Basics of Digital Electronics

Basics of Digital ElectronicsBasics of Digital Electronics
Prof.Anjali JagtapProf.Anjali Jagtap
anjalij@isquareit.edu.inanjalij@isquareit.edu.in
Prof.Anjali JagtapProf.Anjali Jagtap
anjalij@isquareit.edu.inanjalij@isquareit.edu.in
Department of Electronics andTelecommunicationDepartment of Electronics andTelecommunication
International Institute of InformationTechnology,International Institute of InformationTechnology,
PunePune –– 411057411057

Digital SignalsDigital Signals
An electrical signal with two discrete levels (high and low)
Two discrete levels are represented by binary digits 0 and 1
referred as Binary number system.
Gorge Boole introduced binary number system with algebra
developed “Boolean Algebra”
Represented in two different ways
• Positive logic system
• Negative logic system

Digital system typesDigital system types
Combinational logic system/circuits
• An output at any instant depends only on inputs applied at
that instant.
• Example – Adder, subtractor, Comparator etc
• Basic building block – logic gates
Sequential logic system/circuits
• An output at any instant depends only on inputs applied at
that instant as well as on past inputs/outputs.
• Example – counters, sequence generator/ detector etc
• Requires memory
• Basic building block – Flips and logic gates

Logic GatesLogic Gates
Basic logic gates
• AND gate
• Logical Multiplication
• Two input gate shown

Basic logic gates
•OR gate
• Logical Addition
•NOT/Inversion gate
• Logical inversion
• Single input single output gate

••Universal logic gatesUniversal logic gates
• NAND gate
• NOR gate

••Special gatesSpecial gates
• Ex-OR gate
• Ex-NOR gate

Boolean AlgebraBoolean Algebra
Mathematician George Boole developed
rules for manipulation of binary variables.
Rules :
• A+0=A
• A+1=1• A+1=1
• A+A=A
• A+A’=1
• A.0=0
• A.1=A
• A.A=A
• A.A’=0
• A.(B+C)=AB+AC

Boolean AlgebraBoolean Algebra
• A+BC=(A+B).(A+C)
• A+A.B=A
• A.(A+B)=A
• A+A’.B=A+B
• A.(A’+B)=A.B
• A.B+A’.B’=A
• (A+B).(A+B’)=A
• A.B+A.C’=(A+C).(A’+B)
• (A+B).(A’+C)=AC+A’B
• AB+A’C+BC=AB+A’C
• (A+b).(A’+C).(B+C)=(A+B).(A’+C)

De Morgan’s TheoremDe Morgan’s Theorem
• (A.B)’=A’+B’
• (A+B)’=A’.B’

Number SystemNumber System
Number
System
Base or radix Symbols used
(di or d-f)
Weight assigned to
position
Example
i -f
Binary 2 0,1 2i 2-f 10101.10
Octal 8 0,1,2,3,4,5,6,7 8i 8-f 3547.25
Decimal 10 0,1,2,3,4,5,6,7
,8,9
10i 10-f 974.27
Hexadecimal 16 0,1,2,3,4,5,6,7
,8,9,A,B,C,D,
E,F
16i 16-f FA9.46

Quantities/CountingQuantities/Counting
Decimal Binary Octal Hexadecimal
0 0000 00 0
1 0001 01 1
2 0010 02 2
3 0011 03 3
4 0100 04 4
5 0101 05 5
6 0110 06 6
7 0111 07 7
8 1000 10 8
9 1001 11 9
10 1010 12 A
11 1011 13 B
12 1100 14 C
13 1101 15 D
14 1110 16 E
16 1111 17 F

Number System conversionNumber System conversion
•Binary to decimal
• Multiply each bit by 2n, n is the “weight” of the bit
• The weight is the position of the bit, starting from 0
on the right
• Add the results• Add the results
Example
(110101)2 = ( )10
= 1x25+1x24+0x23+1x22+0x21+1x20
= 32+16+0+4+0+1
= (53)10

•Binary to octal
• Group bits in threes, starting on right
• Convert to octal number
ExampleExample
(110101)2 = ( )8
= 110 101
= 6 5
= (65)8

•Binary to hexadecimal
• Group bits in fours, starting on right
• Convert to hexadecimal number
ExampleExample
(110101)2 = ( )16
= 11 0101
= 0011 0101
= (35)16

•Decimal to binary
• Divide by two, keep track of the remainder
• First remainder is bit 0 (LSB, least-significant bit)
• Second remainder is bit 1Group bits in fours, starting
on right
Example
(53) = ( )(53)10 = ( )2
= (110101)2

•Decimal to octal
• Divide by eight, keep track of the remainder
• First remainder is bit 0 (LSB, least-significant
bit)
• Second remainder is bit 1Group bits in fours,
starting on rightstarting on right
Example
(53)10 = ( )8
= (65)8

•Decimal to hexadecimal
• Divide by 16, keep track of the remainder
• First remainder is bit 0 (LSB, least-significant bit)
• Second remainder is bit 1Group bits in fours, starting on
right
Example
(53) = ( )(53)10 = ( )16
=
= (35)16 `

•Octal to binary
• Convert each octal digit to a 3-bit equivalent
binary representation
ExampleExample
(65)8 = ( )2
= 110 101
= (110101)2

•Octal to decimal
on the right
• Add the results• Add the results
Example
(65)8 = ( )10
= 6x81+5x80
= 48+5
= (53)10

•Octal to hexadecimal
• Use binary as an intermediary.
Example
(65)8 = ( )16(65)8 = ( )16
= 110 101
= 11 0101
= 0011 0101
= (35)16

•Hexadecimal to binary
• Convert each hexadecimal digit to a 4-bit
equivalent binary representation.
ExampleExample
(6A)16 = ( )2
= 0110 1010
= (1101010)2

•Hexadecimal to octal
• Use binary as an intermediary.
Example
(6A)16 = ( )8(6A)16 = ( )8
= 0110 1010
= 1 101 010
= 001 101 010
= (152)8

•Hexadecimal to decimal
on the right
• Add the results
ExampleExample
(6A)16 = ( )10
= 6x161+Ax160
= 6x161+10x160
= 96 + 10
= (106)10

Complement representationComplement representation
• One’s complement format
• In binary number system, each bit is complimented.
Example
(0100101)2 = (1011010) one’s complement form
• Two’s complement format• Two’s complement format
• In binary number system, each bit is complimented and
binary 1 is added.
• Used to represent negative number.
Example
(0100101)2 = (90)10
= (1011010)2 one’s complement form
= (1011010 + 1)2
= (1011011)2 = (-90)10 2’s complement

Basics of Digital Electronics

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