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# Electronics and Communication Engineering : Digital circuits, THE GATE ACADEMY

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THE GATE ACADEMY's GATE Correspondence Materials consist of complete GATE syllabus in the form of booklets with theory, solved examples, model tests, formulae and questions in various levels of difficulty in all the topics of the syllabus. The material is designed in such a way that it has proven to be an ideal material in-terms of an accurate and efficient preparation for GATE.

Quick Refresher Guide : is especially developed for the students, for their quick revision of concepts preparing for GATE examination. Also get 1 All India Mock Tests with results including Rank,Percentile,detailed performance analysis and with video solutions

GATE QUESTION BANK : is a topic-wise and subject wise collection of previous year GATE questions ( 2001 – 2013). Also get 1 All India Mock Tests with results including Rank,Percentile,detailed performance analysis and with video solutions

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### Electronics and Communication Engineering : Digital circuits, THE GATE ACADEMY

1. 1. DIGITAL CIRCUITS For EC / EE / IN By www.thegateacademy.com
2. 2. Syllabus Digital Circuits THE GATE ACADEMY PVT.LTD. H.O.: #74, Keshava Krupa (third Floor), 30 th Cross, 10 th Main, Jayanagar 4 th Block, Bangalore-11 : 080-65700750,  info@thegateacamy.com © Copyright reserved. Web: www.thegateacademy.com Syllabus for Digital Circuits Boolean algebra, minimization of Boolean functions; logic gates; digital IC families (DTL, TTL, ECL, MOS, CMOS). Combinatorial circuits: arithmetic circuits, code converters, multiplexers, decoders, PROMs and PLAs. Sequential circuits: latches and flip-flops, counters and shift- registers. Sample and hold circuits, ADCs, DACs. Semiconductor memories. Microprocessor(8085): architecture, programming, memory and I/O interfacing. Analysis of GATE Papers (Digital Circuits) Year ECE EE IN 2013 6.00 5.00 5.00 2012 6.00 5.00 5.00 2011 9.00 5.00 10.00 2010 9.00 8.00 8.00 Over All Percentage 7.5% 5.75% 7%
3. 3. Contents Digital Circuits THE GATE ACADEMY PVT.LTD. H.O.: #74, Keshava Krupa (third Floor), 30 th Cross, 10 th Main, Jayanagar 4 th Block, Bangalore-11 : 080-65700750,  info@thegateacamy.com © Copyright reserved. Web: www.thegateacademy.com Page I CC OO NN TT EE NN TT SS Chapter Page No. #1. Number systems & Code Conversions 1 –35  Base or Radix of a Number System 1 – 2  System Conversions 2 – 6  Coding Techniques 6 – 9  Error Detecting Codes 9 – 16  Number System Arithmetic 17 – 24  Signed Binary Numbers 25 – 27  Assignment 1 28 – 30  Assignment 2 30 – 31  Answer Keys 32  Explanations 32 – 35 #2. Boolean Algebra & Karnaugh Maps 36 – 62  Boolean Algebra 36  The Basic Boolean Postwater 36 – 42  Karnaugh Maps (k-maps) 42 – 45  Comparators 45 – 46  Decoder 46 – 50  Assignment 1 51 – 53  Assignment 2 54 – 55  Answer Keys 56  Explanations 56 – 62 #3. Logic Gates 63 – 90  Logic systems 63 – 66  Relation of basic Gates using NAND & NOR gates 66 – 69  Code Converters 69 – 79  Assignment 1 80 – 84  Assignment 2 84 – 86  Answer Keys 87  Explanations 87 – 90 #4. Logic Gate Families 91 – 126  Classification of Logic Families 91  Caracteristics of Digital IC’s 91 – 95  Resistor Transistor Logic 95  Transistor Logic 96  Direct Coupled Transistor Logic Gates 96 – 97
4. 4. Contents Digital Circuits THE GATE ACADEMY PVT.LTD. H.O.: #74, Keshava Krupa (third Floor), 30 th Cross, 10 th Main, Jayanagar 4 th Block, Bangalore-11 : 080-65700750,  info@thegateacamy.com © Copyright reserved. Web: www.thegateacademy.com Page II  Emitter Coupled Logic Circuit 97 – 98  MOSFET Gates 99 – 103  Operating Regions of MOS Transistor 104  CMOS Inverter 104 – 107  Important Points 107 – 113  Advantages & Disadvatages of Major Logic Families 113 – 115  Assignment 1 116 – 120  Assignment 2 121 – 122  Answer Keys 123  Explanations 123 – 126 #5. Combinational Digital Circuits 127 – 167  Introduction 127  Combinational Digital Circuits 127 – 133  Multiplexers 133 – 141  Flip-Flops 141 – 146  Registers and Shift Registers 146 – 148  Counters 148 – 149  Assignment 1 150 -157  Assignment 2 157 – 160  Answer Keys 161  Explanations 161 – 167 #6. AD /DA Convertor 168 – 185  Introduction 168  D/A Resolution 168 – 170  ADC Resolution 170 – 172  Assignment 1 172 – 176  Assignment 2 176 – 179  Answer Keys 180  Explanations 180 – 185 #7. Semiconductor Memory 186 – 192  Types of Memories 186  Memory Devices Parameters or Chatacteristics 187 – 189  Assignment 1 190  Answer Keys 191  Explanations 191 – 192 #8. Introduction to Microprocessors 193 – 225  Basics 193 – 195  8085 Microprocessers 196  Signal Description of 8085 196 – 200
