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are uni-polar transistors because they perform single channel operation where as BJT
transistors are bipolar junction transistors. The FET transistors have high current gain than
BJT transistors.

JFET (Junction-Field Effect Transistor)
The Junction-Field-Effect transistor (JFET) is an earliest and simple type of FET transistors.
These JFETs are used as switches, amplifiers and resistors. This transistor is a voltage
controlled device. It doesn’t need any biasing current. The voltage applied between gate
and source controls the flow of electric current between source and drain of a transistor.
The JFET transistors are available in both N-channel and P-channel types.

N-Channel JFET
In N-channel JFET the current flow is due to the electrons. When voltage is applied between
gate and source, a channel is formed between source and drain for current flow. This
channel is called N-channel. Nowadays N-channel JFET transistor is most preferable type
than P-channel JFET. The symbols for N-channel JFET transistor are given below.

P-Channel JFET
In this JFET transistor the current flow is because of holes. The channel between source
and drain is called P-channel. The symbols for P-channel JFET transistors are given below.
Here arrow marks indicate the direction of current flow.

MOSFET
Metal-Oxide-Semiconductor Field Effect Transistor (MOSFET) is most useful type of
among all transistors. The name itself indicates that it contains metal gate terminal. The
MOSFET has four terminals drain, source, gate and body or substrate (B). MOSFET has
many advantages over BJT and JFET, mainly it offers high input impedance and low output
impedance. It is used in low power circuits mainly in chip designing technologies.
The MOSFET transistors are available in depletion and enhancement types. Further the
depletion and enhancement types are classified into N-channel and P-channel types.

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N-Channel MOSFET
The MOSFET having N-channel region between source and drain is called N-channel
MOSFET. Here the source and gate terminals are heavily doped with n-type materials and
substrate is doped with p-type semiconductor material. Here the current flow between
source and drain is because of electrons. The gate voltage controls the current flow in the
circuit. N-channel MOSFET is most preferable than P-channel MOSFET because the
mobility of electrons is high than mobility of holes. The symbols for N-channel MOSFET
transistors are given below.

P- Channel MOSFET
The MOSFET having P-channel region between source and drain is called as P-channel
MOSFET. Here the source and drain terminals are heavily doped with P-type material and
the substrate is doped with N-type material. The current flow between source and drain is
because of holes’ concentration. The applied voltage at gate will controls the flow of current
through channel region. The symbols for P-channel MOSFET transistors in depletion and
enhancement types are given below.

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Transistors Based on Function
Transistors are also classified depending on the functions that mean what the transistors
do. Different types of transistors based on their function are explained below.

Small Signal Transistors
The basic function of small signal transistors is to amplify small signals even these
transistors are used for switching purpose. Small signal transistors are available in market
in the form of NPN and PNP transistors. We can see some value on the body of small
signal transistor this value indicates hFE of transistor.
Depending on this hFE value we can understand the capacity of transistor to amplify the
signal. The hFE values are present within the range of 10 to 500. The collector current
value of these transistors is 80 to 600mA. This type of transistors operates with the
frequency range of 1 to 300MHz. The name of the transistor itself indicates that these
transistors amplify small signals which use small voltages and currents, such as few milli
volts and milli amperes of current.

Resource link: learningaboutelectronics.com/images/Small-signal-transistor.png
Small signal transistors are used in almost all types of electronic equipments and also these
transistors are used in several applications, some of them are ON or OFF switches for
general use, LED diode driver, Relay driver, Audio mute function, Timer circuits, Infrared
diode amplifier, Bias supply circuits etc.

Small Switching Transistors
Small switching transistors are the transistors which are primarily used for switching after
that also used for amplification. Like small signal transistors, small switching transistors are
also available in the form of NPN and PNP and these type of transistors are also have hFE
values. The hFE value range for these transistors is from 10 to 200. At hFE value 200 the
transistors are not good amplifiers even though they act as better switches. The collector
current values ranges from 10 to 1000mA. These transistors are used mostly in switching
applications.

Power Transistors
The transistors which are used in the high power amplifiers and power supplies are called
as “power amplifiers”. The collector terminal of this transistor is connected to the base of a
metal device and this structure acts as heat sink which dissipates excess power for the
applications.
These types of transistors are available in the form of NPN, PNP and Darlington transistors.
Here the collector current values range from 1 to 100A. The operating frequency range
from 1 to 100MHz. The power values of these transistors are range from 10 to 300W. The
name of the transistor itself indicates that the power transistors are used in the applications
where high power, high voltage and high current are required.

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High Frequency Transistors
High frequency transistors are used for small signals which operate at high frequencies and
these are used in high speed switching applications. High frequency transistors are also
called as RF Transistors. These transistors have maximum frequency values of about
2000MHz. The collector current (IC) value ranges from 10 to 600mA. These types of
transistors are also available in the form of NPN and PNP. These are mainly used in the
applications of high frequency signals and also this transistor must be ON or OFF at high
speeds only. These transistors are used in HF, VHF, UHF, CATV and MATV oscillator and
amplifier circuits.

Photo Transistor
Photo transistors are the transistors which operate depending on the light that means these
transistors are light sensitive. The general photo transistor is nothing but a bipolar transistor
which contains light sensitive area instead of base terminal. The photo transistors have
only 2 terminals instead of general 3 terminals. The transistor operates depending on the
light. When the light sensitive area is dark then no current flows in transistor i.e. transistor
is in OFF state.

Resource link: learningaboutelectronics.com/images/Phototransistors.jpg

When light sensitive area is exposed to light then a small amount of current generates at
base terminal and it causes to flow large current from collector to emitter. The photo
transistors are available in both BJT and FET transistor types. These are named as photo-
BJTs and photo-FETs.
Unlike photo-BJTs, the photo-FETs are generating gate current by using light which
controls the current flow between drain and source terminals. Photo-FETs are more
sensitive to light than photo-BJTs. The symbols for photo-BJT and photo-FETs are shown
above.

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Unijunction Transistors:

Unijunction transistors are used only as electrically controlled switches. These transistors
do not contain any amplification characteristics because of their design. These are
generally three lead transistors. Now we see the operation of unijunction transistor. If there
is no potential difference between emitter and any one of the base terminals (B1 or B2)
then a small amount of current flows between B1 and B2.
If sufficient amount of voltage is applied to the emitter terminal then high current generates
at emitter terminal and it adds to small current between B1 and B2, then it causes to flow
large current in the transistor. Here the emitter current is the primary current source for total
current in the transistor. The current between the terminals B1 and B2 is very small, due to
this reason these transistors are not suitable for amplification purpose.

4.6 Hall Effect Chip
The most commonly used and widespread method of detecting the magnetic field is the
Hall-effect method among the various sensing technologies. Based on the Hall-effect, there
are numerous Hall-effect sensors or transducers found in a wide variety of applications that
are most commonly used for sensing proximity, speed, current and position.
This is because it is possible to build or construct Hall-effect sensors on integrated circuits
(Ic’s) with ancillary signal processing circuitry on the same silicon die.
Due to advantages like the small size, ruggedness, ease of use and cost integrated Hall-
effect sensors are preferred for many magnetic measurement applications.
Some of the application areas where these Hall-effect transducers are used are; in
industrial control as encoders, speed sensors and end of travel sensors, in computers as
disk drive index sensors and commutation for brushless fans, in automobiles as antilock
braking system (ABS) and ignition timing, in consumer devices as exercise equipment, and
so on.

Theory of Hall-Effect
The Hall-effect is discovered experimentally by Edwin Hall in 1879 at John Hopkins
University. With the instruments available at that time, the voltages obtained from the
materials were extremely low (in the order of micro volts) from the subtle nature of the
experiment.

