- Arithmetic and logic in computer system
Arithmetic and Logic in Computer Systems provides a useful guide to a
fundamental subject of computer science and engineering. Algorithms for
performing operations like addition, subtraction, multiplication, and
division in digital computer systems are presented, with the goal of
explaining the concepts behind the algorithms, rather than addressing
any direct applications. Alternative methods are examined, and
explanations are supplied of the fundamental materials and reasoning
behind theories and examples.
- Recticing Software engineering in 21st century
This technological manual explores how software engineering
principles can be used in tandem with software development tools to
produce economical and reliable software that is faster and more
accurate. Tools and techniques provided include the Unified Process for
GIS application development, service-based approaches to business and
information technology alignment, and an integrated model of application
and software security. Current methods and future possibilities for
software design are covered.
In Electrical Engineering:
The voltage produced by a battery is characterized by one real number
(called potential), such as +12 volts or -12 volts. But the "AC"
voltage in a home requires two parameters. One is a potential, such as
120 volts, and the other is an angle (called phase). The voltage is said
to have two dimensions. A 2-dimensional quantity can be represented
mathematically as either a vector or as a complex number (known in the
engineering context as phasor). In the vector representation, the
rectangular coordinates are typically referred to simply as X and Y. But
in the complex number representation, the same components are referred
to as real and imaginary. When the complex number is purely imaginary,
such as a real part of 0 and an imaginary part of 120, it means the
voltage has a potential of 120 volts and a phase of 90�, which is
physically very real.
Application in electronics engineering
Information that expresses a single dimension, such as linear
distance, is called a scalar quantity in mathematics. Scalar numbers are
the kind of numbers students use most often. In relation to science,
the voltage produced by a battery, the resistance of a piece of wire
(ohms), and current through a wire (amps) are scalar quantities.
When electrical engineers analyzed alternating current circuits, they
found that quantities of voltage, current and resistance (called
impedance in AC) were not the familiar one-dimensional scalar quantities
that are used when measuring DC circuits. These quantities which now
alternate in direction and amplitude possess other dimensions (frequency
and phase shift) that must be taken into account.
In order to analyze AC circuits, it became necessary to represent
multi-dimensional quantities. In order to accomplish this task, scalar
numbers were abandoned andcomplex numberswere used to express the two
dimensions of frequency and phase shift at one time.
In mathematics, i is used to represent imaginary numbers. In the
study of electricity and electronics, j is used to represent imaginary
numbers so that there is no confusion with i, which in electronics
represents current. It is also customary for scientists to write the
complex number in the form a+jb.
In electrical engineering, the Fourier transform is used to analyze
varying voltages and currents. The treatment of resistors, capacitors,
and inductors can then be unified by introducing imaginary,
frequency-dependent resistances for the latter two and combining all
three in a single complex number called the impedance. (Electrical
engineers and some physicists use the letter j for the imaginary unit
since i is typically reserved for varying currents and may come into
conflict with i.) This approach is called phasor calculus. This use is
also extended into digital signal processing and digital image
processing, which utilize digital versions of Fourier analysis (and
wavelet analysis) to transmit, compress, restore, and otherwise process
digital audio signals, still images, andvideosignals.
Introduce the formula E = I � Z where E is voltage, I is current, and Z is impedance.
Complex numbers are used a great deal in electronics. The main reason
for this is they make the whole topic of analyzing and understanding
alternating signals much easier. This seems odd at first, as the concept
of using a mix of real and 'imaginary' numbers to explain things in the
real world seem crazy!. To help you get a clear picture of how they're
used and what they mean we can look at a mechanical example...
We can now reverse the above argument when considering a.c. (sine
wave) oscillations in electronic circuits. Here we can regard the
oscillating voltages and currents as 'side views' of something which is
actually 'rotating' at a steady rate. We can only see the 'real' part of
this, of course, so we have to 'imagine' the changes in the other
direction. This leads us to the idea that what the oscillation voltage
or current that we see is just the 'real' portion' of a 'complex'
quantity that also has an 'imaginary' part. At any instant what we see
is determined by aphase anglewhich varies smoothly with time.
We can now consider oscillating currents and voltages as being
complex values that have a real part we can measure and an imaginary
part which we can't. At first it seems pointless to create something we
can't see or measure, but it turns out to be useful in a number of ways.
- It helps us understand the behaviour of circuits which contain reactance (produced by capacitors or inductors) when we apply a.c. signals.
- It gives us a new way to think about oscillations. This is useful when we want to apply concepts like the conservation of energy to understanding the behaviour of systems which range from simple a mechanical pendulums to a quartz-crystal oscillator.
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