Explains how digital systems such as the computer represent numbers. Covers the basics of boolean algebra and binary math.
Computer architecture
To understand digital signal processing systems, we must
understand a little about how computers compute. The moderndefinition of a
computer is an electronic
device that performs calculations on data, presenting theresults to humans or other computers in a variety of
(hopefully useful) ways.
Organization of a simple computer
Generic computer hardware organization.
The generic computer contains
input devices (keyboard, mouse, A/D (analog-to-digital) converter,
etc.), a
computational unit , and output
devices (monitors, printers, D/A converters). Thecomputational unit is the computer's heart, and usually
consists of a
central processing unit (CPU), a
memory , and an input/output
(I/O) interface. What I/O devices might be present on a givencomputer vary greatly.
A simple computer operates fundamentally in
discrete time. Computers are
clocked devices, in which
computational steps occur periodically according to ticksof a clock. This description belies clock speed: When you
say "I have a 1 GHz computer," you mean that your computertakes 1 nanosecond to perform each step. That is
incredibly fast! A "step" does not, unfortunately,necessarily mean a computation like an addition; computers
break such computations down into several stages, whichmeans that the clock speed need not express the
computational speed. Computational speed is expressed inunits of millions of instructions/second (Mips). Your 1
GHz computer (clock speed) may have a computational speedof 200 Mips.
Computers perform integer (discrete-valued)
computations. Computer calculations can be
numeric (obeying the laws of arithmetic), logical (obeyingthe laws of an algebra), or symbolic (obeying any law you
like).
An example of a symbolic
computation is sorting a list of names. Each computer instruction that performs an elementary
numeric calculation --- an addition, a multiplication, or adivision --- does so only for integers. The sum or product
of two integers is also an integer, but the quotient oftwo integers is likely to not be an integer. How does a
computer deal with numbers that have digits to the rightof the decimal point? This problem is addressed by using
the so-called
floating-point representation of real numbers. At its heart, however,
this representation relies on integer-valued computations.
Representing numbers
Focusing on numbers, all numbers can represented by the
positional notation system .
Alternative number representation systems
exist. For example, we could use stick figure counting orRoman numerals. These were useful in ancient times, but very
limiting when it comes to arithmetic calculations: ever triedto divide two Roman numerals? The
-ary positional
representation system uses the position of digits ranging from0 to
-1 to denote a number.
The quantity
is known as the
base of the number system.
Mathematically, positional systems represent the positiveinteger
as
and we succinctly express
in
base-
as
.
The number 25 in base 10 equals
,
so that the
digits representing this number are
,
, and all other
equal zero. This same number in
binary (base 2) equals 11001(
)and 19 in hexadecimal (base 16). Fractions between zero and
one are represented the same way.
All numbers can be represented by their
sign, integer and fractional parts.
Complex numbers can be thought of as two
real numbers that obey special rules to manipulate them.
Questions & Answers
A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?
A mouse of mass 200 g falls 100 m down a vertical mine shaft and lands at the bottom with a speed of 8.0 m/s. During its fall, how much work is done on the mouse by air resistance
Chemistry is a branch of science that deals with the study of matter,it composition,it structure and the changes it undergoes
Adjei
please, I'm a physics student and I need help in physics
Adjanou
chemistry could also be understood like the sexual attraction/repulsion of the male and female elements. the reaction varies depending on the energy differences of each given gender. + masculine -female.
Pedro
A ball is thrown straight up.it passes a 2.0m high window 7.50 m off the ground on it path up and takes 1.30 s to go past the window.what was the ball initial velocity
2. A sled plus passenger with total mass 50 kg is pulled 20 m across the snow (0.20) at constant velocity by a force directed 25° above the horizontal. Calculate (a) the work of the applied force, (b) the work of friction, and (c) the total work.
you have been hired as an espert witness in a court case involving an automobile accident. the accident involved car A of mass 1500kg which crashed into stationary car B of mass 1100kg. the driver of car A applied his brakes 15 m before he skidded and crashed into car B. after the collision, car A s
can someone explain to me, an ignorant high school student, why the trend of the graph doesn't follow the fact that the higher frequency a sound wave is, the more power it is, hence, making me think the phons output would follow this general trend?
Nevermind i just realied that the graph is the phons output for a person with normal hearing and not just the phons output of the sound waves power, I should read the entire thing next time
Joseph
Follow up question, does anyone know where I can find a graph that accuretly depicts the actual relative "power" output of sound over its frequency instead of just humans hearing
Joseph
"Generation of electrical energy from sound energy | IEEE Conference Publication | IEEE Xplore" ***ieeexplore.ieee.org/document/7150687?reload=true
A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?
