ones couldn’t form a group, because it is not rectangle, and it has 3 cells, normally, the group should contain 1, 2, 3, or 8 cells.But these 2 ones can form a group, these and these also can form a group.u should remember this cell and this cell are adjacent, this cell is on the left side of this cell, this cell is in the right side of this cell, the two cells are the same.So these 4 cells should form a group, and it also satisfy the demand of form the largest group.ok we have formed two groups Step 3 each 1 on the map must be included in at least one group.The ones already in a group can be included in another group as long as the overlapping groups include noncommon ones.Please note this cell, it isn’t only in the group, but also in this group, it belongs to the two groups, these 2 groups are permitted.Because the 2 overlapping groups include noncommon ones.Except this cell , this group has this cell, this group has this, this and this cells.21 Step 4 will give us a rule about how to produce terms.Identify adjacent ones in a group, then see the values of the variable associated with these cells.If the variables will be different and they gets eliminated.Other variables will appear in ANDed form in the term.This map exist 2 groups.We observe this group first, the value of variable C is not changed, it is equal to 1.the value of A is also not changed, it’s equal to 0, but look at variable B, the value is changed from 0 to 1 between adjacent cells, variable B should be eliminated.The other two Variables A, and C will appear in ANDed form in the term, I have to emphasize that this term is written by the method of producing minterm.0 corresponds to complemented variable, 1corresponds to uncomplemented variable.So we get this term.Then we observe this group include 4 cells, the value of variable B is not changed, the others will be eliminated.We get the complemented B.two groups get 2 terms.22 step5 these terms are ORed to get the simplified equation in SOP form.This equation is previous, and this is simplified equation, in fact, it’s a simplest expression, these two equations are equivalent.Now, we have simplified a logical expression using K-map, do you find it is a simple and efficient method? Remember these 5 steps, they are useful.23 After this chapter, we should appreciate the two points.First, you must know how to design a K-map;it’s a basal and important knowledge.When you design a K-map, you should pay more attention to these details.Second, simplification a logical expression using K-map method, we know this method is simplest and most commonly used method, it’s an essential knowledge in this chapter and easy for you to be operated, I will give you some homework to practice yourselves, they are 7, 12, 16, and 18 on the page 188 and 189 respectively.Please treat them seriously, you will get promoted.