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And hence no use with Hall-effect, outside of the laboratory was possible till the
development of suitable materials. The development of semiconductor materials yielded to
the fabrication of high quality transducers for the practical applications of the Hall-effect.
The Hall-effect is the generation of voltage across the opposite edges of current carrying
conductor which is placed in a magnetic field.
When an electric current passes through a conductor placed in a magnetic field, a potential
difference is developed across the conductor in a direction perpendicular to both magnetic
field and the current and its magnitude is proportional to the current and magnetic field.
This is known as Hall-effect and it is basis for many magnetic field measuring instruments
and devices.
Consider the simple setup to illustrate the Hall-effect shown below. A conducting material
or plate is supplied by a battery such that a current I flow through it. A pair of probes of a
voltmeter is connected to the sides of the plates such that measured voltage is zero in the
absence of magnetic field.
When a magnetic field is applied to the plate such that it is right angles to the current flow,
then a small voltage appears for the current distribution in the conductor. This force acts
on the current and crowds the current to the one side of the wire or conductor which
resulting a potential difference across the conductor.
If the polarity of the magnetic field is reversed, then the induced voltage also reversed
across the plate. This phenomenon is the Hall-effect.

The Hall-effect is based on the interaction between external magnetic field and the moving
charge carriers. A side force acting on moving electrons though a magnetic field is given
as

F = qvB
Where B is the magnetic flux density, v is the speed of the electrons and q is an electron
charge. Consider the above figure in which magnetic field deflects the movement of the
charges. A flat conductive strip is placed in a magnetic field and the additional contacts of
the strip on left and right sides are connected to the voltmeter.
The lower and upper terminals of the strip are connected to electric supply source. Due to
the presence of magnetic flux, moving electrons are shifted towards the right side of the
strip by the deflecting force. This results more negative at the right side than left and hence
exists a potential difference.
This voltage is called as a Hall voltage whose magnitude and direction depends on both
magnitude and direction of electric current and magnetic field. The Hall voltage is given as

VH = HIB sinα

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Where h is the coefficient of overall sensitivity, which depends on the plate material,
temperature, and its geometry, α is the angle between the magnetic field vector and Hall
plate and I is the current density.
The overall sensitivity depends on the Hall coefficient, which is the transverse electric
potential gradient per unit current density per unit magnetic field intensity. Thus, the Hall-
coefficient is given as

H = 1/ Ncq
Where c is the speed of the light, N is the number of electrons per unit volume.

Hall-Effect Sensors
Most of the sensors use the Hall-effect to sense the presence of magnetic fields, such
sensors are called as Hall-effect sensors. The basic element of a magnetic sensor is the
Hall-element. These sensors are usually packed in a four-terminal housing in which two
terminals are control terminal and other two are differential output terminals.
The control current is applied at the control terminals whereas the output is observed at the
differential output terminals. A basic Hall-effect sensor converts the magnetic field to
electrical signal.
A magnetic system converts the physical quantities such as position, speed, current,
temperature, etc to a magnetic field which in turn can be sensed by Hall-effect sensors.

Hall-effect sensors are fabricated from silicon material and majorly categorized into two
types, namely basic sensors and integrated sensors. Hall-coefficient and current density of
the active element are the two important parameters to be considered while fabricating the
Hall-effect sensors to produce a high output voltage.
Thus, a high Hall-coefficient and low resistance are the two important requirements of the
Hall element. Some of the materials used for the fabrication of elements in these sensors
include InSb, Ge, InAs and GaAs.

Hall-Effect Integrated Circuit (IC) Sensors
The integrated technology is combined with Hall-effect principle to produce the Hall-effect
IC switches. As compared with optoelectronic or inductive sensors, the Hall-effect ICs are
more effective, less costly and more efficient.
This kind of sensor is a single integrated circuit chip on which various components like
signal amplifiers, Hall-voltage generators and Schmitt trigger circuits are built. These ICs
detect the change in magnetic field strength of a ferromagnetic material, or permanent
magnet, or electromagnet with applied magnetics bias.
These ICs are used in various applications such as alignment control, speed control,
ignition systems, mechanical limit switches, machine tools, computers, keyboards, push
buttons, security systems, etc.

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These ICs are fabricated using silicon-CMOS technology in various configurations. The
above figure shows the Hall-effect sensor IC of 4 pin package. Out of the total 4 pins, 2
pins are connected to the constant voltage source and other two are connected to the
voltmeter.
The arrangement of the connection is shown in figure below. When the magnetic field is
absent, the measured voltage across the sheet is negligible.
When the magnetic field is applied at the biased Hall-effect sensor in such a way that the
flux lines are right angles to the current flowing through the Hall- element, then the voltage
is produced at the output terminals of Hall IC with a magnitude proportional to the magnetic
field strength.

Types of Hall-Effect Sensors
Hall-effect sensors need a signal conditioning circuit to make its output usable for many
other applications. This signal condition circuit does the amplification, voltage regulation,
temperature compensation, linearity, etc. Majorly there are two types of Hall-effect sensors
namely analog and bi-level sensors.

Analog Hall-Effect Sensors
These sensors operate over a broader voltage range and also stable in noisy environments
as compared with a basic Hall-sensor. The below figure shows the analog output Hall-effect
device that produces the analog voltage proportional to the magnetic field to which it is
exposed.
The amplifier is provided with a bias or fixed offset so that when the magnetic field is absent
that bias voltage is appearing across the output which considered as null voltage. The
magnetic field can be either positive or negative at the Hall element.
Hence, the output voltage increases above the null value when the positive magnetic field
is sensed while output decreases below the null value when the negative magnetic field is
sensed.
With these sensors, the output voltage is within the limits which are imposed by the power
supply hence, before reaching the power supply limits, amplifier will start saturates as
shown in figure.
It is to be noted that, the saturation occurs in amplifier, but not in Hall-element, therefore
there is no damage to the Hall-effect sensors from larger magnetic fields.

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Also, these sensors are not quite linear with respect to the magnetic field and hence they
need a proper calibration for high precision measurements. Further, by adding push-pull
transistor, open-collector, or open emitter to the output of differential amplifier, the
interfacing flexibility of the device is increased.

Digital Output Hall-Effect Sensors
The output of these sensors has two levels: ON or OFF. These sensors also called as bi-
level sensors. In addition, the amplifier contains Schmitt trigger with a built-in hysteresis of
the threshold level. This Schmitt trigger arrangement converts the analog signal to the
digital output by comparing differential amplifier output with fixed reference.
Therefore, when the differential amplifier output is more than the reference or preset value,
the Schmitt trigger turns ON while it is falling below the reference value, Schmitt trigger
turns OFF.
The two level output signal as function of magnetic field is shown in figure. In this the
hysteresis eliminates the avoidable oscillations by introducing dead band zone in which
action is disabled after the reference or preset value has passed.

Applications of Hall-Effect Transducers
Depends on the application, Hall-effect sensors are constructed in various configurations.
These are very popular measuring devices used in diverse field of applications like
industrial process control, biomedical, automobiles, telecommunication, automatic tellers,
etc.
These are very widely used as position sensors, liquid level measurement, limit switches
and flow measurement. Some of the devices work based on the Hall-effect such as Hall-
effect current sensors, Hall-effect vane switches, and Hall-effect magnetic field strength
sensors. Some of the applications of the Hall-effect transducers are described below.
Position Sensors
Hall-effect sensors are used for sensing the sliding motion. In this type off sensors there
will be a tightly controlled gap between the hall element and the magnet as shown in figure.
As the magnet moves back and forth at a fixed gap, the induced magnetic field will be
varied. This field will be negative as the element approaches the North Pole and positive
while it approaches the South Pole.

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These sensors are also called as proximity sensors which are used for accurate positioning.
The figure below shows four digital output bipolar sensors which are threaded into
aluminium housing and are actuated by one magnet mounted on a rod.
These sensors generate the signals when magnet moves in acceptable dimensional limits.
From a reference surface, these signals represent the distances measured. This type of
arrangement is also called as multi position sensing. The best example of such application
is the detecting various lens positions for photo processing equipment.

Flow Measurement
The figure below shows the Hall-effect sensor used for measurement of flow. The chamber
is provided with a fluid-in and fluid-out openings through which the fluid flows. A spring
loaded paddle with a threaded shaft arrangement moves the magnetic assembly to and fro
towards the Hall magnet.
As the flow rate increases through the chamber, spring loaded paddle turns the threaded
shaft. So the magnetic assembly raises upwards as the shaft turns and hence the
transducer get energized.
When the flow rate decreases, then spring coil causes the magnetic assembly to go down.
Therefore, the transducer output gets reduced. This whole arrangement is calibrated such
that there will be a linear relationship between the measured voltage and flow rate.

