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Lecture 0: Course Introduction This lecture serves to introduce the topics of digital electronics and logic design and to explain in broad terms the nature of the digital approach and its advantages. Learning Outcomes: On completing this lecture, in addition to getting acquainted with general aspects of this course, you will be able to: Distinguish between and characterise digital and analogue signals and systems; Discuss the advantages of the digital approach; Describe the concept of design hierarchy. 0.1 Digital Signals and Systems Electronic systems, and in particular digital electronic systems, are becoming more pervasive in today’s world. Consider, for example, personal computers, telecommunications and the mobile phone, digital audio devices and television. Basically, an electronic system serves the purpose of transmitting/receiving, processing (ie carrying out a specified transformation), storing, or displaying information about the real world. Such information would be represented in the electronic domain in the form of a time-varying electrical quantity, usually voltage, termed a signal. For example, a microphone produces an electrical representation of speech information while a mobile phone is a good example of a system which carries out all the above listed functions. There are two categories of electronic systems, and, correspondingly, two categories of electrical signals: V(t) t V(nT) nT 2T 4T 6T 8T 10T 0-1 12T 14T Analogue An analogue signal is characterised by a real-valued electrical quantity varying continuously with time, t, within some electrical range imposed by practical considerations. Typically, the electrical quantity would be voltage and the range would be between +15V and -15V. When an analogue signal is sampled at regularly-spaced time instants and each sample is converted into a binary number representation, the resulting sequence of binary numbers is termed a digital signal. Digital The basic constituent of a digital signal is a two-valued electrical quantity which is allowed to change state at discrete moments in time. V(t) VH 1 0 0 1 0 1 1 0 VL t When voltage is used to carry the information, we usually denote the two voltage levels as VH and VL, standing for high voltage and low voltage. In terms of the binary representation, the following mapping is the norm: VH 1 VL 0 We might just note at this point that not all digital signals derive from sampled analogue signals; data and text information are inherently discrete and can be coded directly into binary. Similarly, the time dimension need not always be the independent variable; in a digitised image, for example, the dependent variable of picture intensity may be considered as a function of two-dimensional x-y space suitably discretised into what are known as picture elements or pixels. 0.2 Advantages of the Digital Approach Why is the world increasingly adopting digital technology? Clarity of Operation a digital system either functions correctly or not; there is no performance middle ground. With an analogue system, performance can be variable; eg, analogue television picture quality. Interference/Noise Resistance unwanted electrical interference degrades the quality of an electrical signal. Provided, however, the magnitude of the electrical noise is not excessive, a digital system can still distinguish between the V H and VL. Availability of Complex Building Blocks today’s integrated circuits, from which electronic systems are built, are complex systems in their own right, eg microprocessor or memory devices. Basically, one can build much more functional complexity into a digital system than into an analogue system of the same physical size. 0-2 Manufacturability today’s integrated circuit devices employ a circuit technology known as Complementary Metal Oxide Semiconductor (CMOS). Industry giants such as Intel have developed proven expertise at manufacturing these devices economically. Reliability these CMOS integrated circuit devices tend not to fail; the greatest probability of an electronic system failing lies in either the software or in the associated mechanical apparatus such as the hard-disc drive. Excellent Electrical Performance in terms of speed, power dissipation and the utilisation of silicon area, CMOS gives excellent performance. Programmability it is quite difficult if not impossible to build user programmability/flexibility into an analogue system; by their very nature, digital systems can be made software programmable. Availability of CAD Tools today’s digital electronic systems are very complex, comprising of up to perhaps 10 million transistors. Computer aided design (CAD) tools are necessary to manage the design complexity. Such tools are well developed, particularly for CMOS systems. Mobile Handset System Transmit/Receive Speech, Text, Image Modules Module Arithmetic, Logic, Memory Blocks Logic Block Gate AND/OR/Invert N- and P-channel MOS Transistor CMOS Technology Fabrication Technology 0.3 System Hierarchy Any complex digital system is best conceptualised as a hierarchy of design levels. Essentially this comes down to dividing the system up into progressively smaller and smaller blocks until we get right down to the basic functional unit, the transistor. The entire system may be regarded as being composed of modules, with each module in turn being composed of blocks of logic circuitry. Each logic circuit in its turn is configured from elementary logic gates which are formed from transistor circuits. Eventually, the transistor circuits have to be formed from the particular CMOS fabrication technology. The diagram below illustrates the design hierarchy with respect to the mobile phone handset. The overall design idea is that, for example, we don’t attempt to design directly with transistors a speech module for a mobile phone handset. We think of the speech module in terms of its constituent logic blocks and so on down through the hierarchy. Typically, each level will have its own CAD tool with a CAD framework tying everything together. This particular course is targeted at the middle levels of the hierarchy. The central focus is on basic digital signals and their logic processing with gate networks. Any treatment of 0-3 transistors or transistor circuits will simply be to explain particular aspects of logic circuit performance. Any treatment of logic modules will be to provide an application focus for our logic blocks. 0.4 History and Linkages As might be expected from the titles, there is a correspondence between the domain of two-valued logic circuits and the domain of formal logic as applied to statements (and systems of statements) that can be classed as being true or false. Formal logic was essentially established by the ancient Greek philosopher, Aristotle (384 – 322 BC), and remained relatively undeveloped until given a mathematical framework by the Englishman (and later professor of mathematics at what was then known as Queens College, Cork), George Boole (1815 – 1864), in his book An Investigation into the Laws of Thought, 1854 Boole’s work aroused a great deal of interest in the context of the developing field of telephony and telephone switching in the early 20th century but it wasn’t until the publication by Claude Shannon in 1938 of a paper titled Symbolic Analysis of Relay and Switching Circuits that digital or logic circuits really took off, leading soon to the first digital computers. The mathematical framework, provided by Boole and applied to switching circuits by Shannon, is what we formally study as Boolean algebra. 0.5 Conclusion This course aims at providing a sound foundation in digital electronics and, in particular, logic circuits. It is pitched midway between, on the one hand, the low level of circuit analysis and transistor fabrication and the high level of systems design and software. We also aim to develop some familiarity with the corresponding discipline of formal logic and to enhance the skill of applying logic coherence to the task of formulating convincing arguments. 0-4