The U.S. Naval War College is a Navy's home of thought. Established in 1884, NWC has become the center of naval seapower, both strategically and intellectually. The following issues in national security lecture is specifically designed to offer scholarly lectures to all participants. We hope you enjoy the upcoming discussion and future lectures. Good afternoon and welcome to our fourth issues in national security lecture for this academic year. I'm John Jackson and I will serve as host for today's event. I'd like to note that we are gathered together here in person. We also have a large audience dialed in via Zoom and I extend a very warm welcome to the students and faculty from the officer training command Newport who have also joined us. Over the 2023-2024 academic year we are offering 10 lectures from some of the best scholars in the world, our resident faculty. This is intended to share a portion of the Naval War College's academic experience with the spouses and significant others of our student body. We also welcome participation by the entire Naval War College extended family, including members of the Naval War College Foundation, international sponsors, civilian employees, colleagues throughout Naval Station Newport, and others around the globe. While the primary purpose is to share information and learn together, we do offer documentation in the form of certificates of completion to all participants who attend at least 70 percent of the offered lectures. You can participate here in the audience via Zoom or even by watching the lectures when they're posted on YouTube. We ask you to keep track of how and when you participate and we'll ask you to self-certify your completion toward the end of the series. Our next lecture will be on 23 January 2024 when Professor Jim Holmes will discuss China and zombies. One of the best lectures and by and far the best title of any of our lectures. Okay, on with the main event. At the conclusion of the presentation we'll welcome questions from our in-person audience. Please use the microphones located at each seat, press the button and hold the button while you ask your question. Virtual participants should feel free to ask questions using the chat feature of Zoom and we'll get to as many of them as we can. So let's move on to the educational portion of today's event. Since prior to the end of World War II, U.S. foreign policy concerning the status of Taiwan and its government has shifted repeatedly along with shifts in the global security dynamics. These policy shifts have left us with challenging international law issues that remain just below the surface of U.S.-China and Taiwan relations. Now with the People's Republic of China's increased military and economic clout, China's increasing pressure on Taiwan to reunite with the mainland and a consequential election in Taiwan next month, the year 2024 may be another strategic turning point. This lecture will trace the history of U.S. policy concerning Taiwan from World War II to the present, including which pressures led to policy shifts and consider whether the time is ripe for another shift in U.S. policy concerning our relations with and the status of Taiwan. Our presenter, Dr. Peter Dutton, is Professor of International Law in the College of Stockton Center for International Law. He previously served as Interim Dean of the Center for Naval Warfare Studies and as Director of the China Maritime Studies Institute. A retired Navy Judge Advocate and former Naval Flight Officer, he holds a PhD from King's College London, a JD from the College of William & Mary, an MA from U.S. Naval War College, and a BS from Boston University. He's also an adjunct professor at NYU's School of Law and is a faculty advisor to NYU's U.S. Asia Law Institute. I know of no one better qualified to address the timely important subject of today, so please welcome Dr. Peter Dutton. Thank you John. Thank you very much for that. Thank you John and thank you all for coming this afternoon. I will probably be walking around the stage. That's my normal approach, but before I do, there's a couple things I want to say by introduction and I needed to write them down, so I'll do that from here. The first is that I have to issue a disclaimer, which is the views you're about to hear are my own views, not necessarily that of the Navy or the any other element of the United States government. Additionally, I want to ask a question, really the presentation asks the question, why should we even focus on Taiwan? John, in his introduction, made a couple of remarks about why. We have a consequential election coming up in January 2024, next month in Taiwan, and the shift in government in May 2024, that's when the presidential transition will occur. And this has been a period, the last couple of years have been a period of increased tension between China and Taiwan and the United States over the Taiwan issue. And the United States Secretary of Defense has said, Secretary Austin has said that China is our pacing challenge as a military and Taiwan is the pacing scenario, right? We have to focus on this issue because we may be called into conflict and in fact some have called this the decade of danger. And China's leaders have made clear that Taiwan as a separate entity from the mainland is an issue that has to be resolved eventually, right? And Xi Jinping has said a number of times, the current Chinese leader has said a number of times that this separation cannot go forever. In his vision, the China dream involves unification of all of China's claimed territories. So why should we focus on the history of Taiwan, the history of the evolution of Taiwan and US policy concerning it? Well, perhaps it's because the United States is one of the most significant factors in what happens in the future of Taiwan. We, the United States, have been a very significant component of providing stability in the region through our Taiwan policy in the past. And we have stabilized the situation in the cross-strait region for now at least 75 years with our policies. And because of the pressure that you're seeing in over Taiwan and the status of Taiwan, you're seeing some calls for change in the US China policy. And I think because we have a presidential election coming up in 2024, this will be an issue that you'll probably see some debate over during that time. And so I thought, well, we might as well begin the year with a focus on these big questions. You might be surprised at the title, right? This is a lecture about Taiwan. And I'm asking you to think about from Shimonoseki to Shanghai. And one of the interesting things about the Taiwan policy is how little of Taiwan's future is actually decided on Taiwan. And so the way I've actually set up the discussion today, or the presentation that I'll give you, is looking at where in different cities around the world, Taiwan policy has been made and how these decisions have been affected by the evolution of history over the course primarily of the 20th century. But we have to begin in the 19th century. It's very important. So first of all, where is Taiwan? I know probably everybody in the room knows where Taiwan is and understands a little bit about the geography and why this is important. But we have some people who might be tuning in who aren't familiar with it. So here we have Taiwan. Taiwan is just off the coast of mainland China. It's an island that if, for those of you who are from this area, you know about the size of Massachusetts and Connecticut, that's about the size of Taiwan. Only the population of Massachusetts and Connecticut together is about 15, no, correction, 10 and a half million, 10 and a half million people in Massachusetts and Connecticut combined. In Taiwan, it's about 23 million people. That's the population of all of Australia, a country the size of a continent, but it's also the population of the city of Shanghai, believe it or not. So like Shanghai, Taiwan is a very densely populated area, especially since it's very mountainous, the center of it's very mountainous and not very habitable. So it's a very densely populated area off island off the coast of mainland China that has a very large economy and it's a thriving democracy with a very large economy. It's roughly around 20th or 21st in terms of national economies around the world. But we've also seen, as I mentioned earlier, Chinese pressure on Taiwan increasing over the course of this year. It really began at Spike. This you see the picture on the left here is the PLA, mostly that these are PLA flights around the island of Taiwan. This was in September 2022. There was a spike in September 2022. The month after Nancy Pelosi, Speaker Pelosi visited Taiwan, what you began to see was an increase in pressure by the mainland on Taiwan. And so why? What drove that? Why would the Chinese care? There's members of the House of Representatives that visit countries and localities around the world. Why would China be so upset about this? And so this is one of the questions that I hope to answer for you. And also we have to consider, especially those of us who are in the military, what pressures, what military pressures could be next and what are the policy implications of them. So China's policy is actually crystal clear and easy to understand, right? This is Xi Jinping, the leader of the Communist Party of China and also the President of China, Secretary General. And the PRC perspective, there is one China in the world. And Taiwan is a part of China. It's an inalienable part of China is the PRC perspective. And the People's Republic of China is ruled by the Chinese Communist Party, which is the only legitimate government of all of China. So that's a very simple, very easy to understand. Chinese policy has three components. One China, one government. Taiwan's a part of all of China. It should be under the governance of the People's Republic of China and not separate from the mainland. So China's policy is clear. What about US policy? Well, we've got another half an hour anyway to discuss