Liquid Level Measurement
In this method Hall-effect sensor is used for determining the height of a float thereby the
liquid level in the tank is measured. The below figure illustrates an arrangement of float and

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Hall-effect element or sensor IC in a tank. The float is attached with a magnet such that its
actuation varies the magnetic field distance far or near to the Hall-element.

As the liquid level goes up, the magnet moves closer to the sensor and hence the output
voltage is increased whereas this voltage decreases when liquid level goes down. So this
system provides the simple liquid level measurement without any electrical connections
inside the tank.
RPM Sensors
The speed or RPM sensing is the most common application of Hall-effect sensor. In the
speed sensing, a Hall-effect sensor is placed stationary in such a way that it face the
rotating magnet. This rotating magnet produces the magnetic field required to operate the
sensor or Hall-element.
The rotating magnet arrangement can be different ways depends on the convenience of
the application. Some of these arrangements are mounting individual magnets on the shaft
or hub or by the use of a ring magnet. The Hall sensor gives the output pulses for every
time that it faces the magnet.
Further, these pulses are controlled by the processors to determine and display the speed
in RPM. These sensors can be either digital or linear analog output sensors.

Brushless DC Motor Sensors
The power distribution of the brushless DC motor is controlled by the electronic
commutation instead of the mechanical commutation. Three digital Bipolar Hall effect
sensors are placed at the one end of the stator near the pole faces of the rotor to perform
the electronic commutation.
For operating these sensors, permanent magnet materials are mounted on the rotor shaft.
These sensors measure the position of the rotating magnet so that it determines when the
current should be applied to the current to the motor coils to make the magnets rotate in
the right direction.

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The information sensed by the Hall-effect sensors feed to a logic circuit which further
encodes this information and controls the drive circuit. This type feedback mechanism
offered by Hall-effect sensors to measure the speed and position of the rotor used for many
BLDC motor control applications because of greater flexibility.

Current Sensors
Hall-effect current sensors are used to measure both AC and DC currents. By using the
linear analog Hall-effect sensor, it is possible to measure the current ranging from 250 mA
to thousands of amperes.
This isolated analog output voltage is further digitized; level shifted and temperature
compensated by adding amplifiers.
A current carrying conductor always surrounded by the magnetic field and hence a linear
Hall-effect sensor is placed near this field, then a voltage is developed across the output
terminal of the sensor as shown in figure. This voltage is proportional to the magnetic field
strength around the conductor.

A more sensitive and very efficient isolated current sensing device can be obtained by using
Hall-effect sensors in conjunction with an electromagnet. This arrangement consists of a
slotted ferrite toroid core with a Hall-effect IC sensor positioned in the gap.
The sensor is enclosed by the core and hence the core acts as a flux concentrator as it
focuses the induced magnetic field toward the location where Hall-element is placed as
shown in figure.
By varying the number of windings on the core, a few amperes to the thousands of amperes
current measurements is possible with this sensor. The output voltage of the Hall-effect
sensor is proportional to the current flowing through the windings and hence the current
measurement.

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Temperature or Pressure Sensors
Hall-effect sensors can also be used as pressure and temperature. These sensors are
incorporated with a pressure deflected diaphragm with appropriate magnets. A magnetic
assembly of a bellows actuates to and fro to the Hall-effect element.
In case of pressure measurement, bellows are subjected to the expansion and contraction.
The bellows variation causes to move the magnetic assembly in proximity to the Hall-effect
element. Hence the output voltage produced proportional to the pressure applied.
In case of temperature measurement, bellows assembly is sealed with a gas with known
thermal expansion properties. When the chamber is heated, the gas inside the bellows gets
expanded. This causes a voltage to be produced from sensor proportional to the
temperature.

4.7 Integrated Circuits (ICs)
An Integrated Circuit or an IC is an integration or incorporation of several electronic
components (mainly transistors) on a single device (or chip) made up of a semiconductor
material (usually Silicon).
Almost all electronic devices like TVs, Mobile Phones, Laptops, Audio Players, Routers,
etc. have Integrated Circuit in them.
ICs are again divided into Analog ICs and Digital ICs. Analog ICs work on Analog Signals
like Temperature, Audio, etc. which are continuously varying in nature. Digital ICs on the
other hand, work on Discrete Signals i.e. zero volts and a non-zero volts (like 5V or 3.3V)
that are represented as Binary 0 and 1.

EXERCISE:
State the types of transistor.
Describe the half effect chip and list down the type.
Explain the integrated circuit (IC)

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REFERENCE:

1. Hollembeak, B. (2015). Automotive electricy & electronics (6th ed.). New York:
Cengage.

2. Hollembeak, B. (2015). Shop manual for Automotive electricity & electronics (6th ed.).
USA: Cengage.

3. Halderman, J. (2014). Automotive Electricity and Electronics (Fourth edition.). Boston:
Pearson.

4. Halderman, J. D. (2013). Advanced Automotive Electricity and Electronics. Boston:
Pearson.

5. Chapman, N. (2010). Principles of Electricity & Electronics for the Automotive
Technician (Second edition.). Clifton Park: Delmar.

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Kolej Kemahiran Tinggi Mara
Masjid Tanah, Melaka

INFORMATION SHEET

PROGRAMME DIPLOMA IN AUTOMOTIVE ENGINEERING TECHNOLOGY
SESSION
CODE & COURSE SEMESTER 2
LECTURER
DVA 20212 ELECTRICAL & SHEET NO IS 01
ELECTRONIC FUNDAMENTAL

WEEK 16

TOPIC 5.0 Digital Logic Circuit

SUB-TOPIC 5.1 Analog and digital signal
5.2 Types of signal output
TOPIC 5.3 Bit and bytes.
LEARNING After the lesson, student should be able to:
OUTCOME 1. Identify & diffrentiate types of electronic signal.
2. Know the symbols, Boolean Operation, Truth table for gates

circuits.

5.1Analog and Digital Signal

Difference Between Analog and Digital Signal

Analog and Digital are the different forms of signals. Signals are used to carry information

from one device to another. Analog signal is a continuous wave that keeps on changing

over a time period. Digital signal is discrete in nature. The fundamental difference between

analog and digital signal is that analog signal is represented by the sine waves whereas,
the digital signal is represented by square waves. Let’s us learn some more differences
between analog and digital signal with the help of comparison chart shown below.

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Comparison Chart

BASIS FOR ANALOG SIGNAL DIGITAL SIGNAL

COMPARISON

Basic An analog signal is a continuous A digital signal is a discrete

wave that changes over a time wave that carries information in

period. binary form.

Representation An analog signal is represented A digital signal is represented

by a sine wave. by square waves.

Description An analog signal is described by A digital signal is described by
the amplitude, period or bit rate and bit intervals.
frequency, and phase.

Range Analog signal has no fixed Digital signal has a finite range

range. i.e. between 0 and 1.

Distortion An analog signal is more prone A digital signal is less prone to

to distortion. distortion.

Transmit An analog signal transmit data in A digital signal carries data in

the form of a wave. the binary form i.e. 0 nad 1.

Example The human voice is the best Signals used for transmission
example of an analog signal. in a computer are the digital

signal.

Definition of Analog Signal
Analog signal is a kind of continuous wave form that changes over time. An anlaog signal
is further classified into simple and composite signals. A simple analog signal is a sine wave
that cannot be decomposed further. On the other hand, a composite analog signal can be
further decomposed into multiple sine waves. An analog signal is described using
amplitude, period or frequency and phase. Amplitude marks the maximum height of the
signal. Frequency marks the rate at which signal is changing. Phase marks the position of
the wave with respect to time zero.

An analog signal is not immune to noise hence, it faces distortion and decrease the quality
of transmission. The range of value in an analog signal is not fixed.

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Definition of Digital Signal
Digital signals also carry information like analog signals but is somewhat is different from
analog signals. Digital signal is noncontinuous, discrete time signal. Digital signal carries
information or data in the binary form i.e. a digital signal represent information in the form
of bits. Digital signal can be further decomposed into simple sine waves that are called
harmonics. Each simple wave has different amplitude, frequency and phase. Digital signal
is described with bit rate and bit interval. Bit interval describes the time require for sending
a single bit. On the other hand, bit rate describes the frequency of bit interval.

