Digital Logic Circuit PDF

Digital Logic Circuit Basic Concept Mak(Prof. KIM) A303 010 6201 2453 [email protected] 1 I thought about giving you more effective lectures yesterday evening, and I came up with an efficient plan, and I actu...

Digital Logic Circuit Basic Concept Mak(Prof. KIM) A303 010 6201 2453 [email protected] 1 I thought about giving you more effective lectures yesterday evening, and I came up with an efficient plan, and I actually confirmed that it's possible. Hahaha. It's a powerpoint read function, and I'll actually check it out. Now you can listen to the lecture comfortably with the native English pronunciation. I will try harder to make notes and communicate with you, just to make additional explanations. 2 Before we start, I would like to make a suggestion. To improve language communication for learning, I want you to use Korean when you ask questions and English when I answer. If you are still uncomfortable using Korean, it would be a good idea to use a translator. Of course, I will use a translator if I decide that I can't explain enough in English. Through this, you can learn more sophisticated Korean, and I think it can help me solve my problems that I haven't used English for a long time. As I organized and prepared my lecture notes over the weekend, I thought about whether there would be a more effective lesson plan. Of course, I'm not necessarily asking you to ask questions in Korean. Also, if there is a problem with my English, I want you to correct it. Thank you! 3 History of “Logic” Aristotle (384-322 BC) : ancient Greek philosopher, the beginning of logic is considered to be Aristotle - Aristotle's Logic is well organized in his book Organon. The book consists of six books, and each one deals with various aspects of Logic. - He studied the structure and principles of correct reasoning through logic, especially by developing a syllogism, which laid out the basic framework for logical reasoning. - Syllogism : logical structure that draws conclusions from two premises 1. Major Premise: The Himalayas contain some of the highest peaks in the world. 2. Minor Premise: Mount Everest is located in Nepal. 3. Conclusion: Therefore, Nepal contains one of the highest peaks in the world. 4 History of “Logic” René Descartes (1596-1650) : French philosopher, mathematician, scientist, father of modern philosophy, founder of analytical geometry - Descartes' philosophy contributed to laying the foundation for propositional logic and set theory. His proposition "I think, therefore it exists" is a prime example of philosophical argumentation, suggesting a logical analysis of the truth and falsehood of propositions. - A proposition means a sentence that can clearly judge true or false. For example, a 'smart student' cannot be called a proposition because the standard of smartness may vary from person to person. 5 History of “Logic” These propositions are fundamental to the dichotomy of judging only true and false, and these ideas can be applied in two states: 1 and 0 of the binary digital systems we use today. The concepts used for operations in set theory, such as conjunction, intersection, and complement, can be identified with OR, AND, NOT, the basic concepts we use for circuit design today. Proposition and set theory have directly affected the circuit design for the binary digital systems we currently use. For this reason, the circuits that make up hardware today are called logic circuits. 6 History of “Logic” Blaise Pascal (1623-1662) : French, philosopher, inventor - Pascal's logic is different from Descartes’. Pascal's proposition valued the experience and knowledge of the judge when judging a fact by dichotomy. - Pascal left the famous saying, "Human beings think reeds." This idea means that even under the same circumstances and conditions, the consequences of truth and falsehood may vary, and has had a great influence on the humanities. - However, Pascal makes an important achievement in the history of the development of calculators. 7 History of “Logic” - Pascal invented Pascaline, the world's first mechanical calculator, in 1642. This calculator could mainly perform addition and subtraction, as well as multiplication and division through repeated processes. At the time, calculations had to be done manually, so it took a lot of time and the likelihood of errors was high. Pascaline was designed to solve these problems. Pascal invented this calculator for his father, who was helping with tax collection, and he was only 19 years old, so he seems to be a good son and a genius. - Pascal built a mechanical calculator, but it did not affect today's digital logic circuits. However, it seems that it was enough to attract social attention to the calculator. 