what the US policy is because it's not clear. We have to begin with a little bit of history, though. Taiwan was not always part of China. Taiwan was a separate entity from China up until the late 1500s, early 1600s, when it was actually first colonized primarily by the Dutch and the Spanish. There was some Japanese occupation there, but mostly it was the Dutch and the Spanish in the 1500s and 1600s. And there was an indigenous population on the island that had a culture very much more similar to sort of Polynesian and Southeast Asian island populations, very different from the culture of mainland China. And then we also have to fast forward a little bit to your 1644. I'm not going to give you a detailed history lesson, but what you have to know is that there was a change in dynasty in roughly 1644. It happened over a period of years, actually. But we look at 1644 because the Ming dynasty was conquered by the last Chinese dynasty known as the Qing dynasty. And the Qing dynasty took time for the Qing to conquer all of China. And during that period of time, the Ming loyalists and those who were trying to escape the Civil War, many of them crossed the strait for the first time and began to colonize the island of Taiwan in the 1640s and 1650s. And in that period of time, when the Qing dynasty, the last dynasty, was trying to consolidate its hold. This was also the last holdout of Ming loyalists in that transition period, a sort of historical parallel that is not lost on the People's Republic of China today. So 1644 was when China began to colonize Taiwan or Chinese people began to colonize Taiwan, but it wasn't until later in the 1600s that the Chinese dynasty actually went across the strait and began to take control of Taiwan in order to end the possibility of Ming loyalists of being sheltered there. So in that period of time, between 1644 and the late 1800s actually was a period of increasing Chinese migration to Taiwan and increasing governmental control over the island. So it took about 200 to 250 years for the Chinese to begin to actually control Taiwan, but they did. And now we have to get to the first city that, where Taiwan's destiny was decided, and that first city is not in Taiwan, it's in Japan. Because in 1894 and 1895, Japan and China fought a war and Japan won. And as a result of that war, Japan signed a peace treaty with China in the city of Shimonoseki in the very southern part of the main island, Honshu of Japan. And as a result of that peace treaty, the island of Taiwan was seated, formally seated, by treaty from China to Japan. And so as a matter of international law and international politics, from 1895 forward, the island of Taiwan was no longer Chinese, it was Japanese, it was completely accepted that it was Japanese. Now, this was a period of time, this is some Japanese art from the time period here. And you can see some aspects of this that are really reminiscent of the way in which both the Chinese and the Japanese felt about this conflict. On the right of the Japanese, and you can see that they saw themselves as modern and as on the ascendance, right? So they're standing tall, they're on the ascendance, Japan is on the ascendance during this time period. And China is not there, they're in more traditional clothes and they're bowing. And this is Japanese artwork trying to portray that Japan was on the rise as the leader, the new leader of Asia, the modernizers and the new leaders of Asia. And the Chinese were backward and no longer ought to be the leaders of Asia because they were not strong enough and not modern enough to be. And this is not forgotten by the Chinese today about this particular conflict, right? That the Chinese recognized that part of the reason that they lost Taiwan is that they were not modern enough, they were not strong enough, they did not have the strong enough military power and a strong enough central government to retain control of the island. All right, so there we are. So the policy of the United States as of 1895 was that the island of Taiwan was a part of the empire of Japan. That only makes sense. It was everyone's policy, including China's, by the way. So the next place we need to go is Cairo, Egypt. The second place where Taiwan's status was determined. And in this case, we have to pause for a moment and we have to talk about that period of time. Remember, I said all of the Ming loyalists went to Taiwan and at that time there was an indigenous population on Taiwan. And so there has been a Chinese population, Chinese heritage population on Taiwan for more than 300, almost 400 years. And an indigenous population. And that group of people over time developed an independent identity, an independent identity as being from Taiwan as opposed to being necessarily from China or from connected to the mainland. And that's important because there's a political party that represents that perspective today. It's the DPP or the Democratic Progressive Party. And the party holds the presidential office today. The second party is the Nationalist Party. There we are. The Nationalist Party was led at the time. And the Nationalist Party was the party established at the end of the Qing Dynasty. Remember I said the Qing was the last dynasty? What happened after that dynasty fell in 1911 and 12 was a republic rose up. It was the Republic of China. And the government of that republic was run by the Nationalist Party known as the Kuomindang, KMT or GMT, Kuomindang. And the Kuomindang was led by Chiang Kai-shek, the gentleman on the left. And his wife is on the right. That's an interesting story we can ask about in the Q&A if you like. But she was very active in the negotiations. And this was during World War II, 1943, the very end of 1943, around the time of Thanksgiving in fact. Thanksgiving was celebrated in Cairo. And the President Roosevelt insisted on meeting with Chiang Kai-shek and Winston Churchill prior to going to Tehran. So the three of them met in Cairo. Then they went to Tehran to meet with Stalin. Because what they were deciding at that time was whether to invade Normandy, a cross-strait invasion of Normandy in order to open up a second front in the German front. So the Soviets had been fighting in the east and Britain and the United States were coming to terms with agreeing with Stalin to open up that second front. Now what does Chiang Kai-shek have to do with that? Roosevelt's position was that Chiang Kai-shek was holding down, by continuing to fight the Japanese, was holding down a million Japanese soldiers that the Americans would not have to fight. And in holding down those soldiers, what he was doing was enabling America to shift power to the European theater in order to invade Normandy. And so this, to Roosevelt, Chiang Kai-shek's participation was very important. But Churchill didn't like this at all. He didn't want to give up anything in order to support Chiang Kai-shek. He thought there was enough power that the United States could generate without having to do that. But Roosevelt insisted. But Churchill ensured that there really wasn't anything given to Chiang Kai-shek at that point in time. And so because you have to have success at every major senior leader meeting, there was a communique that came out. And the communique said, Japan shall be stripped of the islands in the Pacific. This was the gift to Chiang Kai-shek for continuing to fight the Japanese, which he has seized or occupied since the beginning of the First World War. And that includes Formosa, that the previous name of Taiwan is Formosa, and the Pescadores. Those are the islands, the Pungu Islands today that are off the coast of Taiwan. So Roosevelt decided to give that American promise that Taiwan and the Pungus would revert to China at the end of the war, once Japan, the imperial owner of Taiwan, had been defeated. So US policy of 1945 was that the status of Taiwan is that it'll be a part of China, right, in accordance with the American commitments made at Cairo. So what happened when on the right you have the Japanese, on the left you have the Chinese, turning over administration of Taiwan at this time, was it something called retro-session? Remember I said the Treaty of Shimonoseki ceded Taiwan from Japan to China? Retro-session would be to cede it back, to return it back to China. Is that what occurred with the exchange of occupation? Or was it a military occupation, like the American military occupation of the main islands of Japan? This is the debate. So the Chinese say, nope, this was the point at which we acquired sovereignty. The mainland says this is the point in which we acquired sovereignty. In fact, the KMT says it as well. This is the point at which we acquired sovereignty over the island and we are, I say the KMT says it, they have said it in the past. Today it's a little bit more of a debate. But the other possibility is that no, this was simply an occupation. And that's an important distinction we'll see why in just a couple of minutes. Alright, so the next important point is Korea. Why? Because, so perhaps I should put Pyongyang, right? Because the North invaded the South in 1950. In fact, it was June, if I recall correctly, June 25, 1950, which is an important date, because it forced President at the time Truman and MacArthur, who was leading American, actually the Allied occupation of the Asian region, including Japan. MacArthur was Supreme Allied Commander at the time. And so a debate and a discussion arose about what to do about Taiwan. Remember, at this point in time, it's been occupied by the Chinese. The question is, has it become under Chinese sovereignty? And as a matter of international law, the answer is no. Why? Because there was no peace treaty that had given the island back from Japan to China. So the best legal answer is it was occupied by Chinese forces and it was not retroceded back. Now that becomes important because Truman decided the strategic, the geostrategic, the location, the geography of Taiwan was more important to retain American control over and not