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were 32 bits long and most arithmetic instructions supported 32-bit arithmetic,
and 24-bit in that the address bus was 24 bits long.
v A 16-bit integer can store 216 (or 65536) unique values. In an unsigned re-
presentation, these values are the integers between 0 and 65535; using two’a
component, possible values range from −32768 to 32767.
Activity 6.4.3 32-Bit Systems
The key learning points here are that:
(i) In computer architecture, 32-bit integers, memory addresses, or other data
units are those that are at most 32 bits (4 octets) wide. Also, 32-bit CPU and
ALU architecture are those that are based on registers, address buses, or data
buses of that size. 32-bit is also a term given to a generation of computers in
which 32-bit processors were the norm.
(ii) The range of integer values that can be stored in 32 bits is 0 through
4,294,967,295 or −2,147,483,648 through 2,147,483,647 using two’s comple-
ment encoding. Hence, a processor with 32-bit memory addresses can directly
access 4 gigabytes of byte-addressable memory memory.
Activity 6.4.4 Kibibyte vs Kilobyte
In this activity we will differentiate between kibibyte and kilobyte. First, we define the kibibyte. That is,
A kibibyte (a contraction of kilo binary byte) is a unit of information or computer storage, established by the International Electrtechnical Commission in 2000.
Its symbol is KiB.
1 kibibyte = 210 bytes = 1 024 byte
You should note that:
The kibibyte is closely related to the kilobyte, which can be used either as a
synonym for kibibyte or to refer to 10³ bytes = 1,000 bytes, whereby
1 kilobyte = 103 = 1000 byte
Thus, the term kibibyte has evolved to refer exclusively to 1,024 bytes.
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You should note that:
If one expects power-of-two values to refer to capacity, and manufacturers use power-
of-ten values, the difference could be substantial.
(i) With a kilobyte (1024 versus 1000), the difference is 2.4%.
(ii) With megabyte (1024² or 1,048,576, versus 1,000,000 - a difference of 4.9%.
(iii) With “gigabytes”, if one uses 1024³, the size of a drive would be expected to
be 1,073,741,824 bytes per gigabyte versus a mere 1,000,000,000 - a difference
of 7.4%.
This should tell you that, confusion can be compounded by the use of both 1,024 and
1,000 in a single definition.
The quoted capacity of 3½ inch HD floppy disks is 1.44 MB, where MB
stands for 1000 times 1024 bytes. The total capacity is thus 1474560 bytes,
or approximately 1.41 MiB.
Example
The above relation can be shown as follows:
1.44 MB = 1.44 × 1000 × 1024 = 0 bytes
Divide this by 1,048,576, i.e.
1.44 × 1000 × 1024
= 1.40625 MiB
1,048,576
Thus, 1.44 MB floppy disks can store 1474560 bytes of data when MB means 1000
times 1024 bytes.
Self Evaluation 6
1. Explain the meaning of the term program in computing.
2. Find the number of input lines that can be coded to 32 bit word
3. Explain what is meant by an instruction and register in computing.
4. Express 3.7 MB in (i) bytes (ii) MiB
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Solution to Self Evaluation 1
1. (a) n = 6.1144 ×1017
i
m−3
(b) 0.01859 s/m
2. This is because, by addition of donor impurity, the number of electrons avail-
able for conduction purposes becomes more than the number of holes available
intrinsically. But the total charge of the semiconductor does not change because
the donor impurity brings in as much negative charge (by way of electrons) as
positive charge (by way of protons in its nucleus).
3. Barrier voltage depends on doping density, electronic charge and temperature.
For a given junction, the first two factors are constant, thus making depending
on temperature. With increase in temperature, more minority charge carriers
are reduced, leading to their increased drift across the junction. As a result,
equilibrium occurs at lower barrier potential. It is found that both for Ge and Si,
decreases by about 2mV / ºC.
Solution to Self Evaluation 2
1. Physical features BJT are that
- The base is lightly doped, with high resistivity material.
