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Digital System Design

by Siva VallepuSiva Vallepu
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Siva Vallepu
Siva Vallepu
Chapter 1 Digital electronics is the branch of electronics based on the combination and switching of voltages called logic levels. Any quantity in the outside world, such as temperature, pressure, or voltage, can be symbolized in a digital circuit by a group of logic voltages that, taken together, represent a binary number. Each logic level corresponds to a digit in the binary (base 2) number system. The binary digits, or bits, 0 and 1, are sufficient to write any number, given enough places. The hexadecimal (base 16) number system is also important in digital systems. Since every combination of four binary digits can be uniquely represented as a hexadecimal digit, this system is often used as a compact way of writing binary information. Inputs and outputs in digital circuits are not always static. Often they vary with time. Time-varying digital waveforms can have three forms: 1. Periodic waveforms, which repeat a pattern of logic 1s and 0s 2. Aperiodic waveforms, which do not repeat 3. Pulse waveforms, which produce a momentary variation from a constant logic level Digital Versus Analog Electronics: The study of electronics often is divided into two basic areas: analog and digital electronics. Analog electronics has a longer history and can be regarded as the “classical” branch of electronics. Digital electronics, although newer, has achieved greater prominence through the advent of the computer age. The modern revolution in microcomputer chips, as part of everything from personal computers to cars and coffee makers, is founded almost entirely on digital electronics. The main difference between analog and digital electronics can be stated simply. Analog voltages or currents are continuously variable between defined values, and digital voltages or currents can vary only by distinct, or discrete, steps. Some keywords highlight the differences between digital and analog electronics: Analog Digital Continuously variable Discrete steps Amplification Switching Voltages Numbers
An example often used to illustrate the difference between analog and digital devices is the comparison between a light dimmer and a light switch. A light dimmer is an analog device, since it can make the light it controls vary in brightness anywhere within a defined range of values. The light can be fully on, fully off, or at some brightness level in between. A light switch is a digital device, since it can turn the light on or off, but there is no value in between those two states. The light switch/light dimmer analogy, although easy to understand, does not show any particular advantage to the digital device. If anything, it makes the digital device seem limited. One modern application in which a digital device is clearly superior to an analog one is digital audio reproduction. Compact disc players have achieved their high level of popularity because of the accurate and noise-free way in which they reproduce recorded music. This high quality of sound is possible because the music is stored, not as a magnetic copy of the sound vibrations, as in analog tapes, but as a series of numbers that represent amplitude steps in the sound waves. Figure 1.1 shows a sound waveform and its representation in both analog and digital forms. The analog voltage, shown in Figure 1.1b, is a copy of the original waveform and introduces distortion both in the storage and playback processes. (Think of how a photocopy deteriorates in quality if you make a copy of a copy, then a copy of the new copy, and so on. It doesn’t take long before you can’t read the fine print.) A digital audio system doesn’t make a copy of the waveform, but rather stores a code (a series of amplitude numbers) that tells the compact disc player how to re-create the original sound every time a disc is played. During the recording process, the sound waveform is “sampled” at precise intervals. The recording transforms each sample into a digital number corresponding to the amplitude of the sound at that point. The “samples” (the voltages represented by the vertical bars) of the digitized audio waveform shown in Figure 1.1c are much more widely spaced than they would be in a real digital audio system. They are shown this way to give the general idea of a digitized waveform. In real digital audio systems, each amplitude value can be indicated by a number having as many as 16,000 to 65,000 possible values. Such a large number of possible values means the voltage difference between any two consecutive digital numbers is very small. The numbers can thus correspond extremely closely to the actual amplitude of the sound waveform. If the spacing between the samples is made small enough, the reproduced waveform is almost exactly the same as the original.
Signal amplitude Voltage Fig. 1.1 a) Original b) Analog representation Voltage c) Digital representation Digital Logic Levels Digitally represented quantities, such as the amplitude of an audio waveform, are usually represented by binary, or base 2, numbers. When we want to describe a digital quantity electronically, we need to have a system that uses voltages or currents to symbolize binary numbers. The binary number system has only two digits, 0 and 1. Each of these digits can be denoted by a different voltage called a logic level. For a system having two logic levels, the lower voltage (usually 0 volts) is called a logic LOW or logic 0 and represents the digit 0. The higher voltage (traditionally 5 V, but in some systems a specific value such as 1.8 V, 2.5 V or 3.3 V) is called a logic HIGH or logic 1, which symbolizes the digit 1. Except for some allowable tolerance, as shown in Figure 1.2, the range of voltages between HIGH and LOW logic levels is undefined. Fig. 1.2 Logic levels based on +5 V and 0 V
Positive and Negative Logic The binary variables can have either of the two states, i.e. the logic ‘0’ state or the logic ‘1’ state. These logic states in digital systems such as computers, for instance, are represented by two different voltage levels or two different current levels. If the more positive of the two voltage or current levels represents a logic ‘1’ and the less positive of the two levels represents a logic ‘0’, then the logic system is referred to as a positive logic system. If the more positive of the two voltage or current levels represents a logic ‘0’ and the less positive of the two levels represents a logic ‘1’, then the logic system is referred to as a negative logic system. If the two voltage levels are 0 V and +5 V, then in the positive logic system the 0 V represents logic ‘0’ and the +5 V represents logic ‘1’. In the negative logic system, 0 V represents logic ‘1’ and 5 V represents logic ‘0’. If the two voltage levels are 0 V and −5 V, then in the positive logic system the 0 V represents a logic ‘1’ and the −5 V represents a logic ‘0’. In the negative logic system, 0 V represents logic ‘0’ and −5 V represents logic ‘1’. Review of Number Systems The study of number systems is important from the viewpoint of understanding how data are represented before they can be processed by any digital system including a digital computer. Different characteristics that define a number system include the number of independent digits used in the number system, the place values of the different digits constituting the number and the maximum numbers that can be written with the given number of digits. The base or radix of a number system is defined as the maximum number of digits or symbols that can be used in any position. The radix of the decimal number system is 10 as it has 10 independent digits, i.e. 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. Similarly, the binary number system with only two independent digits, 0 and 1, is a radix-2 number system. The octal and hexadecimal number systems have a radix (or base) of 8 and 16 respectively. Decimal Number System: The decimal number system is mainly suitable for human beings. As it uses 10 digits in any position of a given number, the base or radix is 10. Example: ,

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