to let the mainland have control over that island after the North invaded the South in Korea. Why? For two primary reasons. One was that Truman looked out at the world and he saw Joseph Stalin, who was still the leader of the Soviet Union, expanding outward, attempting to make more communist countries around the periphery of Asia, right? And so to make the Korean Peninsula communist. China was already communist. Southeast Asians had communist insurgencies. There was communist insurgencies in the Middle East. And also Eastern Europe was becoming increasingly communist. And so Truman looked around and said, we have to stop this. And this was at the very early days of the Cold War and the concept where containment became the American concept. And so Truman said, we need, the geography of Taiwan has strategic importance. He agreed with MacArthur. And so that two days later, they were at the Blair House. This is the house across the street from the White House. Why? Because the White House was under reconstruction at the time. So they met at the Blair House and the president made a decision to reverse Roosevelt's policy. He reversed Roosevelt's policy and said the seventh fleet, U.S. seventh fleet, still based in Yokosuka, Japan, would proceed to Formosa and prevent an attack by the mainland onto Taiwan Formosa. But it would also prevent Chiang Kai-shek, who dearly wanted to go back and conquer the rest of China, would stabilize the situation. That's the second reason that Truman decided to use the seventh fleet to separate Taiwan from the mainland. Because it could give strategic stability to the region. So the first was communist containment and the second was regional strategic stability. So those were the reasons for the policy change. And so the ultimate policy was at that point in time, as of June 27th, was the determination of the future status of Formosa must await the restoration of security in the Pacific. So the status of Taiwan went from an American political commitment to give it back to China when the peace treaty with Japan was finally signed to know the status of Taiwan shall remain undetermined for the time being and wait until restoration of peace and security in the region is established. So American policy regarding Taiwan is tied in part to peace and stability on the Korean Peninsula and in part to regional peace and stability around East Asia more broadly. So now we get to the peace treaty. Now recognize that this came after the Chinese participation in the invasion with North Korea of South Korea. That may not be something that you're aware of, but that part of what Truman's calculus was about wasn't just about Joseph Stalin. It was also about the fact that the Chinese were participating with the North Koreans in attacking South Korea. So at the San Francisco peace treaty, China was not represented at the peace treaty, in part because the Allies could not agree which China should be represented. Now this is two years after the end of the Chinese Civil War in which the Republic of China ended its control of the mainland, not its claim of a right to govern the mainland, but ended its control of the mainland and the Chinese Communist Party took over and established the People's Republic of China. What was left was a small contingency of Chinese forces and the Chinese leadership and the Chinese government on the island of Taiwan plus a few minor outlying islands. That was what was left of the Republic of China and that's what's left of the Republic of China today. Today, after 1949, you've had essentially two governments in this entire area, each of which claims a right to govern all of China, the Republic of China and the Nationalists and the People's Republic of China and the Communists. But at the San Francisco peace treaty, Japan was required to renounce its control over Taiwan, but note that Taiwan as a sovereign entity was not assigned to any other country. Japan just simply walked away and so this was how Truman put into international law and international politics an ambiguous status for the future of Taiwan. That future being waiting until peace and stability are achieved in East Asia. And this was also recognized when Japan made a separate treaty with the Republic of China on Taiwan. It recognized the same essential status. It recognizes that Japan renounced its title and claim to Taiwan and the Pescadores, but it did not assign it to any other country. So the policy as of 1952, the end of this whole crazy period, was that the status of Taiwan, the American policy, was the status of Taiwan is undetermined and will await future action. So now we move to Shanghai, right? Another city also not in Taiwan. And I should say also Beijing, they were both active at the time. And this gentleman on the left, some of you may know Richard Nixon and his wife Pat, Pat Nixon, went to China in 1972. Why? Because Nixon was changing the geopolitical landscape around the world. Nixon was worked very hard to build up Cold War containment policies and decided to weaken the Soviet Union's ability to fight back by opening up and engaging with China. It was a global geopolitical move, a major shift in global geopolitics. So Nixon went to China, spoke with Mao, spoke with Joe Enlai, the Premier and the foreign secretary at the time, and opened up a relationship, began to open up a relationship. It actually took some time, opened up a relationship with Communist China. Now by 1972, many other countries had begun to recognize the People's Republic of China. The number of countries around the world that recognized the People's Republic of China as the legitimate government of all of China outpaced the number of governments that continued to recognize the Republic of China as the legitimate government of all of China. And in this period of time, the Republic of China, remember Chiang Kai-shek and his government lost control of the Chinese seat in the United Nations. Up until this 1971, actually, the Chinese seat in the United Nations was actually occupied by the government on Taiwan, the Republic of China, Chiang Kai-shek, the nationalists. But in that year, it shifted from the nationalists to the communists. And at that point, the People's Republic of China began to be ascendant in international politics. And this is not directly due to Nixon's change in American approach to China, but it's in part a reflection of American policy change. So at this point in time, this is Joe Enlai, by the way, on the right, Richard Nixon, of course, on the left. Now at this point in time, American policy shifted one more time, right? Because global politics were shifting, and so American policy shifted. Nixon said specifically to Joe Enlai, principle one, there is one China, and Taiwan is part of China. So this seems to be a reversal of something going back to the Roosevelt approach that Taiwan would be part of China, as opposed to Truman's approach, which was followed by Kennedy and Johnson after him, that the status of Taiwan would be undetermined. So Nixon's toasting with Joe Enlai says these words, but at the same time he says two other things. He says, our written policy won't be quite that clear, because we have all kinds of interests, bureaucratic interests, that have to be addressed. We also ensure, the second thing he said, was our policy is based on regional peace and stability, right? So the status that even Nixon's policy, where he was willing to go back to that Roosevelt approach, accepting that Taiwan is part of China, was based on non-use of force and non-coercion and no major impacts to regional peace and stability. So even that policy was tied and conditioned on those. So now we come to Washington, because Washington has had a lot to say about the status of Taiwan. After Nixon engaged with Taiwan, there were four things that happened that you should know about. The first thing is that, remember that the seat shifted in 1971 in the UN from the Republic of China, the Nationalists on Taiwan, to the Communist, to Communist China. And Congress began increasingly uncomfortable with the way American policy seemed to be leaving the Republic of China and Taiwan kind of hanging out there. And so Congress passed the Taiwan Relations Act, which made clear that it's American policy, among other things, that our entry into diplomatic relations with Beijing would be based, conditioned on the fact that Beijing would not use force against Taiwan and would not even coerce Taiwan into accepting mainland control. So that's an important component that Congress added to our policy in 1979 with the Taiwan Relations Act. And then there were three communiques that you will hear about, the three communiques. There was the one that Richard Nixon signed, which acknowledged that all Chinese on both sides of the straight claim that there is one China and Taiwan is a part of China. They just disagree on what government should be in charge. But the question is who are the Chinese? Remember I said earlier that there was a separate identity for the people of Chinese heritage that came over in the 16 and 1700s to the mainland. And the ones that came in 1949 after the retreat of the nationalists to Taiwan, sure, they were Chinese. They considered themselves Chinese. But it's not necessarily clear that the rest of them on Taiwan considered themselves Chinese. American policy took advantage of that ambiguity so that Americans could say that all Chinese on both sides of the straight agree that there's one China and Taiwan is a part of China. And we acknowledge that as our policy. And we don't challenge that as our policy. So what are we acknowledging? Well, both the Kuomintang and the communists believe that there's one China, but is that the same as believing that all time when I think the same? Again, we have this ambiguousness built into our policy in order to give us some latitude to shift policy as necessary or to emphasize different aspects of our policy as necessary in accordance with shifting strategic dynamics. The second communique was signed by