- The collector surrounds the emitter region, making it almost impossible for the
electrons injected into the base region to escape being collected, thus making
the resulting value of α very close to unity, and so, giving the transistor a large
β. A cross section view of a BJT indicates that the collector–base junction has
a much larger area than the emitter–base junction.
- The bipolar junction transistor, unlike other transistors, is not a symmetrical
device. This means that interchanging the collector and the emitter makes the
transistor leave the forward active mode and start to operate in reverse mode.
Because the transistor’s internal structure is usually optimized to forward-mode
operation, interchanging the collector and the emitter makes the values of α
and β in reverse operation much smaller than those found in forward operation;
often the α of the reverse mode is lower than 0.5. The lack of symmetry is
primarily due to the doping ratios of the emitter and the collector. The emitter
is heavily doped, while the collector is lightly doped, allowing a large reverse
bias voltage to be applied before the collector–base junction breaks down.
The collector–base junction is reverse biased in normal operation.
- The reason the emitter is heavily doped is to increase the emitter injection
efficiency: the ratio of carriers injected by the emitter to those injected by the
base.
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- For high current gain, most of the carriers injected into the emitter–base
junction must come from the emitter.
Small changes in the voltage applied across the base–emitter terminals causes the
current that flows between the emitter and the collector to change significantly. This effect can be used to amplify the input voltage or current. BJTs can be thought of
as voltage-controlled current sources, but are more simply characterized as current-
controlled current sources, or current amplifiers, due to the low impedance at the
base.
NPN is one of the two types of bipolar transistors, in which the letters “N” and “P”
refer to the majority charge carriers inside the different regions of the transistor. Most
bipolar transistors used today are NPN, because electron mobilty is higher than hole
mobility in semiconductors, allowing greater currents and faster operation.
NPN transistors consist of a layer of P-doped semiconductor (the “base”) between
two N-doped layers. A small current entering the base in common-emitter mode is
amplified in the collector output.
The arrow in the NPN transistor symbol is on the emitter leg and points in the direction
of the conventional current flow when the device is in forward active mode.
A convenient mnemonic device for identifying the symbol for the NPN transistor
and, by elimination, the PNP transistor is “NPN is Not Pointed iN.”
Solution to Self Evaluation 3
1. A specific op-amp may be chosen for its: open loop gain, bandwidth, noise
performance, input impedance, power consumption, or a compromise
between any of these factors.
2. 84.42 mV
3 The output voltage is
⎛ 330
330 ⎞
V = −
V +
V
(
+ 33V )
0
1
2
2
⎝⎜ 33
10
⎠⎟ = − 10V1
= − 1
⎡ 0 50sin 1000
⎤
⎣ (
(
t) + 33 10sin 3000
(
(
t)
⎦
= ⎡0.5sin 1000
⎣
(
t) + 0.33sin 3000
(
t)⎤
⎦
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Soultions to Self Evaluation 4
1. The following four steps will be used for this purpose.
Step 1.
0
1
1
1
Step 2.
½
¼
1/8
Step 3.
½
¼
1/8
Step 4.
½ + ¼ +1/8 = 0.875
∴0.111 = 0.875
2
10
2. 0.77 = 0.110001
10
2
3. 25.625 = 11001.101
10
2
4. i- 13 and 26;
ii- 13 and 6.5
This implies that shifting binary point to right is equivalent to multiplying the
number by 2, while shifting the binary point to the left is equivalent to dividing the
number by 2
5. a. 111 2
b 0010 2
c. 0011 2
6. (i) 11101000
(ii) 1001111
7. (c) i. X = AB + C
ii. X = 1; and X = 1
8 The logic equation which provides the switching function is given by
F = C A.B + C .A.B + C .A.B + C .A.B
0
1
2
3
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For A = B = 0, we get F = C ,0
For A = 0, B = 1, we get F = C1
For A = 1, B = 0, we get F = C2
For A = 1, B = 1, we get F = C3
Thus for C to be selected AB = 10, which enables and will appear at the
2
X 2
C2
output F
Solution to Self evaluation 5
1. (a) -Finite Aperture Time: The sample and hold takes a period of time to capture a sample of the sensor signal. This is called the aperture time. Since the signal
will vary during this time, the sampled signal can be slightly off.
