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Contemporary design homework logic

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May also treat the historical development of feminist philosophy and its critiques. May be taken for credit two times with permission of instructor. A philosophical investigation of the topics of race and racism. The ethics of racial discourse. Anthropological and biological conceptions of race.

The social and political significance of racial categories. Post-racialist conceptions of race. An in-depth analysis of one or more issues in philosophy of law. Topics might include legal positivism and natural law, legal and constitutional interpretation, judicial review within a constitutional democracy, First Amendment jurisprudence, substantive due process and equal protection, the limits of the criminal law, responsibility and punishment, psychiatry and the law, and the moral foundations of civil law.

An in-depth analysis of a central problem, figure, or tradition in political philosophy. Topics may include minority rights, war and peace, political philosophy as it pertains to animals or the environment, immigration, ideal vs. Content may vary. An in-depth exploration of an issue in bioethics. Topics will vary, and may include the ethics of genetic engineering, mental capacity and genuinely informed consent, the just distribution of health care, the ethics of geo-engineering, and the ethics of climate change and health.

May be taken for credit two times. A survey of ethical issues arising in the collection, storage, analysis, consolidation, and application of data. Topics may include data as property and public resource, privacy and surveillance, data and discrimination, algorithms and fairness, and data regulation. Central issues in philosophical aesthetics such as the nature of art and aesthetic experience, the grounds of artistic interpretation and evaluation, artistic representation, and the role of the arts in education, culture, and politics.

A study of philosophical themes contained in selected fiction, drama, or poetry, and the philosophical issues that arise in the interpretation, appreciation, and criticism of literature. Careful, line-by-line translation of passages of intermediate difficulty from German philosophical texts, both classic Kant, Fichte, Hegel, Schopenhauer and contemporary Heidegger, Wittgenstein, Habermas. May be taken for credit six times as topics vary.

LIGM 1D or equivalent level of study recommended. Prerequisites: consent of instructor and preauthorization. Continuation of PHIL in the careful, line-by-line translation of passages of advanced difficulty from German philosophical texts, both classic Kant, Fichte, Hegel, Schopenhauer and contemporary Heidegger, Wittgenstein, Habermas.

May be repeated for credit as topics vary. Prerequisites: consent of instructor or completion of PHIL Classical texts and issues of existentialism. The focus will be on a leading movement in continental philosophy e. Among the issues to be discussed are the existence and nature of God, the problem of evil, the existence of miracles, the relation between reason and revelation, and the nature of religious language.

Independent study by special arrangement with and under the supervision of a faculty member, including a proposal for the honors essay. An IP grade will be awarded at the end of this quarter; a final grade will be given for both quarters at the end of B. Prerequisites: department stamp; consent of instructor. Continuation of A: independent study by special arrangement with and under the supervision of a faculty member, leading to the completion of the honors essay.

A letter grade for both A and B will be given at the end of this quarter. Prerequisites: consent of instructor. Under the supervision of the instructor, student will lead one discussion section of a lower-division philosophy class. The student must attend the lecture for the class and meet regularly with the instructor. Applications are available in the Department of Philosophy. Prerequisites: consent of instructor and department chair, GPA of 3.

Directed individual study by special arrangement with and under the supervision of a faculty member. Introduction to philosophical methods of analysis through study of classic historical or contemporary texts. Writing intensive. Enrollment limited to philosophy entering graduate students.

A study of selected texts or topics in the history of philosophy. Usually the focus will be on a single major text. May be taken for credit nine times with changed content. An introduction to some central issues in ethical theory with emphasis on classic texts or contemporary authors. May be taken for credit three times with changed content. An introduction to one or more central problems in the philosophy of science, or in the philosophy of one of the particular sciences, such as the nature of confirmation and explanation, the nature of scientific knowledge, reductionism, the unity of science, or realism and antirealism.

An introduction to central topics in metaphysics with emphasis on classic texts or contemporary authors. An introduction to central topics in epistemology with emphasis on classic texts or contemporary authors. An introduction to central topics in philosophy of mind with emphasis on classic texts or contemporary authors.