A digital signal is more immune to the noise; hence, it hardly faces any distortion. Digital
signals are easier to transmit and are more reliable when compared to analog signals.
Digital signal has a finite range of values. The range of a digital signal lies between 0 to 1.
Key Differences Between Analog and Digital Signal
1. An analog signal represents a continuous wave that keeps changing over a time period.

On the other hand, a digital signal represents a noncontinuous wave that carries
information in a binary format and has discrete values.
2. An analog signal is always represented by the continuous sine wave whereas, a digital
signal is represented by square waves.
3. While talking of analog signal we describe the behaviour of the wave in respect of
amplitude, period or frequency, and phase of the wave. On the other hand, while talking
of discrete signals we describe the behaviour of the wave in respect of bit rate and bit
interval.
4. The range of an anlaog signal is not fixed whereas the range of the digital signal is finite
and ranges between 0 to 1.
5. An analog signal is more prone to distortion in response to noise, but a digital signal
has immunity in response to noise hence it rarely faces any distortion.
6. An analog signal transmits data in the form of wave whereas, a digital signal transmits
the data in the binary form i.e. in the form of bits.
7. The best example of an analog signal is a human voice, and the best example of a
digital signal is the transmission of data in a computer.

Conclusion:
Digital signal is nowadays replacing the analog signal, but analog signal is still best for
audio transmission.

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5.2 Types of signals
Signals can be classified based on parameter used to classify them such as
a) Nature of independent variable such as time as

 Continuous time signal
 Discrete time signal
b) Nature of dependent variable or signal
 Analog signal
 Digital signal
c) Number of independent variables
 One dimensional signal
 Two dimensional signal
 Multi-dimensional signal
d) Based on periodicity of signal as
 Periodic signal
 Aperiodic signal
e) Based on nature of indeterminacy
 Deterministic signal
 random signal
f) Based on causality
 Casual signal
 Anti-casual signal
 Non casual signal
g) Based on energy content in the signal
 Energy signal
 Power signal
 Neither energy nor power signals.

Continuous time signal, discrete time signal
Continuous time signals are the signals that are defined at a continuum of times i.e. time
can assume any value from (-∞, ∞). It is a one to one mapping of signal for every value
time assumes from (-∞, ∞), for every instance of time there exists a unique and single value
of function f (t). The signal also can have continuum of amplitude values. These signals are
also called as analog signals.
If we sample the signal at discrete intervals of time ignoring the values signal takes for
times other than sampling times, then the signal is defined as discrete signal. The signal
amplitudes are continuous and analog in nature.

analog to discrete signal

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Signals strictly speaking are all continuous time in nature; in discrete signals we are just
ignoring the unwanted information in the signal by taking signal amplitudes at discrete
instants of time.

Analog signals, digital signals
Signals which are continuous in time and amplitude are called analog signals. That is both
independent and dependent variables are continuous in amplitude. All Continuous time
signals are analog signals and vice versa.
Digital signals are one in which time is discrete in nature and amplitude of signals are
quantized i.e. they are allowed to take values from a fixed set of amplitudes. For example,
a binary signal can have only two values zero or one. Digital signals are widely used in
communications as they are less prone to noise.

analog to digital signal conversion

One dimensional signal, two dimensional signal, Multi-dimensional signal
If the signal is a function of only one independent variable such signal is referred to as one
dimensional signal. For example, a noisy voice signal shown in the figure is a one
dimensional signal is a function of only time.
Similarly, if the signal is a function of two dependent variables variable such signal is
referred to as one dimensional signal. For example, a simple black and white picture is a
function of intensity shown in the figure is a two dimensional signal is a function of spatial
coordinates X and Y. At each point (X, Y) an intensity value is assigned and mapped onto
computer screen as a 2D image.
Multidimensional signal is a function of more than two variables. For example, a video
signal is a function of three independent variables which are time and two spatial
coordinates (X, Y).

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1D signal

2D signal
Periodic signal, Aperiodic signal
A signal can be classified as periodic signal if it repeats itself after a time interval of T,
Where T is called period of the signal. Mathematically a signal f(t) is said to be periodic if
f(t+T) = f(t), where the T is the smallest positive non zero value of all possible values of
constants T for which the equality holds then T is said to be period of f(t). For example, a
sine wave is periodic wave which satisfies sin (θ) = sin (2*n*Π+ θ) where n =0, +-1, +-2…
But as per definition of period only 2*pi qualifies as period. Hence sin (θ) is said to be
periodic with period 2* Π.
A signal which is not periodic is said to be Aperiodic signal. Mathematically it can be defined
as a periodic signal with infinite period. Here infinite period signifies that the signal never
repeats itself. Most of the signals we will be dealing are aperiodic in nature.

Periodic signal

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aperiodic signal
Deterministic signal, random signal
A deterministic signal is a signal about which there is no uncertainty with respect to its value
at any time. Deterministic signals are modelled uniquely and completely specified functions
of time. For example, consider a carrier sine wave f (t) = Am*cos (ωc*t) its value at any
instant is completely defined and can be determined with certainty.
A random signal is a signal about which there is some degree of uncertainty before it
actually shows up or before it actually occurs. For example, an outcome of a flipped coin
can be heads or tails we don’t know with 100 % certainty what will be the outcome of the
event of flipping a coin before the coin is flipped. That’s why we assign probabilities on the
possible outcomes based on our past experiences. In the example of flipping a coin we can
say that the outcome can be heads with 50% probability and outcome can be tails with 50%
probability. Noise is a random signal which can be defined in terms of probability.
Casual signal, Anti casual signal, Non casual signal
The notion of causality actually is more apt for systems nevertheless it can be applied to
signals also. A signal is causal if its amplitude is zero for negative instants of time i.e. t < 0.
The causality of a signal depends on time reference (t= 0) at what instant time is initialized
to zero.
A signal is Anti casual signal if its amplitude is zero for positive instants of time t > 0. A non-
casual signal is one whose amplitude is non zero for t < 0 and t > 0.

causal signal

Anti-causal signal

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Non causal signal

Energy signal, Power signal
Consider a resistor of R ohms with the current passing through it is i (t), then the voltage
across the resistor is V (t) = i (t)*R. The instantaneous power dissipated in the resistor is
P = V2(t)/R in terms of voltage signal,
P = i2(t)*R in terms of current signal.
To remove the dependence of resistance and ease the analysis it is customary in signal
analysis to work with one-ohm resistor for which both reduce to same form P = V2(t) = i2(t).
Hence the
instantaneous power associated with signal f(t) is defined as P = |f(t)|2.

Total energy of a signal f(t) is defined as E = as T tends to infinity.

Average power is defined as P = as T tends to infinity.

A signal f(t) is an energy signal if its total energy if finite and non-zero. The average power
associated with an energy signal is zero.
A signal f (t) is a power signal if its average power if finite and non-zero. The energy
associated with a power signal is infinite.
Signals which have infinite power and infinite energy are classified neither as energy
signals or power signals.
Typically, periodic signals and random signals are power signals.

5.3 Gating circuit.
Logic gates are the heart of digital electronics. A gate is an electronic device which is used
to compute a function on a two valued signal. Logic gates are the basic building block of
digital circuits.
Basically, all logic gates have one output and two inputs. Some logic gates like NOT gate
or Inverter has only one input and one output. The inputs of the logic gates are designed
to receive only binary data (only low 0 or high 1) by receiving the voltage input.
The low logic level represents Zero volts and high logic level represents 3 or 5 volts positive
supply voltage.
We can connect any number of logic gates to design a required digital circuit. Practically,
we implement the large number of logic gates in ICs, by which we can save the physical
space occupied by the large number of logic gates. We can also perform complicated
operations at high speeds by using integrated circuits (IC).
By combining logic gates, we can design many specific circuits like flip flops, latches,
multiplexers, shift registers etc.