8 History of “Logic” Let's easily compare Pascal's logic with Descartes' logic. Pascal logic is not applicable to propositions in mathematics. To put it simply, let's say you went on a blind date with the opposite sex today. Suppose your partner is good-looking but not smart. If you value appearance, you will make a positive decision (1), but if you value smartness, you will make a negative decision (0). Descartes' logic does not allow different judgments on the same situation. No matter who judges it, only situations that are always 1 or 0 are put in the category of logic. This Descartes logic influenced set theory and proposition in mathematics, and it became the mathematical background for the binary digital system design that we use today. 9  Basic Concept Digital System Concerned with the interconnection among digital components and modules Best Digital System example is General Purpose Computer Logic Circuit Design Deals with the basic concepts and tools used to design digital hardware consisting of logic circuits Circuits to perform arithmetic operations (+, -, x, ÷) 10  Digital Signal : Decimal values are difficult to represent in elect rical systems. It is easier to use two voltage values than ten. Digital Signals have two basic states: 1 (logic “high”, or H, or “on”) 0 (logic “low”, or L, or “off”) Digital values are in a binary format. Binary means 2 states. A good example of binary is a light (only on or off) on off Power switches have labels “1” for on and “0” for off. 11  Today's lecture table of contents History of Digital System Analog and Digital Signal Need of Digital Signal Binary Digital Signal Representation of digital information 12  History of Digital System George Boole(1815~1864) He made a great achievement in the field of semiotic logic by creating the algebra of logic. The representative paper is as follows. Mathematical Analysis of Logic (1847) An Investigation of Laws of Thoughts; Mathematical Theories of Logic and Probabilities (1854) Claude Shannon(1916~2001) Inventing a way to implement Boolean logic as an electrical circuit. The representative paper is as follows. “A Symbolic Analysis of Relay and Switching Circuits” Boolean Logic and Boolean Algebra were Applied to Digital Circuitry 13  History of Digital System -- Beginning of the Digital Computer Age -- In World War II, the digital(computer) age began due to the need for cryptographic decryption, etc. Alan Turing(1912~1954) Alan Turing was an English mathematician, cryptographer, logician, computer scientist, and a pioneer in computer science. He made a significant contribution to the development of computer science by formalizing algorithms and computational concepts through an abstract model called the Turing machine. He is also famous for the design of the Turing test. The annual Turing Award, which is given to people who have made important achievements in computer science at ACM (Association for Computing Machinery), is named in his honor. He is also called the "father of computer science" for his profound contributions to theoretical computer science and artificial intelligence. 14 2014 movie released A movie starring Alan Turing Running Time 02:06min “The Imitation Game” is a historical drama film that tells the story of Alan Turing 15 Imitation Game(06:19) 16  Analog and Digital Signal Signal is a function, that represents the variation of a physical quantity with respect to any parameter. Analog Signal : A continuous-time signal that represents some other quantity, such as voltage, sound, light, temperature, position, or pressure. 17  Analog and Digital Signal Digital Signal : A signal that represents data as a sequence of discrete values, where each value can only take on one of a finite number of values. This contrasts with an analog signal, which represents continuous. 18  Analog and Digital Signal Professor Mak's tip - Most people misunderstand digital signals as signals that are represented only by 0 and 1. - Digital signals only mean discrete signals, and that's the misunderstanding because most digital systems today are designed as binary systems. - If a digital system was designed as a decimal system, there would be 10 kinds of digital signals, from 0 to 9. - So, why is a digital system designed as a binary system? - Using a binary system, you can take advantage of many advantages, such as being simple to design and easy to implement in semiconductors. 