Prerequisites: graduate standing or consent of instructor. An introduction to central topics in philosophy of language with emphasis on classic texts or contemporary authors. Prerequisites: graduate status or consent of instructor. Study and discussion of classic themes and texts in history of science, sociology of science, and philosophy of science, and of work that attempts to develop an interdisciplinary science studies approach.

Required of all students in the Science Studies Program. Study and discussion of a selected topic in the science studies field with an emphasis on the development of research and writing skills. The topic varies from year to year.

A forum for the presentation and discussion of research in progress in science studies by graduate students, faculty, and visitors. Students must attend the colloquium series for their entire first and second years. May be taken for credit two times with changed content. Continuing the introduction developed in Part I, this course examines recent key topics and problem situations in science studies.

Emphasis is on recent theoretical perspectives and empirical studies in communication, history, philosophy, and sociology of science and technology, and the interplay between them. A study of selected texts or topics from the history of Greek philosophy. Usually centers on works by Plato or Aristotle. May be taken for credit six times with changed content.

A study of selected texts or topics from philosophers of the sixteenth and seventeenth centuries: Descartes, Spinoza, Leibniz, or Locke. A study of selected texts or topics from philosophers of the eighteenth century: for example, Kant or Hume.

A study of the historical development of the analytical movement, with emphasis on major texts. Topics may include identity, personal identity, universals and particulars, modality and possible worlds, causation, reduction, supervenience, freedom and determinism, space and time, and realism versus antirealism. This seminar will cover issues such as rival accounts of knowledge, justification, and warrant, traditional and contemporary perspectives on empiricism, rationalism, and pragmatism, and skepticism.

Contemporary debates on the nature, function, and operation of the mental. May include questions about the mind-body relation, mental causation, perception, consciousness, and mental representation. This seminar will cover current books and theoretical issues in the philosophy of science. May be taken for credit seven times with changed content. Contemporary debates about the study of the mind-brain as studied in one or more of the empirical cognitive sciences.

May include questions about the different strategies of explanation invoked, the conceptions of representation employed, the connections between theoretical models developed. Topics may include metaethics e. The approach may be systematic, historical, or both. Topics may include the nature and limits of state authority, liberty and equality, distributive justice, liberalism and its critics e.

The focus may be on classic texts or contemporary authors. This course is designed for students to gain feedback from students and faculty on works in progress on the topics of agency and responsibility. The course is suitable for those specializing in moral psychology, ethics, agency and responsibility, and for those with special interests in the topics.

May be taken for credit up to nine times for a maximum of nine units. This course meets regularly to discuss primary or secondary literature in the area of German philosophy including Kant, Fichte, Hegel, etc. The reading is designed both for students doing active research in the field and for those seeking to gain some familiarity with it.

Nongraduate students may enroll with consent of instructor. This course meets weekly to provide training in reading and translating philosophical German. Students prepare in advance written translations of assigned passages. The course helps train graduate students preparing to take the Departmental German Exam.

Can be taken nine times for credit with changed content. This course meets biweekly with students reading and presenting material from the phenomenological literature. The course is designed both for students doing active research in phenomenology and for those seeking to gain some familiarity with that tradition.

Investigation of central issues in contemporary philosophy. Content varies but typically will center on a recent and important philosophical book. This course meets weekly to discuss recent books or articles in philosophy of science. This course meets to discuss work in progress in the history of philosophy.

Weekly or biweekly meetings to discuss recent literature in ethics, broadly construed so as to include ethical theory, normative ethics, jurisprudence, and historical traditions in these fields. The course is suitable for those specializing in ethics and for those seeking some familiarity with the field. A research group for graduate students engaged in philosophy or history of the biological sciences.

The group discusses biological, historical, and philosophical articles and books and ongoing research projects. Can be taken nine times for credit with change of content. Focused examination of specific problems or themes in some area of philosophy. A research group for graduate students engaged in philosophy or history of the physical sciences.

