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SWITCHING THEORY AND LOGIC DESIGN LECTURE NOTES B.TECH (II YEAR – II SEM) (2018-19) Prepared by: Mr.K.RAMBABU, Assistant Professor Department of Electronics and Communication Engineering BRILLIANT INSTITUTE OF ENGINEERING & TECHNOLOGY

UNIT - 1 NUMBER SYSTEMS & CODES Introduction about digital system Philosophy of number systems Complement representation of negative numbers Binary arithmetic Binary codes Error detecting & error correcting codes Hamming codes INTRODUCTION ABOUT DIGITAL SYSTEM A Digital system is an interconnection of digital modules and it is a system that manipulates discrete elements of information that is represented internally in the binary form. Now a day’s digital systems are used in wide variety of industrial and consumer products such as automated industrial machinery, pocket calculators, microprocessors, digital computers, digital watches, TV games and signal processing and so on. Characteristics of Digital systems Digital systems manipulate discrete elements of information. Discrete elements are nothing but the digits such as 10 decimal digits or 26 letters of alphabets and so on. Digital systems use physical quantities called signals to represent discrete elements. In digital systems, the signals have two discrete values and are therefore said to be binary. A signal in digital system represents one binary digit called a bit. The bit has a value either 0 or 1. Analog systems vs Digital systems Analog system process information that varies continuously i.e; they process time varying signals that can take on any values across a continuous range of voltage, current or any physical parameter. Digital systems use digital circuits that can process digital signals which can take either 0 or 1 for binary system.

Advantages of Digital system over Analog system 1. Ease of programmability The digital systems can be used for different applications by simply changing the program without additional changes in hardware. 2. Reduction in cost of hardware The cost of hardware gets reduced by use of digital components and this has been possible due to advances in IC technology. With ICs the number of components that can be placed in a given area of Silicon are increased which helps in cost reduction. 3.High speed Digital processing of data ensures high speed of operation which is possible due to advances in Digital Signal Processing. 4. High Reliability Digital systems are highly reliable one of the reasons for that is use of error correction codes. 5. Design is easy The design of digital systems which require use of Boolean algebra and other digital techniques is easier compared to analog designing. 6. Result can be reproduced easily Since the output of digital systems unlike analog systems is independent of temperature, noise, humidity and other characteristics of components the reproducibility of results is higher in digital systems than in analog systems. Disadvantages of Digital Systems Use more energy than analog circuits to accomplish the same tasks, thus producing more heat as well. Digital circuits are often fragile, in that if a single piece of digital data is lost or misinterpreted the meaning of large blocks of related data can completely change. Digital computer manipulates discrete elements of information by means of a binary code. Quantization error during analog signal sampling.

NUMBER SYSTEM Number system is a basis for counting varies items. Modern computers communicate and operate with binary numbers which use only the digits 0 &1. Basic number system used by humans is Decimal number system. For Ex: Let us consider decimal number 18. This number is represented in binary as 10010. We observe that binary number system take more digits to represent the decimal number. For large numbers we have to deal with very large binary strings. So this fact gave rise to three new number systems. i) Octal number systems ii) Hexa Decimal number system iii) Binary Coded Decimal number(BCD) system To define any number system we have to specify Base of the number system such as 2,8,10 or 16. The base decides the total number of digits available in that number system. First digit in the number system is always zero and last digit in the number system is always base-1. Binary number system: The binary number has a radix of 2. As r = 2, only two digits are needed, and these are 0 and 1. In binary system weight is expressed as power of 2. The left most bit, which has the greatest weight is called the Most Significant Bit (MSB). And the right most bit which has the least weight is called Least Significant Bit (LSB).

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