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Simple Diode Logic Gates
Diodes can act like switches, so these are used in digital logic operations and switching.
For low and high impedance states a diode will work in forward bias and reverse bias.
The diode will conduct only in one direction (Forward bias) and it remains closed in reverse
bias condition. So it behaves like a switch. Now let’s see some simple diode logic gates,
which are constructed by using only Diodes and resistors.
OR Gate
The simple OR gate designed by two diodes is shown in the below figure. Inputs are given
to this circuit by the two diodes. In this, the logic HIGH (1) is represented by +5 Volts and
logic LOW (0) is represented by 0 Volts or Ground.
In the circuit below, the two inputs are left unconnected, so the output is 0 i.e. logic low.
If any one of the two inputs is connected to +5 volts, then the diode becomes forward biased
and it will conduct. Thus the output is logic HIGH i.e. 1.
If voltage of +5 V is connected to both the inputs (both diodes), they will be in forward
biased state, which makes the output of OR circuit to set in HIGH logic.
The functioning of OR gate is mathematically given as Z = X + Y, where Z is the output of
the OR gate and X, Y are the inputs. The truth table and logic diagram and circuit diagram
for the logical OR gate is shown below.

AND Gate
The simple AND gate designed by two diodes is shown in the below figure. In this the circuit
driving voltage V is connected to the two parallel connected diodes through a resistor, R.
Inputs are given to this circuit by the two diodes.
In this, the logic HIGH (1) is represented by +5 Volts and logic LOW (0) is represented by
0 Volts or Ground.

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In the below circuit , the two inputs are left unconnected, so the output is also 0 i.e. logic
low.
If any one of the two inputs is connected to +0 volts , then the diode becomes reverse
biased and it will not conduct and makes the output as LOW logic i.e. 0.
If the voltage of +5 V is connected to both the inputs (both diodes) , both the diodes will be
in forward biased state, which makes the output of AND circuit to set in HIGH logic.
The functioning of AND gate is mathematically given as Z = X. Y, where Z is the output of
the AND gate and X, Y are the inputs. The truth table and logic diagram and circuit diagram
for the logical AND gate is shown below.

AND logic circuit Logic Symbol Truth table
Transistor Logic Gates
Like diode, transistor also acts as electronic switch. We can design logic gates using
transistors also. Let’s have a look about the transistor -made logic gates.
NOT Gate
The NOT gate is generally known as an INVERTER. It produces the exact reverse output
to that of given input. It has only one input and one output. The output of NOT gate is always
the complement of its input. When low input signal is connected to the input of the NOT
gate, then the output will be HIGH (logic 1).
Similarly, if high input signal is connected to the input, then the output will be LOW (logic
0). The NOT operation is denoted by ‘-’ bar symbol. If the input of NOT gate is X and output
is Z then the operation of NOT gate is given as Z =X ,̅ said as X bar.

The NOT gate designed by using transistor is shown below. The input is given to the base
of the transistor through a resistor. And this transistor circuit is driven by a +5 volts voltage.

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When the input is connected to low level signal 0 V, then the transistor will be reverse
biased. So no current will flow through it, thus it remains in OFF. As there is no current flow
through transistor, there will be no voltage drop across the resistor. So the output will
correspond to +5 Volts making the output logic HIGH.
But if +5 V connected to the input, the output voltage will become 0. The transistor designed
NOT gate is shown below.

There are two more gates which can be designed by using transistors, they are NAND gate
and NOR gate. These gates are called “Universal gates”.

NAND Gate
The NAND gate has the ability to perform 3 operations such as AND, OR and NOT. This
gate is a combination of NOT & AND gates. The NAND gate output is equal to the inverse
of the AND gate.
The NAND gate has two inputs X and Y, and a single output Z. The inputs are applied to
the diodes which are connected to the transistor. The NAND gate circuit is driven by +5
Volts.
When both inputs are connected to a voltage supply of 5 V, then both diodes D1 and D2
are in OFF state. Then the transistor Q1 is able to drive from the supply voltage through
the resistor. So the transistor is in ON state and the output voltage Vce (Sat) becomes 0.
Similarly, when low level voltage is applied the to the inputs i.e. 0 V, the transistor will be
OFF and the output voltage becomes +5 V. Mathematically NAND gate is represented as
Z =(X.Y) ̅.
So the output of the NAND gate becomes LOW only when both the inputs are high. It
becomes HIGH for any other combination of inputs. The truth table, logic symbol and
transistor circuit diagrams of NAND gate are shown below.

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NOR Gate
NOR gate is the combination of NOT gate and OR gate. The NOR gate output is equal to
the inverse of the OR gate. The NOR gate has two inputs X and Y, and a single output Z.
The transistor designed NOR gate has two n-p-n transistors in it with the voltage supply or
+5 Volts.
When both the inputs of the NOR gate are connected to 0 Volts, then the transistors Q1
and Q2 are in OFF state. So no current flows through the resistor and there is no voltage
drop across the resistor. Then the output voltage is equal to the supply voltage +5 Volts i.e.
HIGH logic level.
If any one of the input is connected to +5 V, then the transistors will be ON state. So the
voltage drop would be high. So the output voltage of the circuit will be 0 V i.e. equal to
ground voltage.
Mathematically NOR gate is represented as Z =(X+Y) .̅
So the output of the NAND gate becomes HIGH only when both the inputs are low. It
becomes LOW for any other combination of inputs. The truth table, logic symbol and
transistor circuit diagrams of NOR gate are shown below.

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EXERCISE:
1. Which of the following symbols represents a NOR gate?

AB
CD
2. Which one of the following truth tables represents the behavoir a NAND gate?

AB

CD
3. What does connecting together the inputs of NAND and NOR gates do?

Help produce multi-input gates
Produce and EXNOR gate
Produce a NOT gate
Damage the gate

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4. How do you make a NAND gate out of an AND gate using inverters (NOT gates)?

Invert the output from the AND gate

Invert both the inputs to the AND gate

Invert one of the inputs to the AND gate

Invert both the inputs and output of the AND gate

5. The universal gate is ………………
a) NAND gate
b) OR gate
c) AND gate
d) None of the above

6.The inverter is ……………
a) NOT gate
b) OR gate
c) AND gate
d) None of the above

7. The inputs of a NAND gate are connected together. The resulting circuit is ………….
a) OR gate
b) AND gate
c) NOT gate
d) None of the above

8. The NOR gate is OR gate followed by ………………
a) AND gate
b) NAND gate
c) NOT gate
d) None of the above

9. The NAND gate is AND gate followed by …………………
a) NOT gate
b) OR gate
c) AND gate
d) None of the above

10.Digital circuit can be made by the repeated use of ………………
a) OR gates
b) NOT gates
c) NAND gates
d) None of the above

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11. The only function of NOT gate is to …………….
a) Stop signal
b) Invert input signal
c) Act as a universal gate
d) None of the above

12. When an input signal 1 is applied to a NOT gate, the output is ………………
a) 0
b) 1
c) Either 0 & 1
d) None of the above

13. In Boolean algebra, the bar sign (-) indicates ……………….
a) OR operation
b) AND operation
c) NOT operation
d) None of the above

14. An OR gate has 4 inputs. One input is high and the other three are low. The output
is …….

a) Low
b) High
c) alternately high and low
d) may be high or low depending on relative magnitude of inputs

15. Both OR and AND gates can have only two inputs.
a) True
b) False

16. The output will be a LOW for any case when one or more inputs are zero in a/an
…………

a) OR Gate
b) NOT Gate
c) AND Gate
d) NAND Gate

17. A single transistor can be used to build …………. gates.
a) OR Gate
b) NOT Gate
c) AND Gate
d) NAND Gate

18. The logic gate that will have HIGH or “1” at its output when any one of its inputs is
HIGH is a/an …………… gate.

a) OR Gate

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b) NOT Gate
c) AND Gate
d) NAND Gate

19. …………. NAND circuits are contained in a 7400 NAND IC.
a) 1
b) 2
c) 4
d) 8

18. Exclusive-OR (XOR) logic gates can be constructed from ………. logic gates.
a) OR gates only
b) AND gates and NOT gates
c) AND gates, OR gates, and NOT gates
d) OR gates and NOT gates

19. ………. truth table entries are necessary for a four-input circuit.
a) 4
b) 8
c) 12
d) 16

20. A NAND gate has ……. inputs and ……. output.
a) LOW inputs and LOW outputs
b) HIGH inputs and HIGH outputs
c) LOW inputs and HIGH outputs
d) None of these

21. The basic logic gate whose output is the complement of the input is ………….
a) OR gate
b) AND gate
c) INVERTER gate
d) Comparator

22. ………. input values will cause an AND logic gate to produce a HIGH output.
a) At least one input is HIGH
b) At least one input is LOW
c) All inputs are HIGH
d) All inputs are LOW

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REFERENCE:

1. Hollembeak, B. (2015). Automotive electricy & electronics (6th ed.). New York:
Cengage.

2. Hollembeak, B. (2015). Shop manual for Automotive electricity & electronics (6th ed.).
USA: Cengage.

3. Halderman, J. (2014). Automotive Electricity and Electronics (Fourth edition.). Boston:
Pearson.

4. Halderman, J. D. (2013). Advanced Automotive Electricity and Electronics. Boston:
Pearson.

5. Chapman, N. (2010). Principles of Electricity & Electronics for the Automotive
Technician (Second edition.). Clifton Park: Delmar.