The group discusses physical, historical, and philosophical articles and books and ongoing research projects. This group provides training in reading and translating philosophical Greek by having students prepare translations of passages and lead discussions. The group helps train graduate students preparing for Departmental Greek Exam. This group provides training in reading and translating philosophical Latin by having students prepare translations of passages and lead discussions.

The group helps train graduate students preparing for departmental Latin exam. Supervised study of individually selected philosophical topics. Units will vary according to enrollment in course. To be taken in fall quarter of third year of philosophy graduate study. Advanced individual research studies under the direction of a member of the staff.

Hours of outside preparation will vary with number of units taken. A course designed to satisfy the requirement that graduate students should serve as teaching assistants, either in the Department of Philosophy or in one of the writing programs offered by the various colleges.

Each PhD candidate must teach the equivalent of quarter time for three academic quarters. Students are permitted to sign up as TAs for a maximum of eighteen quarters. Toggle navigation. HOME courses Philosophy. Philosophy [ undergraduate program graduate program faculty ] All courses, faculty listings, and curricular and degree requirements described herein are subject to change or deletion without notice.

Courses For course descriptions not found in the UC San Diego General Catalog —22 , please contact the department for more information. Introduction to Philosophy 4 A general introduction to some of the fundamental questions, texts, and methods of philosophy. PHIL Introduction to Logic 4 Basic concepts and techniques in both informal and formal logic and reasoning, including a discussion of argument, inference, proof, and common fallacies, and an introduction to the syntax, semantics, and proof method in sentential propositional logic.

Scientific Reasoning 4 Strategies of scientific inquiry: how elementary logic, statistical inference, and experimental design are integrated to evaluate hypotheses in the natural and social sciences. Introduction to Philosophy: The Nature of Reality 4 A survey of central issues and figures in the Western metaphysical tradition. Introduction to Philosophy: Knowledge and Its Limits 4 A study of the grounds and scope of human knowledge, both commonsense and scientific, as portrayed in the competing traditions of Continental rationalism, British empiricism, and contemporary cognitive science.

Science Fiction and Philosophy 4 An introduction to philosophy which uses science fiction to make abstract philosophical problems vivid. Science and Pseudoscience 4 The differences among good science, bad science, and pseudoscience. Science, Philosophy, and the Big Questions 4 An inquiry into fundamental questions at the intersection of science and philosophy. Science, Society, and Values 4 An exploration of the interaction between scientific theory and practice on the one hand, and society and values on the other.

Ethics and Society 4 An examination of ethical principles e. Ethics and Society II 4 An examination of a single set of major contemporary social, political, or economic issues e. Philosophy and the Rise of Modern Science 4 Beginning with the contrast between medieval and early modern thought, the course focuses on the relation of seventeenth-century philosophy and the emergence of modern natural science.

Philosophy between Reason and Despair 4 Introduction to nineteenth-century philosophy, focusing on skepticism about the authority of reason to answer questions about the ultimate meaning and value of human life. Philosophy in the Americas 4 An exploration of central philosophical issues as they have been taken up in the diverse philosophical traditions of the Americas, such as indigenous philosophy, Latin American philosophy, American Pragmatism, and the Civil Rights movement, among others.

Law and Society 4 A survey of philosophical issues concerning law and society, such as the rule of law, the moral limits of the law, individual rights, judicial review in a constitutional democracy, the justification of punishment, and responsibility. First-year Student Seminar 1 The First-year Student Seminar Program is designed to provide new students with the opportunity to explore an intellectual topic with a faculty member in a small seminar setting.

Basic Problem in Philosophy 4 An investigation of a selected philosophical topic through readings, discussions, and written assignments. Hellenistic Philosophy 4 A study of selected texts from the main schools of Hellenistic philosophy—Stoicism, Epicureanism, and Skepticism. History of Analytic Philosophy 4 Central texts, figures, and traditions in analytic philosophy. History of Philosophy: Ancient 4 An examination of ancient Greek philosophy, focusing on major works of Plato and Aristotle.

