GATE Digital Circuits Book

8/10/2019 GATE Digital Circuits Book

1/12


2/12

DIGITAL CIRCUITS

For

EC / EE / IN

By

wwwthegateacademy com
http://www.thegateacademy.com/http://www.thegateacademy.com/http://www.thegateacademy.com/http://www.thegateacademy.com/http://www.thegateacademy.com/http://www.thegateacademy.com/http://www.thegateacademy.com/


3/12

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 i f @th t C i ht d W b th t d

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


4/12


5/12

Contents Digital Circuits


Cross, 10th

Main, Jayanagar 4th

Block, Bangalore-11

080 65700750 i f @th t C i ht d W b th t d 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


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


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


6/12

Contents Digital Circuits


Cross, 10th

Main, Jayanagar 4th

Block, Bangalore-11

080 65700750 i f @th t C i ht d W b th t d 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


7/12

Chapter 1 Digital Circuits


Cross, 10th

Main, Jayanagar 4th

Block, Bangalore-11

080 65700750 i f @th t C i ht d W b th t d 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 ofsomething 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 BinaryNumber 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, 8and 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 writethe 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; 108Octal 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, and3.

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 (-1), where is radix

Example: maximum value of digit in decimal number system = (10 1) = 9.


8/12



Cross, 10th

Main, Jayanagar 4th

Block, Bangalore-11


Positional Number Systems

In a positional number systems there is a finite set of symbols called digits. Each digits havingsome positional weight. Below table shows some positional number system and their possiblesymbols

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

=

156.24

8

= 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 asfollows:

hexadecimal point

System Conversion

Decimal to Binary conversion

(a) Integer number:Divide the given decimal integer number repeatedly by 2 and collect theremainders. This must continue until the integer quotient becomes zero.


9/12



Cross, 10th

Main, Jayanagar 4th

Block, Bangalore-11


Eg: 3710

Operation Quotient Remainder37/2 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 multipliedby 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 invalue from to (-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= X8Integer Quotient Remainder153/8 +1

19/8 +3

2/8 +2

1 0 0 1 0 1

Fig 1


10/12



Cross, 10th

Main, Jayanagar 4th

Block, Bangalore-11


Eg: (0.513)10= X8

(153)10 (8

Eg: Convert 25310to hexadecimal

253/16 = 15 + (13 = D)

15/16 = 0 + (15 =F) .

Eg: Convert the Binary number 1011012to decimal.

101101 = = 32 + 8 + 4 + 1 = 45

(101101)2 = 4510.

Eg: Convert the Octal number 2578to 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 systemSolution ( (

=( (Solution (

Binary to Decimal Conversion (Short Cut Method)

Binary to Decimal Binary octal Decimal

Eg. Convert 101110 into decimal

Solution ( (

(


11/12



Cross, 10th

Main, Jayanagar 4th

Block, Bangalore-11


Note:For converting Binary to octal make group of 3 bit starting from left most bit

Binary to Decimal Conversion (Equation Method)

Where aand the last sum termEg. (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 inbinary 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)8to decimal

( (

Note:In general recursive equation to convert an integer in any base to base 10 (Decimal) is

b aWhere 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


12/12

GATE Digital Circuits Book

Documents