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1. Difference between analog and digital signals, Boolean algebra, Basic and
Universal Gates, Symbols, Truth tables, logic expressions, Logic simplification using
K-map, Logic ICs, half and full adder/subtractor, multiplexers, demultiplexers, flip-
flops, shift registers, counters, Block diagram of microprocessor/microcontroller
and their applications.
Module III: Digital Electronics Fundamentals

2. ANDgate
□The AND gate is an electronic circuit that
gives a high output (1) only if all its inputs
arehigh.
□AND gate takes two or more input signals
and produceonlyoneoutputsignal.
Input InputOutput
A B AB
0 0 0
0 1 0
1 0 0
1 1 1

3. ORgate
□The OR gate is an electronic circuit that
givesahighoutput(1)if oneormoreofits
inputsarehigh.
□OR gate also takes two or more input
signals and produceonlyoneoutputsignal.
Input Input Output
A B A+B
0 0 0
0 1 1
1 0 1
1 1 1

4. NOTgate
□
□
□
□The NOT gate is an electronic circuit that gives a
highoutput(1)ifitsinputislow .
NOT gate takes only one input signal and produce
onlyoneoutputsignal.
TheoutputofNOTgateiscomplementofitsinput.
Itisalsocalledinverter.
InputA OutputA
0
1
1
0

5. TruthTable
□Truthtableisatablethatcontains all
possible values of logical
variables/statements in a Boolean
expression.
No.ofpossiblecombination=
2
n
,wheren=number ofvariablesusedin
aBooleanexpression.

6. TruthTable
□The truthtablefor XY+Zisas
follows:
Dec X Y Z XY XY+Z
0 0 0 0 0 0
1 0 0 1 0 1
2 0 1 0 0 0
3 0 1 1 0 1
4 1 0 0 0 0
5 1 0 1 0 1
6 1 1 0 1 1
7 1 1 1 1 1

7. PrincipalofDuality
□InBooleanalgebrastheduality
Principlecanbeisobtainedby
interchangingANDandORoperators
andreplacing0'sby1'sand1'sby
0's.Comparetheidentitiesonthe
leftsidewiththeidentitiesonthe
right.
Example
X.Y+Z'=(X'+Y').Z

8. Basic Theorem of Boolean
Algebra
T1:Propertiesof0
(a)0+A=A
(b)0A=0
T2:Propertiesof1
(a)1+A=1
(b)1A=A

9. Basic Theorem of Boolean Algebra
T3:Commutative Law
(a)A+B=B+A
(b)AB=BA
T4:AssociateLaw
(a)(A+B) +C=A+(B+C)
(b)(AB)C=A(BC)
T5:DistributiveLaw
(a)A(B+C)=AB+AC
(b)A+(BC)=(A+B)(A+C)
(c)A+A’B=A+B

10. Basic Theorem of Boolean Algebra
T6:Indempotence (Identity)Law
(a)A+A=A
(b)AA=A
T7:Absorption(Redundance) Law
(a)A+AB=A
(b)A(A+B)=A

11. Basic Theorem of Boolean Algebra
T8:Complementary Law
(a)X+X’=1
(b)X.X’=0
T9:Involution
(a)x’’=x
T10:DeMorgan'sTheorem
(a)(X+Y)’=X’.Y’
(b)(X.Y)’=X’+Y’

12. Realization of XOR Gate using NAND and NOR Gates

14. Representation of Boolean expression
Booleanexpressioncanbe
representedbyeither
(i)Sum of Product( SOP) form or
(ii)Product of Sum (POS form) e.g.
AB+AC --------------SOP
(A+B)(A+C) -------POS
In above examples both are in SOP and POS respectively buttheyare
notin StandardSOPandPOS.

15. Canonical form of Boolean Expression
(Standardform)
➢InstandardSOPandPOSeachtermofBoolean
expressionmustcontainalltheliterals(withand
withoutbar)thathas beenusedinBoolean
expression.
➢IftheaboveconditionissatisfiedbytheBoolean
expression,thatexpressioniscalledCanonicalformof
Booleanexpression.