History of Philosophy: Early Modern 4 An examination of seventeenth- and eighteenth-century philosophy, focusing on major works of Descartes, Locke, and Hume. History of Philosophy: Late Modern 4 An examination of late eighteenth and nineteenth-century philosophy, focusing on major works of Kant and Hegel.

Philosophical Methods Seminar 4 This course provides an introduction to the techniques of philosophical inquiry through detailed study of selected philosophical texts and through extensive training in philosophical writing based on those texts. Symbolic Logic I 4 The syntax, semantics, and proof-theory of first order monadic and polyadic predicate logic. Advanced Topics in Logic 4 Topics vary from year to year. Philosophy of Logic 4 Philosophical issues underlying standard and nonstandard logics, the nature of logical knowledge, the relation between logic and mathematics, the revisability of logic, truth and logic, ontological commitment and ontological relativity, logical consequence, etc.

Probability and Decision Theory 4 A survey of theories of rational inference and rational choice, covering topics in probability and decision theory, formal epistemology, and statistics. Metaphysics 4 Central problems in metaphysics, such as free will and determinism, the mind-body problem, personal identity, causation, primary and secondary qualities, the nature of universals, necessity, and identity.

Topics in Metaphysics 4 An in-depth study of some central problem, figure, or tradition in metaphysics. Epistemology 4 Central problems in epistemology such as skepticism; a priori knowledge; knowledge of other minds; self-knowledge; the problem of induction; foundationalist, coherence, and causal theories of knowledge. Philosophy of Language 4 Examination of contemporary debates about meaning, reference, truth, and thought. Philosophy of Mind 4 Different conceptions of the nature of mind and its relation to the physical world.

Moral Psychology 4 The nature of action and psychological explanation. Responsibility 4 A study of the nature and significance of responsibility. Global Justice 4 Social justice issues as they arise across the borders of nation-states. Free Will 4 Investigation into the nature of free will, including arguments for and against its compatibility with a scientific picture of the world and competing accounts of the metaphysics of free will.

The Meaning of Life 4 This course considers whether human life has meaning, and, if so, what meaning it has and under what conditions such meaning may be secured. Philosophy of Emotion 4 The nature, function, and value of emotion. Philosophy of Perception 4 The nature and function of perception. Philosophy of Science 4 Central problems in philosophy of science, such as the nature of confirmation and explanation, the nature of scientific revolutions and progress, the unity of science, and realism and antirealism.

Philosophy of Biology 4 Philosophical problems in the biological sciences, such as the relation between biology and the physical sciences, the status and structure of evolutionary theory, and the role of biology in the social sciences. Philosophy and the Environment 4 Investigation of ethical and epistemological questions concerning our relationship to the environment. Philosophy of Psychology 4 Philosophical issues raised by psychology, including the nature of psychological explanation, the role of nature versus nurture, free will and determinism, and the unity of the person.

Philosophy of the Cognitive Sciences 4 Theoretical, empirical, methodological, and philosophical issues at work in the cognitive sciences e. Philosophy of Neuroscience 4 An introduction to elementary neuroanatomy and neurophysiology and an examination of theoretical issues in cognitive neuroscience and their implications for traditional philosophical conceptions of the relation between mind and body, perception, consciousness, understanding, emotion, and the self.

Philosophy of Social Science 4 Philosophical issues of method and substance in the social sciences, such as causal and interpretive models of explanation, structuralism and methodological individualism, value neutrality, and relativism. Any students violating these rules or committing any other acts of academic dishonesty WILL be turned over to the disciplinary committee for disciplinary action. Design a combinational circuit that multiplies two binary numbers A and B.

A is a 4 bit, and B is a 3-bit binary numbers. Use half-adders, full-adders and AND gates. Digital Systems and Binary Numbers. Quiz on Digital Systems and Binary Numbers. Boolean Algebra and Logic Gates. Gate level Minimization. Combinational Logic. Synchronous Sequential Logic. Topic outline General.

Attendance URL. The goal of this course is to; 1. This course makes significant contributions to the following program outcomes: 1. Announcements Forum. Homework I Assignment. Lecture Notes ppt File. QUIZ 1. Quiz 2.

