DIGITAL ELECTRONICS AND LOGIC
INTRODUCTION
Digital electronics evolved from the principle that transistor circuitry could
easily be designed and fabricated to output one of the two voltage levels
based on the levels placed at its input. The two distinct levels (usually 5V
and 0V) can be represented by 1 and 0.
Numerical Representation
There are two ways of representing the numerical values of quantities:
analog and digital
(i) Analog Representation
It‟s a numerical representation in which a quantity is represented
by a voltage, current, or meter movement that is proportion to the
value of that quantity e.g. car speedometer, the electric iron
thermostat, audio microphone.
(ii) Digital Representation
It‟s a representation in which a quantity is represented by the
symbols called digits e.g. digital watch. That is, digital
representation represents discrete quantities or changes in discrete
steps.
Advantages of digital techniques
Some of the reasons for shifting from analog to digital are:
a) Digital systems are easier to design – this is due the fact that circuits
which are used in digital systems are switching circuits thus easy to
design.
b) Storage of information is easy – this is accomplished by special
switching circuits that can latch onto information and hold it for a time as
long as necessary.
c) Greater accuracy and precision – these systems have a capability to
handle as many digits of precision as needed by simply adding more
switching circuits.
d) Operation can be controlled by a program – it‟s easy to design digital
systems whose operation is controlled by set of stored instruction called a
program.
e) Digital systems are less affected by noise – unwanted fluctuations (or
noise) in voltage are not as critical in digital as it is in analog systems.
This is because in digital systems, the exact value of the voltage is not
important.
f) More digital circuitry can be fabricated on IC devices
1
,Disadvantages of Digital techniques
There is only one major drawback with the digital techniques, that the real-
world problems are analog. Thus to take advantage of digital techniques
when handling analog quantities, the following three steps are used:-
a) Convert the real-world inputs to digital form
b) Process the digital information
c) Convert the digital outputs back to real-world analog form
As an illustration, a flow rate measurement and control system is as shown
in fig. 1.
Analog-to- Digital
Measurin
digital signal
Flow rate g device
converter processing
(analog)
Digital-to Adjusts
Flow rate
analog flow rate
controller
converter
Fig. 1 illustrating a flow measurement and control
system
Examples of Digital Systems
Some of digital systems used in day-to-day life are:-
a) In communication systems
b) Business transactions
c) Traffic control
d) Medical treatment
e) Industrial applications
f) Digital telephones
g) Digital TV and disks
h) Digital cameras
i) Weather monitoring
j) Digital computers
2
, NUMBER SYSTEM AND CODES
Number system can be defined as the representation of values using
special symbols.
There are several number systems but most commonly used ones in
digital electronics are
a) Decimal number system
b) Binary number system
c) Octal number system
d) Hexadecimal number system
Decimal Number System
This number system has a radix or base of 10 that is, it contains ten
unique symbols (or digits) use to represent numbers. These are:
0.1,2,3,4,5,6,7,8,9. Any of these may be use in each position of the
number. (Radix is defined as the number of different digits which can
occur in each position in the number system)
Also this number system is a position-value system which means that the
value of a digit depends on its position. The absolute value of each digit is
fixed but its position value (or place value or weight) is determined by its
position in the overall number. For example,
4 4 4 4
Four Four Forty Four
Thousand Hundred
Fig 2
The weights of each position can be expressed a powers of 10. For
example, the number 3547.216 can be represented as follows:-
3 5 4 7 . 2 1 6
-1
10+3 10+2 10+1 100 10 10-2 10-3
Decimal point
Fig. 3 Illustrating position values as powers of 10 in a
decimal number system
The powers are numbered to the left of the decimal point starting with
0 and to the right of the decimal point starting with -1.
To count beyond 9, two digit formations are used. That is, the second
digit followed by first (10), second followed by second (11), second followed
3
INTRODUCTION
Digital electronics evolved from the principle that transistor circuitry could
easily be designed and fabricated to output one of the two voltage levels
based on the levels placed at its input. The two distinct levels (usually 5V
and 0V) can be represented by 1 and 0.
Numerical Representation
There are two ways of representing the numerical values of quantities:
analog and digital
(i) Analog Representation
It‟s a numerical representation in which a quantity is represented
by a voltage, current, or meter movement that is proportion to the
value of that quantity e.g. car speedometer, the electric iron
thermostat, audio microphone.
(ii) Digital Representation
It‟s a representation in which a quantity is represented by the
symbols called digits e.g. digital watch. That is, digital
representation represents discrete quantities or changes in discrete
steps.
Advantages of digital techniques
Some of the reasons for shifting from analog to digital are:
a) Digital systems are easier to design – this is due the fact that circuits
which are used in digital systems are switching circuits thus easy to
design.
b) Storage of information is easy – this is accomplished by special
switching circuits that can latch onto information and hold it for a time as
long as necessary.
c) Greater accuracy and precision – these systems have a capability to
handle as many digits of precision as needed by simply adding more
switching circuits.
d) Operation can be controlled by a program – it‟s easy to design digital
systems whose operation is controlled by set of stored instruction called a
program.
e) Digital systems are less affected by noise – unwanted fluctuations (or
noise) in voltage are not as critical in digital as it is in analog systems.
This is because in digital systems, the exact value of the voltage is not
important.
f) More digital circuitry can be fabricated on IC devices
1
,Disadvantages of Digital techniques
There is only one major drawback with the digital techniques, that the real-
world problems are analog. Thus to take advantage of digital techniques
when handling analog quantities, the following three steps are used:-
a) Convert the real-world inputs to digital form
b) Process the digital information
c) Convert the digital outputs back to real-world analog form
As an illustration, a flow rate measurement and control system is as shown
in fig. 1.
Analog-to- Digital
Measurin
digital signal
Flow rate g device
converter processing
(analog)
Digital-to Adjusts
Flow rate
analog flow rate
controller
converter
Fig. 1 illustrating a flow measurement and control
system
Examples of Digital Systems
Some of digital systems used in day-to-day life are:-
a) In communication systems
b) Business transactions
c) Traffic control
d) Medical treatment
e) Industrial applications
f) Digital telephones
g) Digital TV and disks
h) Digital cameras
i) Weather monitoring
j) Digital computers
2
, NUMBER SYSTEM AND CODES
Number system can be defined as the representation of values using
special symbols.
There are several number systems but most commonly used ones in
digital electronics are
a) Decimal number system
b) Binary number system
c) Octal number system
d) Hexadecimal number system
Decimal Number System
This number system has a radix or base of 10 that is, it contains ten
unique symbols (or digits) use to represent numbers. These are:
0.1,2,3,4,5,6,7,8,9. Any of these may be use in each position of the
number. (Radix is defined as the number of different digits which can
occur in each position in the number system)
Also this number system is a position-value system which means that the
value of a digit depends on its position. The absolute value of each digit is
fixed but its position value (or place value or weight) is determined by its
position in the overall number. For example,
4 4 4 4
Four Four Forty Four
Thousand Hundred
Fig 2
The weights of each position can be expressed a powers of 10. For
example, the number 3547.216 can be represented as follows:-
3 5 4 7 . 2 1 6
-1
10+3 10+2 10+1 100 10 10-2 10-3
Decimal point
Fig. 3 Illustrating position values as powers of 10 in a
decimal number system
The powers are numbered to the left of the decimal point starting with
0 and to the right of the decimal point starting with -1.
To count beyond 9, two digit formations are used. That is, the second
digit followed by first (10), second followed by second (11), second followed
3