16. Canonical form of Boolean Expression
(Standardform)Contd..
➢InBooleanexpressionAB+ACthe
literalCismissioninthe1
st
term
ABandBismissionin2
nd
term
AC.ThatiswhyAB+ACisnota
CanonicalSOP.

17. Canonical form of Boolean Expression(Standard
form)Contd..
ConvertAB+ACinCanonicalSOP
(StandardSOP)
Sol.AB+AC
AB(C+C’) +AC(B+B’)
ABC+ABC’+ABC+AB’C
ABC+ABC’+AB’C
Distributivelaw

18. Canonical form of Boolean Expression(Standard
form)Contd..
Convert(A+B)(A+C) inCanonical
SOP(Standard SOP)
(A+B+C).(A+B+C’)(A+B’+C)
Sol.(A+B).(A+C)
(A+B)+(C.C’) . (A+C)+(B.B’)
(A+B+C).(A+B+C’).(A+B+C)(A+B’+C) Distributivelaw
Removeduplicates

19. Canonical form of Boolean Expression(Standard
form)Contd..
MintermandMaxterm
IndividualtermofCanonicalSumofProducts
(SOP)iscalledMinterm.Inotherwordsminterm
isaproductofalltheliterals(withorwithout
bar)withintheBooleanexpression.
IndividualtermofCanonicalProductsofSum
(POS)iscalledMaxterm.Inotherwords
maxtermisasumofalltheliterals(withor
withoutbar)withintheBooleanexpression.

20. Minterms&Maxterms for2variables(Derivationof
BooleanfunctionfromTruthTable)
xyIndex Minterm Maxterm
00 0 m
0=x’y’ M
0=x+y
01 1 m
1=x’y M
1=x+y’
10 2 m
2=xy’ M
2=x’+y
11 3 m
3=xy M
3=x’+y’
Themintermm
ishould evaluateto1for eachcombination
ofxandy.
The maxterm is the complement of the minterm

21. Minterms&Maxtermsfor3 variables
MaxtermM
iisthe complementofmintermm
i
M
i= m'
iandm
i=M'
i
x
MaxtermyzIndex Minterm
000 0 m
0=x’ y’ z’M
0 =x+y+z
001 1 m
1=x’ y’ zM
1 =x+y+z’
010 2 m
2=x’ y z’M
2 =x+y’ + z
011 3 m
3=x’ y z M
3 =x+y’+z’
100 4 m
4=x y’ z’M
4 =x’ + y + z
101 5 m
5=x y’ z M
5 =x’+ y + z’
110 6 m
6=xyz' M
6 =x’ + y’ + z
111 7 m
7=xyz M
7 =x'+y'+z'

22. MinimizationofBoolean Expression
(Contd…)
➢AlgebraicMethod
-The differentBooleanrulesandtheoremsareused to
simplifytheBooleanexpressioninthismethod.

23. MinimizationofBoolean Expression
(Contd…)
SolvedProblem
MinimizethefollowingBooleanExpression:
1.a’bc+ab’c’+ab’c +abc’+abc
=a’bc +ab’+ab
= a’bc +a
2.AB’CD’+AB’CD+ABCD’+ABCD
=AB’C +ABC
=AC

24. MinimizationofBoolean
Expression(Contd…)
KarnaughMap
□K-Mapsareaconvenient waytosimplify Boolean Expressions.
□Theycan beusedforupto 4 or5 variables.
□Theyareavisualrepresentation ofa truth table.

25. TruthtabletoK-Map(2variable minterm)
ABP
001
011
100
111
0
1 1
minterms arerepresentedbya
1 in the corresponding
locationintheKmap.
Theexpressionis:
A.B+A.B+A.B
A
B
A’
A
B’
0
1
B
1
1

26. K-Maps(2Variablesk-mapcontd…)
□Adjacent1’scanbe“pairedoff”
□Anyvariablewhichisbotha1andazerointhis
pairingcanbeeliminated
□Pairsmay be adjacenthorizontallyorvertically
A 0
01
1
1
1
1
apair
anotherpair
B is eliminated,
leavingAasthe
term
A is eliminated,
leavingBasthe
term
Afterreductionthe
expressionbecomesA+B
B
The expression is:
A’.B’ +A’.B+A.B

27. □ThreeVariableK-Map
ABCP
0000
0010
0101
0110
1001
1010
1101
1110
A
0
11
00011110
1
1
A.B.C+A.B.C+A.B.C
BC
One square filled in for
each minterm.