Jimmy Carter when he was president. He actually opened up the relationship between the U.S. and China, established diplomatic relationships between the U.S. and Beijing, and shifted away our diplomatic recognition of the Republic of China on Taiwan and established a sort of parallel structure, non-official parallel structure to maintain relations with Taiwan, which we no longer recognized as a separate sovereign entity, separate sovereign government from the mainland. So we couldn't have diplomatic relations with both the island, the Republic of China on Taiwan, and the People's Republic of China on the mainland. So we had to sever those diplomatic relations and make them unofficial. That's what that did in 1979. And then in 1982, Ronald Reagan signed a third communique, which had to do with regulating arms sales and our agreement that over time, in accordance with conditions across the strait that the United States would reduce our arms sales to Taiwan. The Reagan administration was very internally, at least, that meant that we would not be reducing arms sales anytime soon, especially since the mainland began a period of time in which they were building up their military. So the United States has a policy of maintaining a capacity in Taiwan to defend itself. So this is where the arms sales agreements come to. All right, so in Washington, by 1982, after these three communiques were formed and the Taiwan Relations Act was passed by Congress, now the policy is we acknowledge all Chinese on both sides of the strait claim there's one China and Taiwan is a part of China. And our agreement to enter inter-diplomatic relations with the PRC rests on the basis that the future of Taiwan will be settled by peaceful, uncoerced means. So what does uncoerced mean? Again, we leave some policy latitude there. All right, so where are we today? Where are we now? Just last month, there was a meeting between Xi Jinping and President Biden, and you'll see some familiar phrases came out of the communique related to that. Remember, leaders have to have something that they agree on, and so out it goes. This is the US statement, actually. The United States opposes any unilateral changes to the status quo from either side, we have to say either side, in part because what does that mean? That means we don't support Taiwan independence. That's an important component of American policy. We do not actively support Taiwan independence any more than we support the policy, a policy of the mainland to use force to attack or coerce Taiwan and bring it under Chinese control. Second, we expect cross-strait differences to be resolved by peaceful means. This is an important statement because it really, American policy includes peaceful, non-coerced means. The Chinese look at peaceful means as being military means only. In the South China Sea, you see sometimes it's referred to as gray zone. You see all the time the Chinese use Coast Guard vessels to harass and to fairly aggressively attack other boats in the region. You've seen it just in the last couple of weeks. In fact, today there was an article about water cannons used by Chinese Coast Guard vessels and essentially they're called sound cannons used by Chinese Coast Guard vessels to try to deter the Philippines from reinforcing one of its positions in the Spratly Islands. The Chinese call this peaceful means. Why? The Chinese believe that it's below the threshold of military and therefore it's peaceful. Well, it doesn't look peaceful if you're on the receiving end of it. That's why American policy is not just peaceful means but non-coerced means. That's in the Taiwan Relations Act quite specifically. Third, the world has an interest in peace and stability in the Taiwan Strait. This goes back directly to that statement of Xi Jinping I showed you at the beginning which attempts to look at the Taiwan Strait issue as an internal domestic Chinese issue where there is no international interest. This is within the scope of the sovereignty of China only and therefore no international interference should be brooked. Almost as if say Long Island had 75 years ago separated from the United States and this would be only an American internal sovereign issue to bring it back under our control. Like that's the way the Chinese view, the mainland views, the Taiwan issue as a solely sovereign. We're pushing back on that and have since the very beginning and said that the world has an interest in peace and stability in the region and across the Taiwan Strait. We're pushing back on that narrative that there's one China, Taiwan's a part of China. This is an internal affair not for international interference. Eli Ratner, Assistant Secretary of Defense has testified numerous times and so the Biden administration policy in part comes out from Eli Ratner where he says we have not supported Taiwan independence. That's true. We do not support it now. So not in the past and not now. And we stand firmly behind the principle that cross-strait differences should be resolved by peaceful means and by peaceful we include non-coerced. Taiwan, there should be a big but or however there right because however Taiwan is located at a critical node within the first island chain. The first island chain of course being those islands off the coast of Asia extending from the Japanese islands through Taiwan through the Philippine islands and the Indonesian archipelago. The first island chain off the coast of the Asian mainland. So Taiwan is located at a critical node within the first island chain in the Indo-Pacific region and its security is critical to the region's security and the global economy. So we have an interest in the security and stability of Taiwan as it stands today is what he's saying. So we don't support its independence but we do have an interest in its stability and perhaps even if you're Chinese you can be forgiven for looking at this and saying that the United States has an interest in maintaining a separate status for Taiwan from the mainland for as long as possible. And President Biden has on more than one occasion essentially said the same thing. He asked whether U.S. forces would defend the democratically governed island claimed by China. The president replied yes if in fact an unprecedented attack occurred. Right so so we see we're sort of coming full circle from the beginning where we started was a period of increased political tensions in part because the PRC military is now has now grown very strong in the region and our capacity to balance the strategic regional strategic dynamics has become challenged in part because the United States has sent political signals that that that we have an interest in Taiwan and Taiwan as a democratic country as a country where we have a democratic entity and an entity in which we have strong economic relations with and a government that we have an interest in stabilizing in Taiwan. What we've expressed is an interest in Taiwan itself and stability in the region over over 75 years since we very first expressed an interest in stability in East Asia and that hasn't changed at all. So let me conclude here and we'll get to some of your questions. What would be the implications of a Chinese attack on or coercion of Taiwan for U.S. policy? I want to be clear right here that I'm not advocating a change for American policy. American policy has been based on deterrence which has a component of political reassurance deterrence is actually achieved by two in two ways. One is by strong military means a credible military response to the potential use of force by China to settle the issue of Taiwan credible military response. The second is a policy of reassurance. This is the political component of it. This is that our policy regarding Taiwan has built in ambiguity. Why? It has enabled us to maintain to establish and maintain diplomatic relations with the PRC and to and to engage in political relations economic relations for the last 40 years now. But at the same time we have retained sufficient ambiguity about what is the status of Taiwan to allow us to revert to a different policy should we choose. And what would be the basis of that choice? It would be a violation of the larger agreement by which the Chinese use force to resolve the situation. If the Chinese were to use force or coercion to try to resolve the situation that could then drive a change in our policy that says all right well then we're going to be clear that the that will shift policy to be clear that our view of Taiwan is that it is a separate entity from the mainland and its status remains to be determined in the future. That is one possible outcome should Taiwan choose to use force against Taiwan. And so at some point the PRC's action could nullify the past agreements if there is force that is used. Second US policy could change again. We've left that room open to us. And third US policy has asserted that this is not just an internal affair of China settling an old dormant civil war between the communists and the nationalists. This is a matter of international peace and security and stability in the region and of interest to governments around the world. That's the American policy. So again I want to make clear I don't think we should be in any hurry to shift our policy. But if China chooses to use force how would we have a legitimate basis for intervening? My view is twofold. One is the status of Taiwan remains to be determined at a later date. That could become our policy. And second it would be China has breached the agreement for peace and stability in the region and we therefore have a right to use force to restore peace and stability in the region. Thank you for your attention. Okay. Thank you very much sir. Thank you. Thank you all for coming genuinely and for listening to sort of it's always a little hard to know how to engage in this history and policy discussion. But thank you for sort of staying alert and engaging. I appreciate it. So we will be back after the holidays in January and learn more about China. Thank you.