19  Need of Digital Signal All real life signals are analog. Digital signals are used to represent data as a series of discrete values. Unlike continuous analog signals, discrete values can be converted into digital signals for storage, process and transmission. This is because, unlike analog signals, digital signals have the advantage of being resistant to noise, being able to detect and correct errors, and being easy to compress and process data. 20  Need of Digital Signal ADC(Analog-to-Digital Converter) 21  Need of Digital Signal PCM(Pulse-code modulation) is a method used to digitally represent sampled analog signals.(Sampling -> Quantizing -> Encoding) 1. Sampling is the process of converting a continuous-time signal into a discrete- time signal by taking samples of the continuous-time signal at regular intervals. The sampling rate is the number of samples per second and is usually expressed in Hertz (Hz). The Nyquist-Shannon sampling theorem states that the sampling rate must be at least twice the highest frequency component of the signal being sampled. (For human voice, 8000 samples are required in 1 second. 2X4KHz=8KHz) 22  Tip Frequency : Number of times the periodic waveform oscillated in one second. Period : Time taken for a periodic waveform to repeat once. 1 1 T= f = f T 23  Need of Digital Signal 2. Quantizing : After sampling, each sample is quantized to the nearest value within a range of digital steps. In this process, inevitable quantization noise occurs, and quantization noise can be reduced by increasing the number of predetermined bit depth, but there is a disadvantage in that the amount of data increases. 3. Encoding : The number of digital steps is determined by the bit depth, which is the number of bits used to represent each sample. (Larger encoding bits allow more sophisticated representation of data, but more memory is used to represent the data.) 24 Need of Digital Signal 25  Need of Digital Signal DAC(Digital-to-Analog Converter) 26 Supplementary Video (6:38) 27  Binary Digital Signal An information variable represented by physical quantity. For digital systems, the variable takes on discrete values. Two level, or binary values are the most prevalent values. Binary values are represented abstractly by:V(t) Digits 0 and 1 Words (symbols) False (F) and True (T) Logic 1 Words (symbols) Low (L) and High (H) And words On and Off undefine Binary values are represented by values Logic 0 or ranges of values of physical quantities. t Binary digital signal 28  Binary Digital Signal For TTL(Transistor-Transistor Logic) : TTL is a semiconductor device. - In the case of output signals, from 0V to 0.4V is recognized as a logical value 0, from 2.7V to 5V is recognized as a logical value 1. - In the case of input signals, from 0V to 0.8V is recognized as a logical value 0, from 2V to 5V is recognized as a logical value 1. - Undefine range means non-usable. - The reason for the large range of signals is to prepare for noise. 전압 출력신호 입력신호 5V High High 2.7V 2.0V 0.8V 0.4V Low Low 0V 29  Representation of digital information bit(binary digit) : the smallest unit representing a binary digit (0 or 1) 1 nibble = 4 bit, A unit of data representation used when magnetic core memory was used before semiconductor memory was developed. 1 byte = 8 bit, (As semiconductors came out, they began to use the term byte.) 1 word = 4 byte, half word = 2 byte, double word = 8 byte Word is, (The length of a command or data handled by a particular CPU ; typically 4 bytes treated as 1 word) 바이트 니블 비트7 비트6 비트5 비트4 비트3 비트2 비트1 비트0 MSB LSB 30 Metric Prefix ex) ten to the power of six 106 byte = 1 M byte 31  AI Learning: ANI, AGI, ASI ANI(Artificial Narrow Intelligence) Artificial intelligence that can be used for special purposes. Examples include AlphaGo, a Go artificial intelligence, autonomous driving, and artificial intelligence used for medical purposes. AGI(Artificial General Intelligence) Artificial intelligence that can be used for a variety of purposes. ASI(Artificial Super Intelligence) Artificial intelligence that enables learning beyond human knowledge by setting goals on its own. 32 AI Learning: ANI, AGI, ASI (10:38) 33 Homework #1 1. What are the advantages of digital system over analog system? 2. Describe the units used to represent information. 3. Describe the metric prefix. 4. What is the frequency of the waveform as shown in the figure? 34 Homework #2 5. Describe the process of converting an analog signal into a digital signal through the PCM method. 6. How many data can be expressed in n bits? 35 Thank you! See you next time. Mak(Prof. KIM) A303 010 6201 2453 [email protected] 36