-Signal Feedthrough: When the sample and hold is not connected to the signal,
the value being held should remain constant. Unfortunately, some signal does
bleed through the switch to the capacitor, causing the voltage being held to change
slightly.
-Signal Droop: The voltage being held on the capacitor starts to slowly decrease
over time if the signal is not sampled often enough.
(b) The main solution to these problems is to have a small aperture time relative to
the sampling period. This means that if the HCI designer uses a high sampling
rate, the aperture time of the sample and hold must be quite small.
2 - Magnetic isolation is primarily used for coupling power from the computer or
the wall outlet to the sensor. This is done through the use of a transformer.
- Optical isolation is used for coupling the sensor signal to the data acquisition
input. This is usually done through the use of a light emitting diode and a pho-
todetector. This can be integrated into a single IC package such as the 6N139.
The Basic Theory Optical isolation has two basic elements: a light source (usually
a light emitting diode) and a photo-sensitive detector. These two elements are
positioned facing one another and inserted in an electrical circuit to form an op-
tocoupler. The key property of an optocoupler is that there is an insulating gap
between the light source and the detector. No current passes through this gap,
only the desired light waves representing data. Thus the two sides of the circuit
are effectively «isolated» from one another. Primary Application In data com-
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munications, the primary application for optical isolation is in a point-to-point
data circuit that covers a distance of several hundred feet or more. Because the
connected devices are presumably on different power circuits, a ground potential
difference likely exists between them. When such a condition exists, the voltage
of «ground» can be different, sometimes by several hundred volts.
Where a ground potential difference exists, a phenomenon called ground loop-
ing can occur. In this phenomenon, current will flow along the data line in an
effort to equalize the ground potential between the connected devices. Ground
looping can, at the very least, severely garble communications--if not damage
hardware!
Optical isolation solves the problem of ground looping by effectively lifting the
connection between the data line and «ground» at either end of the line. If an
optically coupled connection exists at each end, the data traffic «floats» above
the volatility of ground potential differences.
Solution to self Assessment 6.
1. In computing, a program is a specific set of ordered operations for a computer
to perform. In the modern computer, the program contains a one-at-a-time se-
quence of instructions that the computer follows. Typically, the program is put
into a storage area accessible to the computer. The computer gets one instruction
and performs it and then gets the next instruction. The storage area or memory
can also contain the data that the instruction operates on. (Note that a program
is also a special kind of “data” that tells how to operate on “application or user
data.”)
Programs can be characterized as interactive or batch in terms of what drives them
and how continuously they run. An interactive program receives data from an
interactive user (or possibly from another program that simulates an interactive
user). A batch program runs and does its work, and then stops. Batch programs
can be started by interactive users who request their interactive program to run
the batch program. A command interpreter or a Web browser is an example of an
interactive program. A program that computes and prints out a company payroll
is an example of a batch program. Print jobs are also batch programs.
When you create a program, you write it using some kind of computer language.
Your language statements are the source program. You then “compile” the source
program (with a special program called a language compiler) and the result
is called an object program. There are several synonyms for object program,
including object module and compiled program. The object program contains
the string of 0s and 1s called machine language that the logic processor works
with.
The machine language of the computer is constructed by the language compiler
with an understanding of the computer’s logic architecture, including the set
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of possible computer instructions and the length (number of bits) in an instruc-
tion
2. For 32-bit word, the total number of input lines = 232 − 1 = 4294967295
3. Instruction
An instruction is an order given to a computer processor by a computer program. At
the lowest level, each instruction is a sequence of 0s and 1s that describes a physical
operation the computer is to perform (such as “Add”) and, depending on the parti-
cular instruction type, the specification of special storage areas called registers that
may contain data to be used in carrying out the instruction, or the location in com-
puter memory of data. In a computer’s assembler language, each language statement
generally corresponds to a single processor instruction. In high-level languages, a
language statement generally results (after program compilation) in multiple pro-
cessor instructions
Register.