5. 5. Contents Digital Circuits THE GATE ACADEMY PVT.LTD. H.O.: #74, Keshava Krupa (third Floor), 30 th Cross, 10 th Main, Jayanagar 4 th Block, Bangalore-11 : 080-65700750,  info@thegateacamy.com © Copyright reserved. Web: www.thegateacademy.com Page III  Classification Based on Operation 200 – 204  Classification of Instructions As Per Thier Length 204 – 205  Addressing Modes 205 – 206  Memory Mapped I/O Technique 206 – 208  Interfacing 208 – 209  Assignment 1 210 – 216  Assignment 2 216 – 218  Answer Keys 219  Explanations 219 – 225 Module Test 226 – 246  Test Questions 226 – 240  Answer Keys 241  Explanations 241 -246 Reference Book 247
6. 6. Chapter 1 Digital Circuits THE GATE ACADEMY PVT.LTD. H.O.: #74, Keshava Krupa (third Floor), 30th Cross, 10th Main, Jayanagar 4th Block, Bangalore-11 : 080-65700750,  info@thegateacamy.com © Copyright reserved. Web: www.thegateacademy.com Page 1 CHAPTER 1 Number Systems & Code Conversions Important Points The concept of counting is as old as the evolution of man on this earth. The number systems are used to quantify the magnitude of something. One way of quantifying the magnitude of something is by proportional values. This is called analog representation. The other way of representation of any quantity is numerical (Digital). There are many number systems present. The most frequently used number systems in the applications of Digital Computers are Binary Number System, Octal Number System, Decimal Number System and Hexadecimal Number System. Base or Radix (r) of a Number System The Base or Radix of a number system is defined as the number of different symbols (Digits or Characters) used in that number system. The radix of Binary number system = 2 i .e. it uses two different symbols 0 and 1 to write the number sequence. The radix of Octal number system = 8 i.e. it uses eight different symbols 0, 1, 2, 3, 4, 5, 6 and 7 to write the number sequence. The radix of Decimal number system = 10 i.e. it uses ten different symbols 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 to write the number sequence. The radix of Hexadecimal number system = 16 i.e. it uses sixteen different symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, 9,A, B, C, D, E and F to write the number sequence. The radix of Ternary number system = 3 i.e. it uses three different symbols 0, 1 and 2 to write the number sequence. To distinguish one number system from the other, the radix of the number system is used as suffix to that number. Eg: 102 Binary Numbers; 108 Octal Numbers; 1010 Decimal Number; 1016 Hexadecimal Number; Characteristics of any number system are 1. Base or radix is equal to the number of digits in the system, 2. The largest value of digit is one (1) less than the radix, and 3. Each digit is multiplied by the base raised to the appropriate power depending upon the digit position.  The maximum value of digit in any number system is given by (Ω-1), where Ω is radix Example: maximum value of digit in decimal number system = (10 – 1) = 9.
7. 7. Chapter 1 Digital Circuits THE GATE ACADEMY PVT.LTD. H.O.: #74, Keshava Krupa (third Floor), 30th Cross, 10th Main, Jayanagar 4th Block, Bangalore-11 : 080-65700750,  info@thegateacamy.com © Copyright reserved. Web: www.thegateacademy.com Page 2 Positional Number Systems In a positional number systems there is a finite set of symbols called digits. Each digits having some positional weight. Below table shows some positional number system and their possible symbols Number system Base Possible symbols Binary 2 0, 1` Ternary 3 0, 1, 2 Quaternary 4 0, 1, 2, 3 Quinary 5 0, 1, 2, 3, 4 Octal 8 0, 1, 2, 3, 4, 5, 6, 7 Decimal 10 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 Duodecimal 12 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B Hexadecimal 16 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F  Binary, Octal, Decimal and Hexadecimal number systems are called positional number systems.  Any positional number system can be expressed as sum of products of place value and the digit value. Eg: 75610 = 156.248 = 1  The place values or weights of different digits in a mixed decimal number are as follows: decimal point  The place values or weights of different digits in a mixed binary number are as follows: binary point  The place values or weights of different digits in a mixed octal number are as follows: octal point  The place values or weights of different digits in a mixed Hexadecimal number are as follows: hexadecimal point System Conversion Decimal to Binary conversion (a) Integer number: Divide the given decimal integer number repeatedly by 2 and collect the remainders. This must continue until the integer quotient becomes zero.