A fiery horse with a speed of light, a cloud of dust, and a hearty-hio silver, the lone ranger. Before this exciting adventure, a word from our sponsor, General Mills, makers of Cheerios, the Oats cereal that's ready to eat, bunny-crocker mixes, and Wheaties, the breakfast of champions, present by special recording, the Lone Ranger. Say, when you get home from an afternoon of fun with a gang, aren't you sometimes so hungry you don't think you can wait till supper time? You don't want to spoil your appetite for dinner, but still you need a little something. Well, how about a nice cold glass of milk and a big square of warm gingerbread? Mmm, just the thing. And it's no trouble at all for your mom to whip up a batch if she uses Betty Crocker gingerbread mix. Everything she needs is right there in the package. She just adds water and it's ready to bake. Betty Crocker gingerbread smells so good when she takes it out of the oven, all piping hot and spicy. And you know what tastes real good? A big dab of whipped cream on top. Mmm, have mom bake some soon. Ask her to get Betty Crocker gingerbread mix. Next time she goes to the store. With his faithful Indian companion Tonto, the daring and resourceful mask writer of the plains led the fight for law and order in the early western United States. No where in the pages of history can one find a greater champion of justice. Return with us now to those thrilling days of yesteryear. From out of the past come the thundering hoofbeats of the Great Horse Silver. The Lone Ranger rides again. Are you still there? Two men rode along the trail toward Hilltown. One of them, Phil Martin, was young, about 25. The other was an older, rougher looking man named Blackie Jackens. For some time they rode in silence, then Blackie spoke. I've been your cellmate for two years. You never did say what you were in for. I just didn't want to talk about it, Dan. You want to tell me now? Sure, why not? The happen this way. A little over two years ago I got a job at the express office in Hilltown. Working under an hombre named Sam Eaton, who is the express agent. I was green at the job and just did what I was told. Yeah, then what? Well, I didn't trust eating much. He went to the cafe a lot and gambled all the time. One day he came into the express office and taken a lot of loose papers from his desk. He brought them over to my desk. Martin, I have something here I want you to do. All right, Mr. Eaton, what is it? Well, I've been keeping the record of accounts on these loose sheets. The company is sending an investigator out this way. It comes every once in a while and I want things to be ship shaped for him when he gets here. I see. Here's the company account book. The records are supposed to be kept, Jim. I want you to copy what I have on those sheets into this book. You write a neat hand much better than I do and I want to make a good impression on the investigator. All right, sir. I'll come in and work nights to get it done. Fine, fine. I'll keep it neat and get it finished in time so I can shake it first. It'll mean a lot to this office to have things neat and right. So I went to work and copied those sheets of paper into the book and gave it to Eaton for check. Then what happened? Well, he set a check to all right. The end of the week the investigator came. He was still going over the accounts when I left that evening. The next morning when I went to the office, he and Eaton were already there. And so was the sheriff. The sheriff? Yeah. What for? I didn't think anything of it when I went in. But it wasn't long before I found out what was up. Good morning, Mr. Eaton. We're waiting for you, Martin. Howdy, Phil. Oh, hi, Sheriff. The express investigator asked me to come here. He wants to ask you a few questions, I reckon. That's right, I do. Martin, is this your handwriting in this account book? Yes, sir. The accounts in this office are short over $1,000, Martin. What? It's evident you destroyed some of the way, Bill, so you could make the accounts check. I've asked the sheriff to take you into custody. I'll send a warrant for the arrest on a charge of fit from the express company. Why, then? I'll have to take you in, Phil, so you might as well have come along quite like. But I didn't steal anything from the express company, I tell you. It's a frame-up, that's what it is. I didn't do it. Well, in spite of what I said, they wouldn't believe me. I was given a trial and sentenced to two years in territorial. That's my story. The dirty coyote eating framed you already. Yeah, he did. Now I'm going to get back at him somehow. Even if it means going back to jail for the rest of my life.  In the meantime, the lone ranger and Toto had made camp in the hills outside of Hilltown. Toto, who had gone to town for supplies, returned and reigned up at the campsite. Oh, Scott, hold for that. Well, Toto, any news in Hilltown? Well, Missyfeller in Café. Big, heavy set. Scar on that cheek. Him called Blaggy. Oh, what about him? Well, Himfeller, we meet some time ago. Him have gang. Him go to jail when you catch gang. Hmm, that sounds like Blaggy Jenkins who robbed the stage near Stockton with his gang three years ago. That same fella. Me remember now. He must have just been released from prison. Ah, me hear him say that. Me go into Capé. Him at table in corner with other fella. Me listen, hear what them say. I'm sure glad to meet up with you again, Manuel. You see, I rode over here with a fella I met in prison. He's at that cabin we had along the river, waiting. I came in for supplies and to meet you. And what are these sombrayers think of, senor? Well, he's sort of a green-horned things, Manuel. Claims he was framed in the territorial and that he's going to get even, so. Gives me an idea. Folks around here know he's due to get out. And at his trial, he claimed he was framed. And just what is this idea, senor Blaggy? Maybe we can even that score for him. Get away with a good lot of money. Let's go somewhere else where we can talk. See, we'll ride to the place where he is weighed. As we ride, you can tell me of your plans, senor Blaggy. Let's go. Then leave Capé and ride out of town on East Trail. Me get supplies and come back to camp. I see. I wonder who the fellow is that Blaggy Jenkins plans to frame. Me not know, Kimusubby. After supper, I'll put on disguise and we'll ride into town. We might be able to find out if he really was framed before. Perhaps he'll need a little help to outsmart Jenkins. After they had eaten, the lone ranger and tato prepared to ride into hill town. Removing his mask, the lone ranger disguised his features. Then, saddling Silver and Scout, he and tato mounted. He used to be coming. A short time later, they arrived in town and went into the café. For a short time, they stood unnoticed at the back of the café, watching a card game that was in progress. Then, as the door to the café opened, the lone ranger heard remarks that caused him to gaze intently at the man who entered. Hey, look who's back in town. Hey, what's he just got out of prison? Sam Eaton better watch himself now. Oh, there must be the fellow Blaggy mentioned. Ah, I'm frightened. Hello, Bill. Oh, Chef, it's good to be back in circulation again, isn't it? Yeah, it is, Chef. I wondered why you came back here to Hilltown. Any particular reason? What reasons I have? I'll keep to myself, Chef. You sound better, Tato. I thought I ought to warn you, it's Bill. Seeing as how I'm still Sheriff here and seeing as how me and a lot of others remember what you swore to do when you were sentenced. Just to forget about trying to get even with Sam Eaton. Two years in prison isn't the kind of treatment that makes an hombre forget anything, Sheriff. Another drink, Bill? No, no more. There's the money for that one. So long. Leading the café, the lone ranger put on his mask. Then he and Tato followed Phil along the trail for some distance. Finally, a bend in the trail ahead hit him from their view. A few minutes later, they rode around the bend, but he was not in sight. Look, Kimusabi, he's not in sight now. That's strange. Here on the trail is straight for some distance. I wonder if he turned off. Oh, no, no, no. The shot comes from the left, Kimusabi, from behind Boulder over yonder. Yes, I know. Easy for us to rush him, Kimusabi. What do we do? We resume him, Tato.  All right, mister. The next move is yours. Oh, hoot, huh?  I guess Eaton must be plenty scared to go and hire a couple of gunslingers to follow me. I'm not an outlaw, and neither is my friend, Tato. That mask says different, mister. Forget that mask. We followed you because we want to talk to you. What about? About a man named Blackie Jenkins about Eaton. I don't savvy this at all. Look, Phil, we came as friends, believe me. You claim Sam Eaton framed you into prison. Your bitter feeling against him is more or less natural. I'm going to get even with him. You can count on that. That's what you've told everybody. Because of that statement, you're liable to be framed into prison again, even though you might not make a move against Eaton. What do you mean by that? Before I tell you anything, Phil, I want to make sure you'll make the right moves from now on. Will you come with us to our camp or we can talk? I'll tell you what we've found out, and then we'll make some necessary plans. How about it, Phil? All right, I'll go along with you. Good. It may be that if we plan well and move fast enough, we'll not only save Sam Eaton's life, it'll also save you from being blamed for his murder. Come on, come on! We'll continue our lone ranger adventure in just a moment. All over the country in every direction. How you, how you doing? Here's the question, and here's what's to happen. Happy people have to say, Eaton, are we decent? Do, do, do an OK. OK. Yup, take Mickey Mantle, born in Oklahoma. Star with the New York Yankees. From out west, we're a man's a man. And what a man is Mantle? Say, Mickey's been eating Wheaties for years. Now listen, here's another champion with plenty of zing in his swing. Zing, that's a service ace for champion Pancho Gonzalez, a native Californian. He hits them hard, he makes them swish, and in the morning enjoys his dish of Wheaties. Sure, lip smack and taste ticklin' rib stickin' good. And there's a whole kernel of wheat in every Wheaties' flake. Keep on eatin' your Wheaties, and you will do, do, do an OK. OK. Now to continue. The Lone Ranger persuaded Phil Martin to go with him and Tonto to their camp. There they told Phil what Tonto had overheard in the cafe when Blackie talked to Mantle. What are we gonna do? It's up to us to prevent you from being blamed for another crime that someone else intends to