28. GroupingthePairs
A 00 01 11
0
11 1
equatestoB.CasA
iseliminated.
10
1
Here, we can “wrap
around”andthis
pair equates to A.C
asBiseliminated.
Ourtruthtablesimplifiesto
A.C +B.Casbefore.
BC
ThreeVariableK-Map(Contd…)

29. ExpressionisABC+A’BC’+A’BC+ABC’
Groups of4in ablock can beused toeliminatetwo
variables:
QUAD=A’BC+A’BC’+ABC+ABC’
=A’B+AB
=B
BC
A 00011110
0 11
1 11
ABCY
0000
0010
0101
0111
1000
1010
1101
1111
ThreeVariableK-Map(Contd…)
Groupsof4

30. Four Variable K-Map

31. half adder

32. Sum= A XOR B Carry = A AND B

34. Full adder
Inputs Outputs
A B Cin S (Sum) Cout(Carry)
0 0 0 0 0
0 0 1 1 0
0 1 0 1 0
0 1 1 0 1
1 0 0 1 0
1 0 1 0 1
1 1 0 0 1
1 1 1 1 1

35. Sum, S = A ⊕B ⊕Cin
Carry, C= AB + ACin+ BCin

36. Half Subtractor
Inputs Outputs
A B d (Difference)b (Borrow)
0 0 0 0
0 1 1 1
1 0 1 0
1 1 0 0

38. Full Subtractor
Inputs Outputs
Minuend (A)Subtrahend (B)Borrow (Bin)Difference (D)Borrow (Bout)
0 0 0 0 0
0 0 1 1 1
0 1 0 1 1
0 1 1 0 1
1 0 0 1 0
1 0 1 0 0
1 1 0 0 0
1 1 1 1 1

39. Difference,d=A ⊕B ⊕bin = A′B′bin+AB′b′in+A′Bb′in+ABbin
Borrow, b=A′B + (A ⊕B)′bin

41. multiplexers

42. the implementation of 4:1 Multiplexer using truth table and gates.

44. De-Multiplexer

45. Selection Inputs Outputs
S
1 S
0 Y
3 Y
2 Y
1 Y
0
0 0 0 0 0 I
0 1 0 0 I 0
1 0 0 I 0 0
1 1 I 0 0 0

47. flip-flops
SR Flip-Flop

48. S R Qt+1
0 0 Qt
0 1 0
1 0 1
1 1 -
statetableofSRflip-flop.

49. Present Inputs Present StateNext State
S R Qt Qt+1
0 0 0 0
0 0 1 1
0 1 0 0
0 1 1 0
1 0 0 1
1 0 1 1
1 1 0 x
1 1 1 x
thecharacteristictableofSRflip-flop.

50. Q(t)Q(t+1)S R
0 0 0 x
0 1 1 0
1 0 0 1
1 1 x 0
Excitation Table

51. JK Flip-Flop

52. J K Qt+1
0 0 Qt
0 1 0
1 0 1
1 1 Qt'
state tableof JK flip-flop

53. Present Inputs Present
State
Next State
J K Qt Qt+1
0 0 0 0
0 0 1 1
0 1 0 0
0 1 1 0
1 0 0 1
1 0 1 1
1 1 0 1
1 1 1 0
characteristictableofJKflip-flop.

54. Excitation table
Q(t)Q(t+1)J K
0 0 0 x
0 1 1 x
1 0 x 1
1 1 x 0

55. D Flip-flop
D Q(t+1)
0 0
1 1
Truth Table

56. Characteristic Equation
Q(t+1) = D(t)
Q(t) Q(t+1) D
0 0 0
0 1 1
1 0 0
1 1 1
Excitation Table

57. T Flip-Flop

58. D Qt+1
0 Qt
1 Qt’
state tableof T flip-flop.
Inputs Present StateNext State
T Qt Qt+1
0 0 0
0 1 1
1 0 1
1 1 0
thecharacteristic tableof T flip-flop.