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There are lots of ways to put a roof over your head. Typically, those are simply represented by complementing the appropriate representation:. Combinational logic is great, but without adding sequential circuitry, modern computing would not be possible. Sequential circuitry is what adds memory to our logical systems. As mentioned earlier, combinational logic produces results after a delay. That delay varies according to lots and lots of things: the manufacturing process of the parts involved, the temperature of the silicon, the complexity of the circuit.

If the output of a circuit is dependant upon results from two other combinational circuits and the results arrive at different times which they will, in the real world , a combinational circuit will "glitch" briefly, outputting a result which may not be consistent with the desired operation. A sequential circuit, however, only samples and propagates the output at specific times.

If the input changes between those times, it is ignored. The sampling time is usually synchronized across the entire circuit and is referred to as the "clock". When a computer's "speed" is cited, this is the value in question. It is possible to design "asynchronous" sequential circuits, which do not rely on a synchronized global clock. However, those systems pose great difficulties, and we won't be discussing them here.

As a side note, any section of digital logic will have two characteristic delay values: the minimum delay time and the maximum delay time. If the circuit fails the minimum delay time i. If that circuit is part of a larger device, like a computer CPU, the entire device is garbage and cannot be used. If the maximum delay time fails i. Maximum delay times tend to go up as the silicon forming a circuit warms up, which is why computers become unstable when they overheat or as the clock speed is increased as is the case with overclocking.

As is the case with combinational logic, there are several basic circuit elements which form the building blocks of sequential circuits. These blocks are built up from the basic combinational elements, using feedback from the output to stabilize the input. They come in two "flavors": latches and flip-flops. While the terms are frequently used interchangeably, latches are generally less useful, as they are not clocked; we'll focus on flip-flops.

The simplest type of flip-flop is the D-type. D flip-flops are simple -- upon a clock edge normally rising, although they can be found with a built-in inverter to clock in on the falling edge instead , the input is latched to the output. Usually, the clock input is denoted by the small triangle impinging on the symbol. Most flip-flops provide two outputs: the "normal" output, and the complemented output.

Only slightly more complex is the T-type. The 'T' stands for "toggle. If the input is a 0, the output remains the same. As with the D-type, the complement of the output is usually provided. A useful function of the T flip-flop is as a clock division circuit. If T is held high, the output will be the clock frequency divided by two. A chain of T flip-flops can thus be used to produce slower clocks from a device's master clock.

Finally, we have the JK-type. The JK-type is the only one of the three which truly requires a truth table to explain; it has two inputs J and K , and the output can be left the same, set, cleared, or toggled, depending on the combination of input signals present. Of course, as with all flip-flops, the input at the moment of the clock is the only thing that matters. All sequential circuits have what are called " setup " and " hold " times, as well as a propagation delay.

Understanding these three things is critical to designing sequential circuits that work as expected. The setup time is the minimum amount of time before a rising clock edge occurs that a signal must arrive at the input of a flip-flop in order for the flip-flop to latch the data correctly. Likewise, the hold time is the minimum time a signal must remain stable after the rising clock edge occurs before it can be allowed to change.

While setup and hold times are given as minimum values, the propagation delay is given as a maximum. Simply put, the propagation delay is the greatest amount of time after a falling edge at the clock before you can expect to see the signal on the outputs. Here's a graphic explaining them:. Note that in the above image, transitions are drawn as being slightly angled. This serves two purposes: it reminds us that clock and data edges are never truly right angles and will always have some non-zero rise or fall time, and it makes it easier to see where the vertical lines marking the various times intersect with the signals.

The combination of these three values determines the highest clock speed a device may use. If the propagation delay of one part plus the setup time of the next part in the circuit exceeds the time between the falling edge of one clock pulse and the rising edge of the next, the data will not be stable on the input of the second component, causing it to behave in an unexpected manner. Failing to adhere to setup and hold times can lead to a problem called "metastability".

When a circuit is in a metastable state, the output of a flip-flop can oscillate rapidly between the two normal states -- often at a rate far above the clock rate of the circuit. Metastability problems can range from spurious operation up to damage of the chip, since they can increase current consumption.