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Kolej Kemahiran Tinggi Mara
Masjid Tanah, Melaka

INFORMATION SHEET

PROGRAMME DIPLOMA IN AUTOMOTIVE ENGINEERING TECHNOLOGY
SESSION
CODE & COURSE SEMESTER 2
LECTURER
DVA 20212 ELECTRICAL & SHEET NO IS 02
ELECTRONIC FUNDAMENTAL

WEEK 17

TOPIC 5.0 Digital Logic Circuit

SUB-TOPIC 5.4 Binary number
5.5 Octal and Hexadecimal Number
TOPIC 5.6 Boolean algebra & logic gates
LEARNING 5.7 Combinational Logic Circuit
OUTCOME
After the lesson, student should be able to:
1. Convert Binary numbering systems to Denary and

Hexadecimal numbering system.
2. Calculate using Binary and Hexadecimal system.

Bit and Bytes

What is a Bit?
A Bit is the basic unit in computer information and has only two different values, normally
defined as a 0 or 1. These values can be interpreted as on or off, yes or no, true or false,
etc. It just depends on the binary code.

What is a Byte?
A Byte is just 8 Bits and is the smallest unit of memory that can be addressed in many
computer systems. The following list shows the relationship between all of the different
units of data.

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0 (Off) or 1 (On) = 1 Bit

8 Bits = 1 Byte

1,024 Bytes = 1 Kilobyte

1,024 Kilobytes = 1 Megabyte

1,024 Megabytes = 1 Gigabyte

1,024 Gigabytes = 1 Terabyte

1,024 Terabytes = 1 Petabyte

1,024 Petabytes = 1 Exabyte

1,024 Exabytes = 1 Zettabyte

Let's take a look at a simple text file I created called sample.txt. It contains only eight (8)
characters, four (4) upper case and four (4) lower case letters. I created my text file
using Notepad, so it is encoded using the American National Standards Institute (ANSI)
standard binary code.

A sample text file with only eight characters opened in a text editor
Now the closest we can get to viewing raw binary code is to open my sample text file in a
hexadecimal file editor. Hexadecimal digits allow for more human friendly representation of
binary code.

A sample text file with only eight characters opened in a hexadecimal editor
Since the ANSI code standard is actually a revision of the American Standard Code for
Information Interchange (ASCII) code, we'll need to use that standard for references to
binary information. Using the table of ASCII printable characters on Wikipedia we can find
the binary code equivalent.

Character Hexadecimal Binary

A 41 01000001

a 61 01100001

B 42 01000010

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b 62 01100010

C 43 01000011

c 63 01100011

D 44 01000100

d 64 01100100

So, as you can see, each character contains 8 bits or 1 byte and the whole sample.txt file
is 8 bytes in size. Now to put this in perspective, I created a Microsoft Word document
(sample.docx) with the same characters as the sample text file.

A sample Microsoft Word file with only eight characters opened in Microsoft Word

A sample Microsoft Word file with only eight characters opened in a hexadecimal editor
Here you can see all of the underlying formatting and the size has increased significantly.
The sample.docx file is almost 12 kilobytes (11,513 bytes) in size, but contains only eight
(8) characters.

What is 32-bit / 64-bit?
The terms 32-bit and 64-bit define the fixed-size piece of data a processor can transfer to
and from memory. So, in theory, 64-bitcomputers can handle data twice as fast 32-
bit systems.
The 32-bit computer architecture is most commonly known as x86and was based on
the Intel 8086 / 8088 processor. The Intel 8086 / 8088 processor was found in the original
stand-alone Pac-Man video arcade console. The term for 64-bit computer architecture
is x64, a little straighter forward.

5.5 Binary Numbering System

The binary numeral system is a base-2 numeral system, that is, a system with only two
symbols, 0 and 1.

Binary numbers are used in digital electronic circuits in computer-based devices, where
they can direct switches, or so-called logic gates, either to be turned on or turned off.

In computer science one binary digit is usually called a “bit”.

How does the binary numeral system work?
Binary numbers are counted the same way as numbers of the decimal numeral system,
but where each digit of a decimal number can have ten different values, because there
are ten different symbols (0,1,2,3,4,5,6,7,8,9), each digit of a binary number can have

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only two values (0 and 1).

Like in the decimal numeral system the first numbers only have one digit, which increases
by one at a time. When all symbols for that digit have been used, the digit turns back into
the first symbol in line again, which is 0, and another digit is added to the left of it. The
new added digit starts with the second symbol in line, which is 1, and increases by one
every time the first digit has made a round of symbols and so forth.

Example

The table shows how to count from 0 to 8 in the binary numeral system.

Decimal Binary
numbers numbers

00

11

2 10

3 11

4 100

5 101

6 110

7 111

8 1000

In the decimal numeral system, you increase the number of possible combinations of
numbers tenfold, for each digit you add. With one digit you can make 10 different
numbers (0,1,2,3,4,5,6,7,8,9). With two digit you can make 102=100 different numbers (0-
99). With three digits you can make 103=1000 different combinations of numbers (0-999)
and so forth. So the number of possible combinations of numbers, you can make, is given
by powers of 10. The power increases by one for each digit you add.

In the binary numeral system you get only twice as many combinations of numbers, every
time you add a digit. So each digit you add gives an increase of combinations of numbers
given by powers of 2. With one digit you can make 2 numbers (0 and 1). With two digits
you can make 22=4 different numbers (0,1,10 and 11) and so forth.

Conversion from decimal to binary numeral system
As explained above each digit of the binary numeral system has a value given as powers
of 2, indicating how many combinations of numbers you can make, when that digit is
added.

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In order to convert numbers from decimal to binary numeral system, you have to make a
list of these values in reverse order.

Number of digit 10 9 8 7 6 5 4 3 2 1 0

Powers of 2

Value in decimal
numeral system

Binary digit

Then you work your way systematically through the number from left to right.

For example, we want to convert 233 to a binary number.

You make the table like the one above, but only with the “Values in decimal numeral
system” that are smaller than 233, that is, from 128 down.

128 64 32 16 8 4 2 1

Then we go through the numbers from left to right.
Is 233 greater than or equal to 128? Yes it is, and we write 1 in the field below 128.

128 64 32 16 8 4 2 1

1

Then we calculate 233 - 128 = 105
Is 105 greater than or equal to 64? Yes it is, and we write 1 in the field below 64.

128 64 32 16 8 4 2 1

11

and calculate 105 - 64 = 41
Is 41 greater than or equal to 32? Yes it is, and we write 1 in the field below 32.

128 64 32 16 8 4 2 1

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111

and calculate 41 - 32 = 9
Is 9 greater than or equal to 16? No it isn’t, and we write 0 in the field below 16.

128 64 32 16 8 4 2 1

1110

Is 9 greater than or equal to 8? Yes it is, and we write 1 in the field below 8.

128 64 32 16 8 4 2 1

11101

and calculate 9 - 8 = 1
Is 1 greater than or equal to 4? No it isn’t, and we write 0 in the field below 4.

128 64 32 16 8 4 2 1

111010

Is 1 greater than or equal to 2? No it isn’t, and we write 0 in the field below 2.

128 64 32 16 8 4 2 1

1110100

Is 1 greater than or equal to 1? Yes it is, and we write 1 in the field below 1.

