Electronics and Communication Engineering : Digital circuits, THE GATE ACADEMY

DIGITAL CIRCUITS

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Syllabus 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, [email protected] © 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%

Contents Digital Circuits


Cross, 10th

Main, Jayanagar 4th

Block, Bangalore-11 : 080-65700750, [email protected] © 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


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



Answer Keys 56


#3. Logic Gates 63 – 90 Logic systems 63 – 66

Relation of basic Gates using NAND & NOR gates 66 – 69

Code Converters 69 – 79



Answer Keys 87


#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



Cross, 10th

Main, Jayanagar 4th

Block, Bangalore-11 : 080-65700750, [email protected] © 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



Answer Keys 123


#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


Answer Keys 161


#6. AD /DA Convertor 168 – 185 Introduction 168

D/A Resolution 168 – 170

ADC Resolution 170 – 172



Answer Keys 180


#7. Semiconductor Memory 186 – 192 Types of Memories 186

Memory Devices Parameters or Chatacteristics 187 – 189

Assignment 1 190

Answer Keys 191


#8. Introduction to Microprocessors 193 – 225 Basics 193 – 195

8085 Microprocessers 196

Signal Description of 8085 196 – 200



Cross, 10th

Main, Jayanagar 4th

Block, Bangalore-11 : 080-65700750, [email protected] © 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



Answer Keys 219


Module Test 226 – 246 Test Questions 226 – 240 Answer Keys 241

Explanations 241 -246

Reference Book 247

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, [email protected] © 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.



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.



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



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 ( ⏟

⏟

( (



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

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7

31 254 2039

8 8 8

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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

Electronics and Communication Engineering : Digital circuits, THE GATE ACADEMY

Education

number system arithmetic

contents digital circuits

hexadecimal number system

combinational digital

syllabus digital circuits

radix of binary number

number sequence

radix of octal number