While metastability usually resolves on its own, by the time it does so, the system may be in a totally unknown state and need to be completely reset to restore proper operation. A common way in which metastability issues arise is when a signal crosses clock domains -- in other words, when a signal passes between devices which are being clocked by different sources.

Since the clocks are not synchronized and even if the clocks are at the same nominal frequency, reality dictates that they will be slightly different , eventually a clock edge and a data edge are bound to be too close for comfort, resulting in a setup time violation. A simple fix for this issue is to run all inputs into a system through a pair of cascaded D flip-flops. Even if the first flip-flop goes into metastability, it will hopefully have settled down to a steady state before the next clock pulse, allowing the second flip-flop to read the correct data.

This results in a one-cycle delay in incoming data edges, which is almost always insignificant compared to the risk of metastability. All of this can be applied in the programming world, as well. Most programs are simply decision trees: "if this is true, then do this". To explain this, we'll use C-code in an Arduino context.

When we talk about "bitwise" logic, what we really mean is logical operations which return a value. Take, for example, this piece of code:. We can do a bitwise operation using 'a' and 'b' and putting the result into 'c'. Here's what that looks like:. In other words, the each bit in the result is equal to the operation applied to the two corresponding bits in the operands:. Okay, that's great, but what of it?

It turns out we can do some pretty useful things by using bitwise operators to manipulate registers: we can selectively clear, set, or toggle single bits, check to see if a bit is set or clear, or if several bits are set or clear. Here are some examples using these operations:. Another useful bitwise operation that can be performed on a piece of data is a bit shift. This is simply a slide of the data left or right by a certain number of places; data which is shifted out disappears and is replaced by a 0 being shifted in from the other end.

We'll demonstrate some uses of bit shifting later. One very useful application for bit shifts is multiplication and division: each right shift is the same as a division by two although remainder information is lost and each left shift is the same as a multiplication by two. This is useful because multiply and divide are often very time expensive operations on small processors, like the Arduino's, but bit shifts are usually very efficient.

It is generally quite important that the values compared be of the same data type; unexpected things can happen if you compare a "byte" and an "int", for example. They're more like what we tend to think of as conjunctions: "If it's not raining, and it's windy, go fly a kite". Translated into C, that sentence might look like this:. Note the parentheses around the two subclauses.

Though not strictly necessary, it's good practice to keep your code as readable as possible by grouping subclauses together. We could just as easily have had a numeric value in one of the subclauses:. This clause will send me out to fly a kite, so long as it's not raining, but only if there's some wind or I'm not busy I will try and fly with no wind. Again, note the parentheses. Now that we can create complex logical statements, let's look at the things we can do with the answers to those questions.

With those three statements, I'll never fly a kite if I'm really busy, and if I'm not really busy, and it's not a good day for it, I'll just keep working. Let's change the else if to if , like so:. Now, if we've got a nice kite flying day on our hands, even if I'm really busy, I'll only work harder for a very, very short period--basically, right up until I notice that it's nice out.

Furthermore, if it's not a nice day, my work harder status will be downgraded to just plain old work immediately after I start working harder! In the first case, the LED may be on for some time, or off for some time. In the second case, however, regardless of the state of the "reallyBusy" flag, the LED will turn off almost instantly after the first if statement turned it on, and you'd find yourself sitting around wondering why the "reallyBusy" light never turns on!

The switch statement only allows us to check equivalence, but since that's a fairly common thing to want to do, it comes in pretty handy. There are two really important things to notice about this: the "break;" statements and the "default:" case.

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If the circuit fails the minimum delay time i. If that circuit is part of a larger device, like a computer CPU, the entire device is garbage and cannot be used. If the maximum delay time fails i. Maximum delay times tend to go up as the silicon forming a circuit warms up, which is why computers become unstable when they overheat or as the clock speed is increased as is the case with overclocking.

