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- Digital Electronics Circuit - DEC
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- Master of Computer Applications
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known as digitizing. For multiple channels of transmission, Time Division Multiplexing is used. Digital control systems are fast replacing analog control systems. In digital control systems the error is in the form of digital pulses. Digital computers have revolutionalized the concept of computers. Their capability ranges from simple calculations to complex calculations using numerical techniques. Many computing tasks which required hours and days take only a few minutes on digital computers. Digital signal processing is concerned with the representation of continuous time (analog) signals in digital form. It is based on Claude Shannon’s∗ sampling theorem which states that “A band limited continuous time signal can be reconstructed in its entirety from a sequence of samples taken at intervals of less than 1 where fN is the highest frequency 2f N present in the signal.” It is essential that the analog signal is band limited which limits how much it can change between samples. The sampling rate has to high to be ensure accuracy. Since the initial signal is always analog and the final required signal is also mostly analog, a digital system requires three essential aspects (1) conversion of analog signal to digital form (2) transmission of digital signal (3) reconstruction of analog signal from the received digital signal as shown in Fig. 1.1 A continuous time function x(t) is converted into a digital signal x(n) by an analog to digital (A/D) converter. The output of discrete time system is y(n) and is converted to continuous time function by digital to analog (D/A) converter. The discrete time system, in digital communications, is a digital communication channel. To achieve high fidelity, the sampling rate may have to be very high say 50000 samples per second. Each sample may be encoded by (say) 18 bits. The frequency fs (in Fig. 1.1) must be more than twice fN the highest frequency in the analog signal. Very large scale integration (VLSI) digital circuits have capability to sample at very fast rate so that high fidelity is achieved. ∗ Sampling is done to convert analog signal to digital signal. 214 MCA-203

x(t) A/D Converter x(n) Discrete Time system y(n) D/A converter y(t) Clock (Period T = 1/fs) Clock (Period T = 1/fs) Fig. 1.1 Digital system A DSP (digital signal processing) chip is the core of digital system used in cellular phones, modems, disk drives, digital automotive systems etc. It was invented only about 15 years ago but its applications have grown tremendously. Digital methods have the following advantages over analog methods : 1. Digital devices work only in two states (say on and off). Thus their operation is very simple and reliable. 2. Digital display is very accurate and can be read at a fast speed. Human error is eliminated. 3. Electronic components exhibit change in behaviour due to ageing, change of ambient temperature etc. Therefore, the behaviour of analog circuits tends to be somewhat unpredictable. However, digital circuits are free from these defects. 4. Digital ICs are very cheap and compact in size. 5. Variety of digital ICs are available. 6. Power requirement of digital circuits is very low. 7. Digital systems have the characteristic advantage of memory. Thus information can be stored over a period of time. The space required for this stage is very small. One compact disc∗ can store information contained in many books. 8. Digital systems have high fidelity and provide noise free operations. 9. By integrating system peripheral functions on a DSP chip, the reliability can be enhanced and cost reduced. 10. When volumes are high, they can be manufactured at low cost. 11. The same digital system can be used with a variety of software for a number of tasks. 12. ∗ Standardisation & Repeatability. A compact disc is known s CD. MCA-203 215

1.3 BASIC DIGITAL CIRCUITS In a digital system there are only a few basic operations performed, irrespective of the complexities of the system. These operations may be required to be performed a number of times in a large digital system like digital computer or a digital control system, etc. The basic operations are AND, OR, NOT, and FLIP-FLOP. The AND, OR, and NOT operations are discussed here and the FLIP-FLOP, which is a basic memory element used to store binary information (one bit is stored in one FLIP-FLOP). 1.3.1 The And Operation A circuit which performs an AND operation is shown in Fig. 1.2. It has N inputs (N ≥ 2) and one output. Digital signals are applied at the input terminals marked A, B, …, N, the other terminal being ground, which is not shown in the diagram. The output is obtained at the output terminal marked Y (the other terminal being ground) and it is also a digital signal. The AND operation is defined as : the output is 1 if and only if all the inputs are 1. Mathematically, it is written as Y = A AND B AND C … AND N =A⋅B⋅C⋅… ⋅N = ABC …N …(1.1) Ao Bo oY No Fig. 1.2 The standard symbol for an AND gate where A, B, C, … N are the input variables and Y is the output variable. The variables are binary, i.e. each variable can assume only one of the two possible values, 0 or 1. The binary variables are also referred to as logical variables. Equation (1.1) is known as the Boolean equation or the logical equation of the AND gate. The term gate is used because of the similarity between the operation of a digital circuit and a gate. For example, for an AND operation the gate opens (Y = 1) only when all the inputs are present, i.e. at logic 1 level. Truth Table Since a logical variable can assume only two possible values (0 and 1), therefore, any logical operation can also be defined in the form of a table containing all MCA-203 216

possible input combinations (2N combinations for N inputs) and their corresponding outputs. This is known as a truth table and it contains one row for each one of the input combinations. For an AND gate with two inputs A, B and the output Y, the truth table is given in Table 1.1. Its logical equation is Y = AB and is read as “Y equals A AND B”. Since, there are only two inputs, A and B, therefore, the possible number of input combinations is four. It may be observed from the truth table that the input−output relationship for a digital circuit is completely specified by this table in contrast to the input−output relationship for an analog circuit. The pattern in which the inputs Table 1.1 Truth table of a 2-input AND gate Inputs Output A B Y 0 0 0 0 1 0 1 0 0 1 1 1 are entered in the truth table may also be observed carefully, which is in the ascending order of binary numbers formed by the input variables. (See Chapter 2). MCA-203 217

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## rymond kagoda

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