commit. You have plans, maybe? No, nothing definite, Tonto. We'll discuss a plan as we ride toward town. All right, let's get the horses now and get started. Meantime the sheriff went to Sam Eaton's room at the hotel. Well, Sheriff, come on in. Thank you, Mr. Eaton. What brings you here? I came to warn you that Phil Martin's back in town. He got out of jail this week. Well, thanks for warnin' me, Sheriff. I'm goin' down to the express office shortly, and I carry a gun so I won't get upset over a weakling like Phil Martin. Maybe I ought to go along with you just in case. Oh, no, no need for that. Just as you say. But I'll sort of keep my eyes peeled, anyway. I'll be gettin' along now. Good night, and thanks for coming over, Sheriff. Don't worry about me. I can take care of myself. Leaving the hotel, the sheriff went to his office. A short time later, one of his deputies entered hurriedly. Sheriff, come on up, sir. What's up, Hank? What are you so excited about? I trailed that hombre Phil Martin from the cafe a while ago, like you told me to. Well, where'd he go? He started out of town followed by two other hombres. And the way it went, I'm put on a black mask. What? They met up with Martin. I got around to bend the trail just in time to see him right away together. And then what? Well, they went to wear the mask, man. The other one, an Indian, was campin' out. After talkin' a while, they headed back to her town. I led out by a shortcut and came to tell you. I'll bet Martin tied up with a couple of vows and all is supposed to get back at Sam Eaton. Don't get some men together. And we'll ride out and grab them before they can do any harm. Hurry up now. All right, Sheriff. The lone ranger with Toto and Phil rode along the trail toward town in the bright moonlight. As they rounded the bend in the trail near the town, they were confronted by the sheriff and his posse riding the other way. We'll soon be at the edge of Hilltown. That's right. Maybe we go... Look, Kim and Tommy. There's the posse.   We've got all three of you covered. Don't try to go for your guns. Here, Sheriff. Look at this. Uh, bullet. What? Uh, silver bullet. It's made of silver, all right, but that don't mean anything to me, mister. Then perhaps this note will mean something. Uh, note? I don't save you all this. I suggest you read it, Sheriff. Uh, signed by United States Marshal Drew Pecos. Yes, my Indian friend Toto and I rode our way to Pecos. We stopped to camp for the night near here when we learned about the plot against Eaton. How come the Marshal sent you this note anyway?  Well, we've helped the Marshal in the past, Sheriff. And I've learned that there's a large outlaw gang operating near Pecos. Marshal Drew apparently wants us to aid him in the gang's capture. That's right. You spoke of the plot against Eaton. That's why we came to stop Martin. Phil Martin doesn't intend to get even now, Sheriff. But we do know that two other men planned something against Eaton, knowing that everyone would suspect Phil Martin. Now, if they succeed, they'll eventually become vicious outlaw gang leaders. They must be stopped now. Turn around, boys. We'll head back to town and have the masked man and Indian go with us. Get up there! A short time later, Sam Eaton was going over papers at his desk in the express office. When the door opened, and Blackie and Manuel entered. Well, what can I do for you, man? The first thing you can do is to open the safe, mister. Open the safe? What do you mean? It is not good to argue, senor. Hurry up. Get to the safe. Well, all right. All right, go on. Open it. I am. Get the stuff out of there, Manuel. Say, senor. So, here is plenty of gold here. We hit just at the right time, seems like. There are bags of it. Put to them in my pockets, Manuel. See. And here they are. And these are the one I'll carry. All right. Now that you've robbed the safe and got that gold, why don't you leave? And have you run to the sheriff, eh? No, mister. We aren't that local. Well, what are you going to do? He asked what we're going to do, Manuel. Shall I let him guess? Oh, perhaps senor Eaton has some more questions before we give him a bullet. You know my name. Look, let's take the gold. Tie me up if you want, and then you can get away. Oh, no, no. You could describe us too well. If we plug you, they'll think our friend Martin did it. Martin? He sent you here? Maybe. After all, he did say he'd give it to you. Look, if he's waiting outside, call him in. I'll do anything. I'll admit I framed him.  He called blood. Well, Martin told the truth at that. You did frame him. I don't blame him for wanting to get even. But we will get even for him. May I say you're blocking? Any time we get these over with, no? Yeah, that's right. Oh, no, no, no. Don't do it. I'll clear Martin. I'll admit I fixed the accounts. Listen to me, please. The only thing is, Eaton, Martin will never know that we're plugging you into leaving. Then he'll get the blame and go back to prison to hang. This is it, Eaton. Someone shoot through the window. I get through, Eaton. Drop that gun, you. Get on, buddy. He's the sheriff. You will not be tempted. Oh, get him, Tonneau. Oh, my arm. The Indians wrote me. Sheriff, are you all right? Just creased the back of my hand. Lucky Tonneau was right next to me. Good work, Sheriff. Thank him when you got here in time.  They robbed the safe. The gold is in their pockets. Yeah, we were lucky to get here. I think they were sent here by Phil Martin. I'm sure of it. Even though they said that... That's a lion you know, Eaton. Martin. Yep, it's Phil Martin. He and the rest of us were outside the door. We heard everything that was said in here, including you admitting that you framed Martin two years ago. Sheriff, I'm sure you and your men can take care of these crooks. I suggest you hold Eaton until the express company decides what they want to do in his case. I'll hold them all right. And believe me, I'll recommend that the express company make Phil Martin their agent in Eaton's place to make up for what he went through. Do you really think they'd do that? I think they will, Phil. Well, come along, Tonneau. We're through here. Adios, Phil. Adios. Goodbye. Thanks for everything. Goodbye. Well, that mask man sure had things figured out right. I still don't know exactly who he is, though. One thing I do know, Sheriff, he's the man who put Blackie Jenkins behind bars with his gang.  I reckon Blackie can tell you who that masked ombre is. All right, Jenkins, if you know, then speak up. Yeah, what kind of a loman are you anyway if you never heard who that mask ombre is? Y'all know he's a lone ranger. Lone ranger? I don't think you can hear it. The righted feature of the Lone Ranger Incorporated is produced by Kendall Campbell Muir Incorporated. A part of the Lone Ranger is played by Brace Beamer, your announcer, Fred Foy. Listen to the Lone Ranger brought to you by special recording Mondays through Fridays at this same time.


Backroads is made possible by the Minnesota Arts and Cultural Heritage Fund, with money by the vote of the people November 4th, 2008. My name is Cory Campbell. I'm originally from Central Michigan and I'm an old time musician, focusing mainly on claw hammer banjo and fiddle tunes. And when did you first get into music? I started playing music about 10 or 11 years ago right after high school. I just kind of dabbling with acoustic guitar, some electric, and then just moving more towards acoustic folk music, banjo and fiddle type stuff. And when did you first start performing music? I first started performing probably about five years into it just as like an open mic duet, just some people in the local music scene around my college, just kind of informally jamming and playing at parties and things like that. And then later on I was in a classic rock and country cover band. Who are you to old time music? Well like I said, I was hanging around that coffee shop a lot and on Tuesday nights they had an old time jam with about five people sitting around playing fiddle, guitar, bass.  After a while I would just go there every Tuesday night and I decided to approach these guys and see if I could sit in and play some banjo with them. That's the other thing about old time music is it's very welcoming, it's very collaborative, so of course they're like sure, you know, and I just kind of, I didn't know much but I just followed along and eventually just learned by ear. So what's it like performing that style of music? Well I like performing old time music because it can be very trance-like. Kind of the main objective of old time is to immerse yourself in the tune and really get into the groove of it. And so that makes for an easy place to perform, to kind of go to while you're performing. Originally I was pretty shy, you know, with music and everything so old time really helped me open up to be able to perform well in front of people I think. Right, yeah, this tune is called Crow and the Spruce Tree. I figured that name out back in Michigan but I think coming here was really the place to finish the tune. Since you came from the Michigan music scene, now you're in the Minnesota music scene, what's kind of like the community in Minnesota been like? Well the community in Minnesota has been great, very welcoming. There is a lot of music going on here, that's something I never really knew when I was younger. I'm from Michigan, it's kind of a small town, you got to drive about half hour to 45 minutes to get to anything culturally relevant. So there wasn't a lot of music going on, definitely not a lot of old time. I was lucky to find the people that I did but it seems like there's a lot more going on in Minnesota and I'm glad to be here and be a part of it. Another one that I wrote probably about five years ago, it's called the Melting Snow. It was wintertime right before I moved out of Michigan. I just went through a breakup that I didn't really see coming and I was just feeling really lost, you know, and it was the end of winter which is always kind of difficult. I just started playing the banjo too, probably only about three months into it and it just kind of came out one day and that's kind of how all of my songwriting kind of happens. Whenever I plan a song it just never really works out but then I'll be just messing around either sitting in my backyard or on the porch or something and all of a sudden I start playing something and it's like, whoa, this could be a song. So yeah, that was probably the first good banjo tune that I wrote and I'm looking forward to playing that for you guys tonight and seeing what people get out of it. Thanks everybody. Thanks for coming. Thanks for sticking around.