As is the case with combinational logic, there are several basic circuit elements which form the building blocks of sequential circuits. These blocks are built up from the basic combinational elements, using feedback from the output to stabilize the input. They come in two "flavors": latches and flip-flops. While the terms are frequently used interchangeably, latches are generally less useful, as they are not clocked; we'll focus on flip-flops.

The simplest type of flip-flop is the D-type. D flip-flops are simple -- upon a clock edge normally rising, although they can be found with a built-in inverter to clock in on the falling edge instead , the input is latched to the output. Usually, the clock input is denoted by the small triangle impinging on the symbol.

Most flip-flops provide two outputs: the "normal" output, and the complemented output. Only slightly more complex is the T-type. The 'T' stands for "toggle. If the input is a 0, the output remains the same. As with the D-type, the complement of the output is usually provided. A useful function of the T flip-flop is as a clock division circuit.

If T is held high, the output will be the clock frequency divided by two. A chain of T flip-flops can thus be used to produce slower clocks from a device's master clock. Finally, we have the JK-type. The JK-type is the only one of the three which truly requires a truth table to explain; it has two inputs J and K , and the output can be left the same, set, cleared, or toggled, depending on the combination of input signals present.

Of course, as with all flip-flops, the input at the moment of the clock is the only thing that matters. All sequential circuits have what are called " setup " and " hold " times, as well as a propagation delay. Understanding these three things is critical to designing sequential circuits that work as expected. The setup time is the minimum amount of time before a rising clock edge occurs that a signal must arrive at the input of a flip-flop in order for the flip-flop to latch the data correctly.

Likewise, the hold time is the minimum time a signal must remain stable after the rising clock edge occurs before it can be allowed to change. While setup and hold times are given as minimum values, the propagation delay is given as a maximum. Simply put, the propagation delay is the greatest amount of time after a falling edge at the clock before you can expect to see the signal on the outputs.

Here's a graphic explaining them:. Note that in the above image, transitions are drawn as being slightly angled. This serves two purposes: it reminds us that clock and data edges are never truly right angles and will always have some non-zero rise or fall time, and it makes it easier to see where the vertical lines marking the various times intersect with the signals. The combination of these three values determines the highest clock speed a device may use. If the propagation delay of one part plus the setup time of the next part in the circuit exceeds the time between the falling edge of one clock pulse and the rising edge of the next, the data will not be stable on the input of the second component, causing it to behave in an unexpected manner.

Failing to adhere to setup and hold times can lead to a problem called "metastability". When a circuit is in a metastable state, the output of a flip-flop can oscillate rapidly between the two normal states -- often at a rate far above the clock rate of the circuit. Metastability problems can range from spurious operation up to damage of the chip, since they can increase current consumption.

While metastability usually resolves on its own, by the time it does so, the system may be in a totally unknown state and need to be completely reset to restore proper operation. A common way in which metastability issues arise is when a signal crosses clock domains -- in other words, when a signal passes between devices which are being clocked by different sources. Since the clocks are not synchronized and even if the clocks are at the same nominal frequency, reality dictates that they will be slightly different , eventually a clock edge and a data edge are bound to be too close for comfort, resulting in a setup time violation.

A simple fix for this issue is to run all inputs into a system through a pair of cascaded D flip-flops. Even if the first flip-flop goes into metastability, it will hopefully have settled down to a steady state before the next clock pulse, allowing the second flip-flop to read the correct data.

This results in a one-cycle delay in incoming data edges, which is almost always insignificant compared to the risk of metastability. All of this can be applied in the programming world, as well. Most programs are simply decision trees: "if this is true, then do this". To explain this, we'll use C-code in an Arduino context. When we talk about "bitwise" logic, what we really mean is logical operations which return a value.

Take, for example, this piece of code:. We can do a bitwise operation using 'a' and 'b' and putting the result into 'c'. Here's what that looks like:. In other words, the each bit in the result is equal to the operation applied to the two corresponding bits in the operands:. Okay, that's great, but what of it? It turns out we can do some pretty useful things by using bitwise operators to manipulate registers: we can selectively clear, set, or toggle single bits, check to see if a bit is set or clear, or if several bits are set or clear.