128 64 32 16 8 4 2 1

11101001

So 233 converted to binary number is 11101001.
Conversion from binary to decimal numeral system

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If you want to convert a number from binary to decimal numeral system, you need to add
together the value of each number 1 appearing in the number.

For example, we want to convert 101101 to decimal number.

Value 64 32 16 8 4 2 1

Binary digits 1 0 1 1 0 0 1

We add together the values of all number 1 appearing in the number:

64 + 16 + 8 + 1 = 89

So the binary number 1011001 is equal to the decimal number 89.

5.6 Hexadecimal Numbers
The one main disadvantage of binary numbers is that the binary string equivalent of a large
decimal base-10 number can be quite long.
When working with large digital systems, such as computers, it is common to find binary
numbers consisting of 8, 16 and even 32 digits which makes it difficult to both read or write
without producing errors especially when working with lots of 16 or 32-bit binary numbers.
One common way of overcoming this problem is to arrange the binary numbers into groups
or sets of four bits (4-bits). These groups of 4-bits use another type of numbering system
also commonly used in computer and digital systems called Hexadecimal Numbers.

Hexadecimal Number String
The “Hexadecimal” or simply “Hex” numbering system uses the Base of 16 systems and
are a popular choice for representing long binary values because their format is quite
compact and much easier to understand compared to the long binary strings of 1’s and 0’s.
Being a Base-16 system, the hexadecimal numbering system therefore uses 16 (sixteen)
different digits with a combination of numbers from 0 through to 15. In other words, there
are 16 possible digit symbols.
However, there is a potential problem with using this method of digit notation caused by the
fact that the decimal numerals of 10, 11, 12, 13, 14 and 15 are normally written using two
adjacent symbols. For example, if we write 10 in hexadecimal, do we mean the decimal
number ten, or the binary number of two (1 + 0). To get around this tricky problem
hexadecimal numbers that identify the values of ten, eleven, . . ., fifteen are replaced with
capital letters of A, B, C, D, E and F respectively.

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Then in the Hexadecimal Numbering System we use the numbers from 0 to 9 and the
capital letters A to F to represent its Binary or Decimal number equivalent, starting with the
least significant digit at the right hand side.
As we have just said, binary strings can be quite long and difficult to read, but we can make
life easier by splitting these large binary numbers up into even groups to make them much
easier to write down and understand. For example, the following group of binary
digits 1101 0101 1100 11112 are much easier to read and understand than
11010101110011112 when they are all bunched up together.
In the everyday use of the decimal numbering system we use groups of three digits or 000’s
from the right hand side to make a very large number such as a million or trillion, easier for

us to understand and the same is also true in digital systems.
Hexadecimal Numbers is a more complex system than using just binary or decimal and is
mainly used when dealing with computers and memory address locations. By dividing a
binary number up into groups of 4 bits, each group or set of 4 digits can now have a possible
value of between “0000” (0) and “1111” (8+4+2+1 = 15) giving a total of 16different number
combinations from 0 to 15. Don’t forget that “0” is also a valid digit.
We remember from our first tutorial about Binary Numbers that a 4-bit group of digits is
called a “nibble” and as 4-bits are also required to produce a hexadecimal number, a hex
digit can also be thought of as a nibble, or half-a-byte. Then two hexadecimal numbers are
required to produce one full byte ranging from 00 to FF.
Also, since 16 in the decimal system is the fourth power of 2 (or 24 ), there is a direct
relationship between the numbers 2 and 16 so one hex digit has a value equal to four
binary digits so now q is equal to “16”.
Because of this relationship, four digits in a binary number can be represented with a single
hexadecimal digit. This makes conversion between binary and hexadecimal numbers very
easy, and hexadecimal can be used to write large binary numbers with much fewer digits.
The numbers 0 to 9 are still used as in the original decimal system, but the numbers
from 10 to 15 are now represented by capital letters of the alphabet from A to F inclusive
and the relationship between decimal, binary and hexadecimal is given below.
Hexadecimal Numbers

Decimal Number 4-bit Binary Number Hexadecimal Number
0
1 0000 0
2
3 0001 1
4
5 0010 2

0011 3

0100 4

0101 5

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6 0110 6
7 0111 7
8 1000 8
9 1001 9
10 1010 A
11 1011 B
12 1100 C
13 1101 D
14 1110 E
15 1111 F
16 0001 0000 10 (1+0)
17 0001 0001 11 (1+1)
Continuing upwards in groups of four

Using the original binary number from above 1101 0101 1100 11112 this can now be
converted into an equivalent hexadecimal number of D5CF which is much easier to read
and understand than a long row of 1’s and 0’s that we had before.
So by using hexadecimal notation, digital numbers can be written using fewer digits and
with a much less likelihood of an error occurring. Similarly, converting hexadecimal based
numbers back into binary is simply the reverse operation.
Then the main characteristics of a Hexadecimal Numbering System is that there are 16
distinct counting digits from 0 to F with each digit having a weight or value of 16 starting
from the least significant bit (LSB). In order to distinguish Hexadecimal numbers from
Denary numbers, a prefix of either a “#”, (Hash) or a “$” (Dollar sign) is used before the
actual Hexadecimal Number value, #D5CF or $D5CF.
As the base of a hexadecimal system is 16, which also represents the number of individual
symbols used in the system, the subscript 16 is used to identify a number expressed in
hexadecimal. For example, the previous hexadecimal number is expressed as: D5CF16
Counting using Hexadecimal Numbers

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So we now know how to convert 4 binary digits into a hexadecimal number. But what if we
had more than 4 binary digits how would we count in hexadecimal beyond the final letter F.
The simple answer is to start over again with another set of 4 bits as follows.
0…to…9, A, B, C, D, E, F, 10…to…19, 1A, 1B, 1C, 1D, 1E, 1F, 20, 21…. etc.
Do not get confused, 10 or 20 is NOT ten or twenty it is 1 + 0 and 2 + 0 in hexadecimal. In
fact, twenty does not even exist in hex. With two hexadecimal numbers we can count up
to FF which is equal to decimal 255. Likewise, to count higher than FF we would add a third
hexadecimal digit to the left so the first 3-bit hexadecimal number would be 10016, (25610)
and the last would be FFF16, (409510). The maximum 4-digit hexadecimal number
is FFFF16 which is equal to 65,535 in decimal and so on.

Representation of a Hexadecimal Number

MSB Hexadecimal Number LSB

168 167 166 165 164 163 162 161 160

4.3G 2.6G 16M 1M 65k 4k 256 16 1

This adding of additional hexadecimal digits to convert both decimal and binary numbers
into a Hexadecimal Number is very easy if there are 4, 8, 12 or 16 binary digits to convert.
But we can also add zeros to the left of the most significant bit, the MSB if the number of
binary bits is not a multiple of four.
For example, 110010110110012 is a fourteen-bit binary number that is to large for just three
hexadecimal digits only, yet too small for a four hexadecimal number. The answer is to
ADD additional zeros to the left most bit until we have a complete set of four bit binary
number or multiples thereof.

Adding of Additional 0’s to a Binary Number

Binary Number 0011 0010 1101 1001

Hexadecimal Number 3 2 D 9

The main advantage of a Hexadecimal Number is that it is very compact and by using a
base of 16 means that the number of digits used to represent a given number is usually
less than in binary or decimal. Also, it is quick and easy to convert between hexadecimal
numbers and binary.

Hexadecimal Numbers Example No1
Convert the following Binary number 1110 10102 into its Hexadecimal number equivalent.

DPP C2(b)

Binary Number = 111010102
Group the bits into four’s starting from the right hand side

= 1110 1010

Find the Decimal equivalent of each individual group

= 14 10 (in decimal)

Convert to Hexadecimal using the table above

=E A (in Hex)

Then, the hexadecimal equivalent of the binary number
1110 10102 is #EA16

Hexadecimal Numbers Example No2
Convert the following Hexadecimal number #3FA716 into its Binary equivalent, and also into
its Decimal or Denary equivalent using subscripts to identify each numbering system.

#3FA716

= 0011 1111 1010 01112

= (8192 + 4096 + 2048 + 1024 + 512 + 256 + 128 + 32 + 4 + 2 + 1)

= 16,29510

Then, the Decimal number of 16,295 can be represented as:-
#3FA716 in Hexadecimal
or
0011 1111 1010 01112 in Binary.