Dear learners, welcome to the session. In this session, we will discuss about one of the most important circuit of computer called combinational circuits. If you look into computers, one of the key requirement is that it, for example, it adds two numbers. How that addition takes place or how a subtraction, if it is to be done, how that particular thing takes place? Well, it is with the help of these circuits called combinational circuit. What do we mean by combinational circuit? How do we create combinational circuit? This is what we are going to discuss in this particular session. Circuits does not mean a combination. What it means that you have a given set of inputs, you have some circuit in between and you have certain outputs coming out of the circuit based on those internal processes or based on those internal circuitry which we place. Now, what are the basic circuitry which is going to be there? Well, since you are dealing with computers, they are either going to be AND gates or gates or NOT gates, right? So this is what a combinational circuit will do. It will take some input, there will be then a circuit which will process the data and there will be an output. And that circuit formation will be based on our logic. So if we want to do addition, the logic will be accordingly adjusted. If you want to do subtraction, logic will be accordingly adjusted. So let us look some details about combinational circuit. So before we go to the slide, let us have the slide show on, right? So combinational circuits are interconnected circuits of gates according to certain rules to produce an output depending on its input value. This is precisely what I said. A well-formed combinational circuit should not have feedback loops. Now, this is very, very important for you to understand. Many a times, I do not know whether you are familiar with distillation processing or not. You must be because you have a refinery in Guwahati. Now within the distillation processing, what happens whenever there are columns, the bottom most column, there is a purge, right? There is a purge, there is some kind of purge means when you are distilling petroleum, from the top you get natural gases and from the bottom you get lube oil and those kinds of heavy products, right? But all the time we recycle some of this, the purge which we call, we recycle it. And why we do it? So that in all the columns, a minimum level of liquid is maintained. If we do not do that, then the built up is not going to take place because whatever is coming in is going to go out. But with the help of this recycle or purge, the built up is somewhat bigger rather than the input and output. Now that is a theory behind flip-flop and the circuits which we call sequential circuits, right? So wherever there is a feedback, the circuits are sequential circuits. Wherever there is no feedback, the circuits are combinational circuits. So a well formed combinational circuit should not have a feedback loop. That is one of the reasons. Can be represented as a network of gates, obviously that is what we are talking about. Since we are talking about computer, we are talking about and or not gates or a combination of functionally complete set of gates. Now what are these functionally complete set of gates? You must read from your books or for the studies, you will find this particular term. Can be represented as a network of gates, can be expressed by truth table or a Boolean expression. Whatever you want to define a combinational circuit, you need to design it with the help of a truth table or a Boolean expression and using those Boolean expression, you can do the drawing or whatever you want to do with the combinational circuits. The output of the combinational circuit is related to its input by a combinational function, which is independent of time. Therefore, for an ideal combinational circuit, the output should change instantaneously according to changes in input, but in actual case, there is slight delay. The delay is normally proportional to the depth or number of levels that is maximum number of gates on any path from input to output. Now this is typical property of any flow circuit. Suppose you have a canal in Brahmaputra, a canal coming out of Brahmaputra and there is a barrage, obviously when you will open the gate from the barrage, the water will take some time to reach a particular point down the line 1 kilometer or 2 kilometer down the line. So is the case with the combinational circuits, the gates, there are number of gates available in between. So it is going to take some time, the current or the logic nature, the current or the voltage is going to pass through these circuits and only then it will be reaching out of it. Therefore, you will have to have a slight delay, ideally no delay, just like your switch. As soon as you switch on, electricity is on, but then technically there is a mild delay which is not measurable by us. The basic design issues relate to combinational circuits are, so now what we are now, so this is what combinational circuit is all about, there is an input, process and output. So what are the basic issues with this particular combinational circuit? After all what we want to do, obviously what we want to do, we want to do the minimization of number of gates. Why we want to do minimization of number of gates, lesser are the number of gates, lesser is the delay, as well as lesser is the circuit requirement. If you are talking about circuit design, then the more number of gates will form a bigger circuit, is it not? And more expensive circuit too. So this is what is required and the depth of the circuit should not exceed a specific level. Otherwise the gated delay will be too much and probably computer is not going to accept that kind of a situation. Number of input lines to a gate which is called fan in and to how many gates its output can be fed which is called fan out are constrained by the circuit power constraints. So this is another constraint which exists in any combinational circuit and which has to exist in any combinational circuit. For example you are using, let us say you are using electricity at home.  So people who deal with this kind of a situation, no or maybe inverters you might be dealing with at house. So inverter the limit is let us say 625 kVA, then hardly 3 lights or 4 fans can work with it. You try to put another it will be off. That is what fan in and fan out as far as combinational circuit is all about. Now how do we represent the canonical or the standard form as far as logical expressions are concerned and how are they related to the kind of this combinational circuit. Let us have a look at it. The first form is called sum of product form of standard representation of Boolean algebraic expression. This is also called SOP, short for SOP. For example is A and B dash that is negation of B plus that is R, A and B. So this represents a sum of product form, a term of sum of product expression that contains every variable of that function either in the true or complement form is called a min term. So this is the definition which most of the time you encounter the min term and for example what we have given A that A and B and C plus A and B then only ABC is min term why because A, B and C are appearing either in the normal form which is ABC or in the complement form. They can also appear as A dash, B dash, C dash any one of them in any kind of format. Probably A can be A dash and BC that will be an acceptable term. Similarly A, B dash, C dash will be an acceptable min term but A dot B, A and B which is not a min term because it does not contain C. So this is the definition for min term and this has its connotation with Carnot's map in the sense that in Carnot's map you represent a truth table and that is actually represented by a min term. The term A dash, A and B and C will be only one, only if A equals one, B equals one and C equals one. This is the only possibility when this particular min term will be having a value one otherwise it would not be having a value one. And that is why we will be representing one in the Carnot's map against them. For any other combination of the values of ABC, the min term A and B and C will have a value zero. This is simple logic, A and B has to be one only if A equals to one and B equals to one otherwise it will have a false value which is untrue. The opposite of it is called product of some form which basically represents plus within the bracket and and plus happens to be R and and as the conjunction of the two. Max term is the term of POS that is product of some expression which contains all the variables of the function in true or complimented form. For example, in F equals to ABC equals A plus B plus C. So A or B or C and A plus B dash max term is only AB A plus B plus C. Now the advantage, the basic feature of max term is that A plus B plus C will have zero value only for one particular case. For all other cases it will have one value and what is that case A equals zero, B equals zero and C equals zero. For all other combinations of values of ABC, it will have a value one. This is the significance of max term. Many a times solving problems for combinational circuits using Carnot's map, you will use this particular term in a different connotation where you will be drawing a different kind of Carnot's map. For the time being, we will not be using the max term, we will be using the min term based Carnot's map. So once we are familiar with the basic combinational circuit issues, let us move on to one of the core important issue for the design of combinational circuits and that is minimization of gates. What we want to do is that we want to minimize the circuit or the number of gates utilized in a particular circuit. To do so, what we can do is either algebraic simplification which somewhat, I mean there are Boolean functions and all that, which are somewhat difficult, there are Carnot's map, which we are going to discuss and there is a Quinn-Maxikovsky method which is beyond the scope of this particular course