Here are some examples using these operations:. Another useful bitwise operation that can be performed on a piece of data is a bit shift. This is simply a slide of the data left or right by a certain number of places; data which is shifted out disappears and is replaced by a 0 being shifted in from the other end. We'll demonstrate some uses of bit shifting later. One very useful application for bit shifts is multiplication and division: each right shift is the same as a division by two although remainder information is lost and each left shift is the same as a multiplication by two.

This is useful because multiply and divide are often very time expensive operations on small processors, like the Arduino's, but bit shifts are usually very efficient. It is generally quite important that the values compared be of the same data type; unexpected things can happen if you compare a "byte" and an "int", for example.

They're more like what we tend to think of as conjunctions: "If it's not raining, and it's windy, go fly a kite". Translated into C, that sentence might look like this:. Note the parentheses around the two subclauses. Though not strictly necessary, it's good practice to keep your code as readable as possible by grouping subclauses together. We could just as easily have had a numeric value in one of the subclauses:. This clause will send me out to fly a kite, so long as it's not raining, but only if there's some wind or I'm not busy I will try and fly with no wind.

Again, note the parentheses. Now that we can create complex logical statements, let's look at the things we can do with the answers to those questions. With those three statements, I'll never fly a kite if I'm really busy, and if I'm not really busy, and it's not a good day for it, I'll just keep working.

Let's change the else if to if , like so:. Now, if we've got a nice kite flying day on our hands, even if I'm really busy, I'll only work harder for a very, very short period--basically, right up until I notice that it's nice out. Furthermore, if it's not a nice day, my work harder status will be downgraded to just plain old work immediately after I start working harder!

In the first case, the LED may be on for some time, or off for some time. In the second case, however, regardless of the state of the "reallyBusy" flag, the LED will turn off almost instantly after the first if statement turned it on, and you'd find yourself sitting around wondering why the "reallyBusy" light never turns on!

The switch statement only allows us to check equivalence, but since that's a fairly common thing to want to do, it comes in pretty handy. There are two really important things to notice about this: the "break;" statements and the "default:" case. It's not strictly necessary; if there's no default case, than nothing happens if all the matches fail. Of course, you usually want something to happen, and it's best not to assume that it's impossible for all matches to fail.

It can be used inside of any type of conditional more on that later , and in this case, a failure to include a break at the end of each case will result in code after the case being executed, even if subsequent case matches fail. So far, we've looked at code for making a decision once. What if you want to repeat an action, over and over, as long as a condition holds? That's where while and do When your code reaches a while statement, the program evaluates the conditional "Is it windy?

Once code execution is complete, the conditional will be evaluated once more. If the conditional is still "TRUE", the code will execute again. This repeats over and over, until the conditional evaluates to "FALSE" or a break statement is encountered. You can nest an if statement or a switch , or another while , or in fact anything you want inside your while loop:. So, with that loop, I'll fly my kite until the wind gives out or my boss gets mad at me.

In this case, the code inside the brackets runs once, even if the conditional is false. In fact, for many application areas, even small programmable logic devices PLDs , the mainstays of the s and early s, are rapidly disappearing. The burgeoning market for smaller, lower power, and more portable devices has driven high levels of integration into almost every product. This also has changed the nature of optimization; the focus is now on what goes into each chip rather than on the collection of individual gates needed to realize the design.

The optimizations of today are more and more often made at the architecture level rather than in the switches. Hardware designers now spend the majority of their time dealing with software. Specifically, the tools needed to efficiently map digital designs onto the emerging programmable devices that are growing ever more sophisticated. They capture their design specifications in software with description languages appropriate for describing the parallelism of hardware; they use software tools to simulate their designs and then to synthesize it into the implementation technology of choice.

Design time is reduced radically as market pressures require products to be introduced quickly, at the right price and performance. In fact, the contemporary digital designer must have a broader un derstanding of the discipline of computation than ever before, including both hardware and software.

In this second edition, we provide this broader perspective. See the Prentice-Hall site for the book. Katz and Gaetano Borriello Check regurlarly for new information.