Digital circuits : Electrical & Communication Engineering, THE GATE ACADEMY

DIGITAL CIRCUITS For

EC / EE / IN By

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Syllabus

Digital Circuits

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 shiftregisters. 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%

th

th

th

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Contents

Digital Circuits

CONTENTS Chapter #1.

#2.

#3.

#4.

Page No.

Number systems & Code Conversions

1 –35

         

1–2 2–6 6–9 9 – 16 17 – 24 25 – 27 28 – 30 30 – 31 32 32 – 35

Base or Radix of a Number System System Conversions Coding Techniques Error Detecting Codes Number System Arithmetic Signed Binary Numbers Assignment 1 Assignment 2 Answer Keys Explanations

Boolean Algebra & Karnaugh Maps

36 – 62

        

36 36 – 42 42 – 45 45 – 46 46 – 50 51 – 53 54 – 55 56 56 – 62

Boolean Algebra The Basic Boolean Postwater Karnaugh Maps (k-maps) Comparators Decoder Assignment 1 Assignment 2 Answer Keys Explanations

Logic Gates

63 – 90

      

63 – 66 66 – 69 69 – 79 80 – 84 84 – 86 87 87 – 90

Logic systems Relation of basic Gates using NAND & NOR gates Code Converters Assignment 1 Assignment 2 Answer Keys Explanations

Logic Gate Families

91 – 126

    

91 91 – 95 95 96 96 – 97

Classification of Logic Families Caracteristics of Digital IC’s Resistor Transistor Logic Transistor Logic Direct Coupled Transistor Logic Gates th

th

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Contents          

#5.

#6.

#7.

#8.

Digital Circuits

Emitter Coupled Logic Circuit MOSFET Gates Operating Regions of MOS Transistor CMOS Inverter Important Points Advantages & Disadvatages of Major Logic Families Assignment 1 Assignment 2 Answer Keys Explanations

97 – 98 99 – 103 104 104 – 107 107 – 113 113 – 115 116 – 120 121 – 122 123 123 – 126

Combinational Digital Circuits

127 – 167

         

127 127 – 133 133 – 141 141 – 146 146 – 148 148 – 149 150 -157 157 – 160 161 161 – 167

Introduction Combinational Digital Circuits Multiplexers Flip-Flops Registers and Shift Registers Counters Assignment 1 Assignment 2 Answer Keys Explanations

AD /DA Convertor

168 – 185

      

168 168 – 170 170 – 172 172 – 176 176 – 179 180 180 – 185

Introduction D/A Resolution ADC Resolution Assignment 1 Assignment 2 Answer Keys Explanations

Semiconductor Memory

186 – 192

    

186 187 – 189 190 191 191 – 192

Types of Memories Memory Devices Parameters or Chatacteristics Assignment 1 Answer Keys Explanations

Introduction to Microprocessors

193 – 225

  

193 – 195 196 196 – 200

Basics 8085 Microprocessers Signal Description of 8085 th

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Contents         

Digital Circuits

Classification Based on Operation Classification of Instructions As Per Thier Length Addressing Modes Memory Mapped I/O Technique Interfacing Assignment 1 Assignment 2 Answer Keys Explanations

Module Test

200 – 204 204 – 205 205 – 206 206 – 208 208 – 209 210 – 216 216 – 218 219 219 – 225

226 – 246

 Test Questions  Answer Keys  Explanations

226 – 240 241 241 -246

Reference Book

247

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Chapter 1

Digital Circuits

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.

2.

3.

Base or radix is equal to the number of digits in the system, The largest value of digit is one (1) less than the radix, and 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.

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Chapter 1

Digital Circuits

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.

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Chapter 1

Digital Circuits

Eg: 3710 Operation 37/2

Quotient 18

Remainder +1

18/2

9

+0

9/2

4

+1

4/2

2

+0

2/2

1

+0

1/2

0

+1

1

0

0 1

0 1

Fig 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

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Chapter 1

Digital Circuits

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.

2.

A binary will all ‘n’ digits of ‘ ’ has the value 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 (⏟ ⏟

(

(

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Chapter 1

Digital Circuits

Note: For converting Binary to octal make group of 3 bit starting from left most bit Binary to Decimal Conversion (Equation Method) Where Eg. ( 1

a and →the last sum term to decimal 0 1 1 +

1

2

+

2

1

2

3

So (

+

6

2

12

6

13

(

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

1

1 + 2

1 + 6

0 + 14

1 + 28

0 + 58

1 + 116

1 + 234

1 + 470

1 + 942

0 + 1886

1

3

7

14

29

58

117

235

471

943

1886

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 3

7 + 24

8 3 (

31

8

6 + 248 254

8

7 + 2032 2039

(

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

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