Hexadecimal Numbers Summary
Then to summarise. The Hexadecimal, or Hex, numbering system is commonly used in
computer and digital systems to reduce large strings of binary numbers into a sets of four
digits for us to easily understand. The word “Hexadecimal” means sixteen because this
type of digital numbering system uses 16 different digits from 0-to-9, and A-to-F.
To convert binary numbers into hexadecimal numbers we must first divide the binary
number up into a 4-bit binary word which can have any value from 010 (00002)
to 1510 (11112) representing the hexadecimal equivalent of 0 through to F.

DPP C2(b)

EXERCISE:

Try converting these numbers from binary to decimal:
 10
 111
 10101
 11110

Change the following number to binary (Base Two) 32

A. 00100000
B. 00100001
C. 01000000
D. 00110000

Change the following number to binary (Base Two)12
A. 00001100
B. 00001010
C. 10000100
D. 00000111

Change the following number to binary (Base Two)74
A. 00101010
B. 01100100
C. 01001010
D. 01011010

Change the following number to binary (Base Two)255
A. 11101110
B. 11111111
C. 01010101
D. 11111110

Change the following number to binary (Base Two)100
A. 01100100
B. 01101100
C. 01011001
D. 01101100

Change the following number to binary (Base Two)128
A. 10000100
B. 01000000
C. 10000000
D. 11000000

DPP C2(b)

Change the following number to binary (Base Two)63
A. 00011111
B. 00111100
C. 00111111
D. 01111110

Change the following number to binary (Base Two)23
A. 00010111
B. 00011011
C. 00010110
D. 00110111

Convert 00110110 to its Base Ten number

Convert 00000101 to its Base Ten number
Convert the binary number 11001 to decimal. The answer is

A. 25
B. 13
C. 3

Convert the decimal number 45 to binary
A. 11100
B. 101101
C. 10100

Convert the hexadecimal number B2 to binary
A. 100011
B. 11011
C. 10110010

Convert the binary number 11011 to hexadecimal
A. 1A
B. B1
C. 1B

Convert the decimal number 20 to hexadecimal
A. 14
B. 11
C. 1B

Convert the hexadecimal number 2C to decimal
A. 3A
B. 34
C. 44

DPP C2(b)

REFERENCE:

1. Hollembeak, B. (2015). Automotive electricy & electronics (6th ed.). New York: Cengage.
2. Hollembeak, B. (2015). Shop manual for Automotive electricity & electronics (6th ed.). USA:

Cengage.
3. Halderman, J. (2014). Automotive Electricity and Electronics (Fourth edition.). Boston:

Pearson.
4. Halderman, J. D. (2013). Advanced Automotive Electricity and Electronics. Boston:

Pearson.
5. Chapman, N. (2010). Principles of Electricity & Electronics for the Automotive

Technician (Second edition.). Clifton Park: Delmar.



DPP C2(b) -2

Kolej Kolej Kemahiran Tinggi MARA
Masjid Tanah, Melaka.

INFORMATION SHEET

PROGRAMME : DIPLOMA IN AUTOMOTIVE ENGINEERING TECHNOLOGY
SESSION :
CODE/COURSE : OCTOBER – DECEMBER 2021 SEMESTER : 3
LECTURER : SHEET NO : 1
DKV21273 STATICS &
DYNAMICS

MOHD FARDZLEE ABD PATAH WEEK : 1

TOPIC : FORCE VECTOR
SUB-TOPIC :
1.1Scalars and Vectors Quantities
1.2Vector Operation
1.3Vector Addition of Force
1.4Addition of a System of Coplanar
1.5Cartesian Vectors
1.6Additional and Subtraction of Cartesian Vectors
1.7Position Vectors
1.8Force Vector Directed Along a Line
1.9Dot Product

LEARNING After completing the course, students should be able to:
OUTCOME : 1. Determine moment in force system resultant for 3D.
2. Determine forces and moments in equilibrium state.
3. Determine the centroids and moment of inertia of rigid body.
4. Analyze the motion of a body in curvilinear and angular.

Page 1 of 37

DPP C2(b) -2

CONTENT:

PENGENALAN

Ilmu mekanik boleh dipecahkan kepada dua bahagian iaitu statik dan dinamik. Statik ditakrif
sebagai sains fizikal untuk menerangkan keadaan sesuatu jasad atau sistem yang berada dalam
keadaan keseimbangan atau pegun apabila dikenakan daya-daya. Sebenarnya, statik menyamai
kes yang khusus bagi dinamik, iaitu apabila pecutan sifar. Sesuatu jasad tidak akan mengalami
anjakan atau putaran apabila daya-daya yang bertindak padanya berada dalam keseimbangan. Ini
bermakna, daya-daya luar yang lebih dikenal sebagai daya tindakan, diimbangi daya tindak balas
yang diwujudkan pada sokong jasad tersebut.

Dalam bidang kejuruteraan, kebanyakan struktur yang dianalisis berada dalam keadaan statik,
misalnya bangunan, jambatan, jalan raya, empangan dan lain-lain. Bagaimanapun terdapat
beberapa struktur yang berada dalam pergerakan, contohnya jasad yang jatuh di bawah tarikan
graviti, kereta yang sedang bergerak, mesin yang berputar, getaran pegas dan lain-lain. Struktur
sedemikian digolongkan dalam mata pelajaran yang berasingan, yang lebih dikenal sebagai ilmu
dinamik. Terdapat pula sesetengah struktur yang memerlukan kedua-dua analisis statik dan
dinamik, contohnya analisis bangunan (terutama bangunan tinggi) yang mengambil kira kesan
getaran akibat gempa bumi atau angin yang kuat. Oleh sebab mata pelajaran statik adalah asas
dalam ilmu mekanik, maka subjek ini perlu difahami benar-benar supaya pelajar kejuruteraan
mempunyai kebolehan dan kemahiran untuk menyelesaikan sebarang masalah dengan cara yang
paling ringkas, padat dan tepat. Kebanyakan konsep yang digunakan dalam statik memerlukan
pengetahuan matematik asas dan tidak melibatkan formula-formula atau penyelesaian yang rumit.
Pemahaman kepada masalah atau rajah sangat penting sebelum membuat penyelesaian.

ISTILAH UMUM

Zarah: Jasad yang mempunyai saiz yang kecil dan boleh diabaikan ukuran-ukurannya.

Jasad tegar: Jasad yang terdiri daripada gabungan banyak zarah. Jasad yang tidak mengalami
ubah bentuk atau berlaku ubah bentuk yang boleh diabaikan apabila daya
dikenakan terhadapnya.

Masa: Kuantiti yang menunjukkan tempoh pergerakan sesuatu jasad khususnya dalam
mata pelajaran dinamik.

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DPP C2(b) -2

Jisim: Ukuran sifat tekun sesuatu bahan, iaitu rintangannya terhadap perubahan
Ruang: pergerakan.

Daya: Bidang geometri yang diduduki jasad atau daya dengan kedudukannya
dinyatakan dalam ukuran lelurus atau sudut dengan arah-arah yang tertentu.
Koordinat ditentukan daripada keadaan ruang, misalnya untuk dua dimensi
terdapat dua koordinat bebas dan bagi tiga dimensi terdapat tiga koordinat bebas.

Tindakan suatu jasad kepada jasad yang lain. Daya mempunyai ciri-ciri berikut :-
• magnitud (kuantiti atau nilai)
• arah atau sudut yang merujuk sesuatu garis rujukan
• titik tindakan

SKALAR DAN VEKTOR
Terdapat dua jenis kuantiti yang digunakan dalam statik iaitu kuantiti skalar dan kuantiti vektor.

Skalar ialah kuantiti yang mempunyai magnitud atau nilai sahaja, contohnya masa, luas, isi padu,
ketumpatan, kelikatan dan kelajuan.

Vektor ialah kuantiti yang mempunyai magnitud dan arah, misalnya halaju, anjakan, daya, pecutan,
momen dan momentum. Umumnya, setiap vektor diwakili sebatang anak panah untuk
menunjukkan arahnya.

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DPP C2(b) -2
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