8. 8. Chapter 1 Digital Circuits THE GATE ACADEMY PVT.LTD. H.O.: #74, Keshava Krupa (third Floor), 30th Cross, 10th Main, Jayanagar 4th Block, Bangalore-11 : 080-65700750,  info@thegateacamy.com © Copyright reserved. Web: www.thegateacademy.com Page 3 Eg: 3710 Operation Quotient Remainder 37/2 18 +1 18/2 9 +0 9/2 4 +1 4/2 2 +0 2/2 1 +0 1/2 0 +1 Note: The conversion from decimal integer to any base-r system is similar to the above example except that division is done by r instead of 2. (b) Fractional Number: The conversion of a decimal fraction to a binary is as follows: Eg: 0.6875510 = X2 First, 0.6875 is multiplied by 2 to give an integer and a fraction. The new fraction is multiplied by 2 to give a new integer and a new fraction. This process is continued until the fraction becomes 0 or until the numbers of digits have sufficient accuracy. Eg: Integer value 1 0 1 1 ( Note: To convert a decimal fraction to a number expressed in base r, a similar procedure is used. Multiplication is done by r instead of 2 and the coefficients found from the integers range in value from to (Ω-1).  The conversion of decimal number with both integer and fraction parts are done separately and then combining the answers together. Eg: (41.6875)10 = X2 4110 = 1010012 0.687510 = 0.10112 Since, (41.6875)10 = 101001.10112. Eg: Convert the Decimal number to its octal equivalent: 15310 = X8 Integer Quotient Remainder 153/8 +1 19/8 +3 2/8 +2 1 0 0 1 0 1 Fig 1
9. 9. Chapter 1 Digital Circuits THE GATE ACADEMY PVT.LTD. H.O.: #74, Keshava Krupa (third Floor), 30th Cross, 10th Main, Jayanagar 4th Block, Bangalore-11 : 080-65700750,  info@thegateacamy.com © Copyright reserved. Web: www.thegateacademy.com Page 4 Eg: (0.513)10 = X8 (153)10 ( …… 8 Eg: Convert 25310 to hexadecimal 253/16 = 15 + (13 = D) 15/16 = 0 + (15 =F) . Eg: Convert the Binary number 1011012 to decimal. 101101 = = 32 + 8 + 4 + 1 = 45 (101101)2 = 4510. Eg: Convert the Octal number 2578 to decimal. 2578 = = 128 + 40+7 = 17510. Eg: Convert the Hexadecimal number 1AF.23 to Decimal. 1AF.2316 = Important Points 1. A binary will all ‘n’ digits of ‘ ’ has the value 2. A binary with unity followed by ‘n’ zero has the value it is an n + 1 digit number e.g. (a) Convert binary 11111111 to its decimal value Solution: All eight bits are unity. Hence value is = 255 (b) Express as binary Solution: is written as unity followed by zero 10000000000 Same rule apply for other number code Eg. Express in octal system Solution ( ( = ( ( Solution ( Binary to Decimal Conversion (Short Cut Method) Binary to Decimal Binary → octal → Decimal Eg. Convert 101110 into decimal Solution (⏟ ⏟ ( (
10. 10. Chapter 1 Digital Circuits THE GATE ACADEMY PVT.LTD. H.O.: #74, Keshava Krupa (third Floor), 30th Cross, 10th Main, Jayanagar 4th Block, Bangalore-11 : 080-65700750,  info@thegateacamy.com © Copyright reserved. Web: www.thegateacademy.com Page 5 Note: For converting Binary to octal make group of 3 bit starting from left most bit Binary to Decimal Conversion (Equation Method) Where a and →the last sum term Eg. ( to decimal So ( ( Note: we can use calculator (scientific) but there is a limit of digit as input in calculator. We can use transitional way of multiplying each digit with (where n is the position of digit in binary number) and adding in the last but for large binary digit its again a tedious task Eg. ( to decimal So ( ( Octal to Decimal Conversion (Equation Method) Above equation can be used for octal to decimal conversion with small modification Eg. convert (3767)8 to decimal ( ( Note: In general recursive equation to convert an integer in any base to base 10 (Decimal) is b a Where b → base of the integer. Binary Fraction to Decimal Since conversion of fractions from decimal to other bases requires multiplication. It is not surprising that going from other bases to decimal required a division process 3 3 7 + 24 6 + 248 2032 7 31 254 2039 8 8 8 + 1 1 1 0 1 0 1 1 1 1 0 2 6 14 28 58 116 234 470 942 1886 1 3 7 14 29 58 117 235 471 943 1886 + + + + ++ + + + + 1 1 1 + 2 0 + 6 12 1 3 6 13 2 2 2 + 1