In a computer, a register is one of a small set of data holding places that are
part of a computer processor. A register may hold a computer instruction, a storage address, or any kind of data (such as a bit sequence or individual charac-
ters). Some instructions specify registers as part of the instruction. For example,
an instruction may specify that the contents of two defined registers be added
together and then placed in a specified register. A register must be large enough
to hold an instruction - for example, in a 32-bit instruction computer, a register
must be 32 bits in length. In some computer designs, there are smaller registers
- for example, half-registers - for shorter instructions. Depending on the processor
design and language rules, registers may be numbered or have arbitrary names.
4. (i) 3788800 bytes (ii) 3.61 MiB
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XI. Compiled list of all key concepts
Intrinsic conductivity- Is the conductivity of a semiconductor that is associated with
the semiconductor itself and is not contributed by impurities. At any given temperature
equal numbers of charge carriers: electrons and holes are thermally generated, and
it is these which give rise to the intrinsic conductivity.
Intrinsic semiconductor - Is a pure semiconductor in which the electrons and hole
densities are equal under condition of thermal equilibrium. In practice absolute purity
is unattainable and the term is applied to nearly pure materials.
Extrinsic semiconductor – Is asemiconductor in which the charge carrier concen-
tration is dependent is dependent upon impurities or other imperfections.
Depletion layer: Is a space-charge region in a semiconductor in which there is a net
charge due to insufficient mobile charge carriers. Depletion layers are formed, for
example, at the interface between a p-type and n-type semiconductor in the absence
of an applied field. They are also formed at the interface of a metal and a semicon-
ductor.
Rectifier- Is an electrical device that permits current to flow in only one direction
and can thus make alternating into direct current. It operates either by suppressing or
attenuating alternate half-cycles of the current waveform or by reversing them. The
most common rectifiers are semiconductor diodes.
Threshold voltage- Is the voltage at which a particular characteristic of an electric
device first occurs. For an insulated-gate field-effect transistor, it is the voltage at
which channel formation occurs.
Leakage- Is the flow of an electric current, due to imperfect insulation, in a path
other than that intended.
Leakage current- Is a fault due to leakage. It is small in magnitude compared with
that of a short circuit.
Amplifier- Is a device for reproducing an electrical input at an increased intensity.
If an increased e.m.f.is produced operating into a high impedance, the device is a
voltage amplifier, and if the output prodvides an appreciable current flow into a re-
lativiely low impedance, the device is a power amplifier. The most commonly used
amplifiers operate by transistors.
Logic circuit- Is a circuit designed to perform a particular logical function based on
the concepts of “and”, “either-or”, etc. Normally these circuits operate between two
discrete voltage levels, i.e. high and low logic levels, and are described as binary logic
circuits. Logic using three or more logic levels is possible, but not common.
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Logic gates- Is a device used to implement the elementary logic functions. These
basic gates include among others: AND gate; Inverter (NOT gate); NAND gate;
NOR gate…
Transducers- Is any device for converting a nonelectrical signals (or vice versa), the
variations in the electrical signal being a function of the input. The transducers are
used as measuring instruments and in the electroacoustic field, the term being applied
to gramophone pick-ups, the microphones, and loudspeakers. The physical quantity
measured by the transducer is the measurand, the portion of the transducer in which
the output originates is the transducer elements, and the nature of the operation is
the transduction principle. The device in the transducer that responds directly to the
measurand is the sensing element and the upper and lower limits of the measurand
value for which the trandsucer provides a useful output is the dynamic range.
Microprocessor- Is the integration of a number of useful functions into a single IC
package. These functions are the ability to execute a stored set of instructions to carry
out user defined tasks, and the ability to be able to access external memory chips to
both read and write data from and to the memory.