59. Q(t) Q(t+1)T
0 0 0
0 1 1
1 0 1
1 1 0
Excitation Table

60. Shift Register
•SISO: Serial-in Serial-out: It permits the insertion of data serially and taking the output also in a
serial manner.
•SIPO: Serial-in Parallel-out: Here the data is inserted serially either from the left or right
direction. But the output is taken parallely.
•PISO: Parallel-in Serial-out: This type of shift register allows the parallel input of data bit, but
the output is taken serially.
•PIPO: Parallel-in Parallel-out: PIPO shift register permits both in and out of data bit in a parallel
manner.
Definition: A shift register is a sequential logic circuit that acts as a unit to store and transfer
binary data.

62. Serial-In Parallel-Out shift Register (SIPO)

63. Parallel-In Serial-Out Shift Register (PISO)

64. Parallel-In Parallel-Out Shift Register (PIPO) –

65. Applications of shift Registers –
•The shift registers are used for temporary data storage.
•The shift registers are also used for data transfer and data manipulation.
•The serial-in serial-out and parallel-in parallel-out shift registers are used to
produce time delay to digital circuits.
•The serial-in parallel-out shift register is used to convert serial data into
parallel data thus they are used in communication lines where
demultiplexing of a data line into several parallel line is required.
•A Parallel in Serial out shift register us used to convert parallel data to
serial data.

66. Counters
A special type of sequential circuit used to count the pulse is known as a counter, or a collection of flip flops
where the clock signal is applied is known as counters.
There are the following types of counters:
•Asynchronous Counters
•Synchronous Counters

67. Asynchronous or ripple counters
TheAsynchronous counteris also known as theripple counter
Block Diagram

68. Signal Diagram

69. Synchronous counters
In theAsynchronous counter, the present counter's output passes to the input of the next counter.
Logical Diagram

70. Signal Diagram

71. Block diagram of microprocessor/microcontroller and their applications.

72. Applications
Household Devices
•Theprogrammable thermostatallows the control of temperature at homes.
•High-end coffee makers, Washing machines, and radio clocks contain microprocessor technology.
•Some other home items that contain microprocessors are: microwaves, toasters, televisions, VCRs, DVD
players, ovens, stoves, clothes washers, stereo systems,
Industrial Applications of Microprocessors
Some industrial items which use microprocessors technology include: cars, boats, planes, trucks, heavy machinery,
elevators, gasoline pumps, credit-card processing units, traffic control devices,

73. Transportation Industry
•Automobiles, trains and planes also use microprocessor technology.
Computers and Electronics
•Microprocessor-drives technology is the brain of the computer. They are used in all type of computers
ranging from microcomputers to supercomputers.
•A cell phone or mobile device executes game instructions by way of the microprocessor.

74. In Medicals
•Many medical devices, like an insulin pump, are typically controlled by a microprocessor. The microprocessors
perform various functions, such as processing data from bio-sensors, storing measurements, and analyzing results.
Instrumentation
•Microprocessor is also very useful in the field of instrumentation. Function generators, frequency counters,
frequency synthesizers, spectrum analyses and many other instruments are available, when microprocessors are
used as controller.
Entertainment
•The use of microprocessor in entertainment equipment, toys and home entertaining applications is making them
more useful and full of features.

75. Office Automation and Publication
•Microprocessor based system with software packages has changed the office environment. Microprocessors
based systems are being used for spread sheet operations, word processing, storage etc.
Communication
•In communication the telephone industry is most important. In this industry, microprocessors are used in digital
telephone sets, telephone exchanges and modem etc.
•The use of microprocessor in satellite communication, television, has made teleconferencing possible.
•Railway reservation and airline reservation system also uses microprocessor technology. WAN (Wide Area
Network) and LAN (Local Area Network) for communication of vertical information through computer network.