itself. Let's discuss about the Carnot's map to demonstrate how this algebra, the process of minimization of the gates can be carried out. But let me warn you here, then when you are going to industry for this particular thing, people are not using these methods anymore. These are for your own intellectual development. Now these things has been taken over by programming languages and many, many, many more different concept. But to begin with, you must always know this particular concept so that you can move on to the greater concept. So let us discuss it with the help of a problem, an example. Let's look into the problem. Assume that you are asked to design a circuit that accepts three bits as input and generates an output zero if the input bit represents a non-prime number, else produces an output one. Now this is the given problem that we have three-bit input and one will be generated as an output if the given combination of or equivalent digital number is prime. Now what are those different prime numbers? We have two, right? Okay, prime numbers. So we have two, we have three, then we have five and then we have seven. So we have four prime numbers. So what we need to do, the very first thing which we need to do, represent the given problem in the form of a truth table. We got to do that. Why? Because our logic should get reflected into the truth table. Remember, truth table is what? Truth table is a form of minterm. So let's look into the decimal equivalent, decimal zero. We have all three zero, output should be zero because that's not a prime number. One, right? One is represented as zero, zero, one. One is also not a prime number. Remember that. Two is a prime, so output you can see is one, three is also a prime, four is not a prime, five is a prime, six is not a prime and seven is a prime. So we are able to represent the whole logic of the problem into the form of a truth table. Now what? Now we have six, in fact, five more steps to do. And I would like to draw, in fact, demonstrate each one of those. But let me first read those steps for you and then I would like to demonstrate each one of them for you. The first one is draw a Carnaut's map. So how do we draw that? Step three is map the truth table onto the Carnaut's map. So we would like to do the mapping of truth table into the Carnaut's map. Then identify and mark the adjacent terms. So this is still this point we will have be using with minterm. But from this point onwards, we will convert minterm, we will try to combine minterms for optimization of k. So we will try to find adjacent. I'll talk about what is adjacent a little bit when I'm discussing, then find the minimal expression that is what we are going to do and finally draw the resultant logic diagram. So this is exactly what we are going to do with the help of, let's say this time with the help of a pen and paper. So as step two, what we are going to do, we have drawn a K map. This particular K map, as you can see, have eight boxes. Each of this box is represented for one minterm. What we are going to do? We are going to represent a on this side and bc on this side of this particular K map. When we are representing a, what are the possible values of a, 0 or 1? So this is what we have represented. What are the possible values of bc? Bc can be 0, 0 or the next can be 0, 1. Now the third in this particular series should be 1, 0 but in Karnaugh's map, there is a typical condition that the next bit or next sequence, whatever we represent, should change only in one bit and the one bit which is going to change in this particular case is moving this particular 0 to 1. So it is going to be 1, 1 and the last in this particular case will be 1, 0. So 0, 0, 0, 1, 1, 0, 1, 1. Why we are representing like that? Because in each of these, there is only change in one bit only that you can notice. Here the changes between c. Here the changes once again between c and what is in this particular case, what is changing? b is changing over here, 0 to 1 and b is not changing over here. So you can see the way the changes are being made into the Karnaugh's map. So this is the Karnaugh's map. As we said, we have drawn the Karnaugh's map as step 2. Now from this step, let's move on to step 3 that is the truth table. Now the truth table, 0, 0, 0, we won't draw 0, 0, 0, any case. We will be drawing only for where the value is 1 and the first case in that particular case is for the case of 2 and that case of 2 is 0, 1, 0. So this is a is 0, b is 1, b is 1, a is 0, b is 1 and c is 0 which happens to be 2. So this is where the 1 appears. This is a min term. And the value of a is 0, the value of b is 1 and the value of c is 0, which happens to be 2, the value is 1. The next case is 3 which is 0, 1, 1. So 1 appears here. What is the next case? Next case is we have 5, 5 is 1, 0, 1, 5 is, so this is 5. Then 6 is not prime, 7 which is 1, 1, 1. So 7 is the last case. So now what we have done? We have converted the min terms into the Carnhouse map. We have translated the min terms into the Carnhouse map now. From here onwards, we move on to step 4. And what was the step 4? Step 4 was to find the adjacent cell. Let's try to find the adjacent cell. Now what are adjacent cell? Here what we said, they change only in one bit. So these two are the adjacent cell. And these two are the adjacent cells. We are slightly unlucky because in case of this one, had we had this one over here, then these four cells would have made an adjacent cell pair. If four cell make an adjacent cell pair, then you will find two variables will be eliminated. When only two cells are making adjacent cell pair, then only one of the cell will be, or one of the variable will be eliminated. What is changing? Let's identify how it is. What is the value of A for this particular row? The value of A is 0. So A prime is 1. And B in this particular case is 1 in both the cases. So B equals to 1. And C, 1 or 0, it does not matter. So what is the expression for this particular case? A dash and B. The value of C does not matter because the value of C is either 0 or 1. For both the cases, it has to be 1. Therefore, A dash dot B is going to be the optimized expression for this. Similarly, for this particular case, please note, what is the value of A? In this particular case, A is 1. So we don't have to create A dash. The value of B is changing from 0 to 1 in this particular case, isn't it? So B gets eliminated and the value of C is 1. Therefore, the B changes. So B is not needed. Similarly, in this particular case, C is not needed and the expression becomes EC. So the overall expression becomes A dash B plus AC. So this term plus this term. So this is actually the step number 5. This is the optimized expression which I get. Now I want to draw the equivalent diagram, circuit diagram for it. So let me draw the equivalent circuit diagram. Now what we have? An input A here. So A can be negated. So the A becomes A dash, A can be straight. This is A. Now if we once again, so A dash and A, with A dash we have B. So we draw a B here. And there is an end gate. It goes through the end gate. What is the equivalent expression? A dash B. In this particular case, we have A and we have another input C. So both of them goes to an end gate. And what is the output of this end gate, AC? And these two in outputs then go through a R gate because our expression was plus in between. So plus is an R gate. So what we get is A dash B plus AC. So that is our output. Now what you basically have? You have three inputs, A, B, C. And what you will be producing? You will be producing any of the output. Let's try to test this particular thing. For example, if A is equal to 1, B is equal to 1, C is equal to 1. What is the total? These are 7. So it should show us an output 1. Let's try it. A and C brings us A dash B becomes 0 and AC becomes 1. So A dash B plus AC equals to 0 plus 1 equals to 1. So output is 1. So that's correct for the case. Let's try another. When we have A equals to 0, B is equal to let's say 0 and C equals to 1, which is the case of when we are talking about 1, we are expecting a false result. So A is 0, therefore A dash is 1. So A dash is 1, B in this case is 0. So 1 and 0 becomes 0. In the A is 0, so AC becomes 0. So both the terms are 0, therefore output is equals to 0. So what you get for the case when input is 1, you get a 0 means it is not a prime. This is prime. So you can try for any combination. What you have done, instead of 4 gates, in fact, there were 4 places where 1 was appearing. You could have done 3 gates for this. In fact, one gate for this, one for this, one for this and one for this. You could have 4 gates and then all of them should have been odd together to make it 5. We have reduced the number of gates to 1, 2 and 3 overall. So this is the way we have done the minimization of gate. What next? From here, where will we move on? You should practice this kind of a thing. You should try drawing K maps for 4 variables A, B, C, D and likewise. Remember one thing, whenever there is a problem, the first thing you must do is to draw the truth table. If you are able to draw the truth table for Carnaut's map, half of the battle is 1. So concentrate on drawing the truth table. Then after it is plain mathematics. But before drawing the truth table, you have got to understand the logic, what you want as an output. Remember these combinational circuits are designed on the basis of given problem. So you define the problem domain. Once you have defined the problem domain, input gets fixed and the output gets fixed. That is what is your truth table. If you know your input, you know your output, draw the truth table in the form of minterms and then simplify. Unfortunately, Carnaut's map are not useful when the number of variables go beyond 6. Then we are not using these Carnaut's map. But this is a very good logical start to know about your computer and its logic circuit. First, try solving such problems and discuss it with your counselors from time to time. For the time being, thank you for being with me.