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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 b -ary positional representation system uses the position of digits ranging from0 to b -1 to denote a number. The quantity b is known as the base of the number system. Mathematically, positional systems represent the positiveinteger n as

d k d k 0 b 1 n k 0 d k b k
and we succinctly express n in base- b as n b d N d N 1 d 0 . The number 25 in base 10 equals 2 10 1 5 10 0 , so that the digits representing this number are d 0 5 , d 1 2 , and all other d k equal zero. This same number in binary (base 2) equals 11001( 1 2 4 1 2 3 0 2 2 0 2 1 1 2 0 )and 19 in hexadecimal (base 16). Fractions between zero and one are represented the same way.
d k d k 0 b 1 f k -1 d k b k
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

how does Neisseria cause meningitis
Nyibol Reply
what is microbiologist
Muhammad Reply
what is errata
Muhammad
is the branch of biology that deals with the study of microorganisms.
Ntefuni Reply
What is microbiology
Mercy Reply
studies of microbes
Louisiaste
when we takee the specimen which lumbar,spin,
Ziyad Reply
How bacteria create energy to survive?
Muhamad Reply
Bacteria doesn't produce energy they are dependent upon their substrate in case of lack of nutrients they are able to make spores which helps them to sustain in harsh environments
_Adnan
But not all bacteria make spores, l mean Eukaryotic cells have Mitochondria which acts as powerhouse for them, since bacteria don't have it, what is the substitution for it?
Muhamad
they make spores
Louisiaste
what is sporadic nd endemic, epidemic
Aminu Reply
the significance of food webs for disease transmission
Abreham
food webs brings about an infection as an individual depends on number of diseased foods or carriers dully.
Mark
explain assimilatory nitrate reduction
Esinniobiwa Reply
Assimilatory nitrate reduction is a process that occurs in some microorganisms, such as bacteria and archaea, in which nitrate (NO3-) is reduced to nitrite (NO2-), and then further reduced to ammonia (NH3).
Elkana
This process is called assimilatory nitrate reduction because the nitrogen that is produced is incorporated in the cells of microorganisms where it can be used in the synthesis of amino acids and other nitrogen products
Elkana
Examples of thermophilic organisms
Shu Reply
Give Examples of thermophilic organisms
Shu
advantages of normal Flora to the host
Micheal Reply
Prevent foreign microbes to the host
Abubakar
they provide healthier benefits to their hosts
ayesha
They are friends to host only when Host immune system is strong and become enemies when the host immune system is weakened . very bad relationship!
Mark
what is cell
faisal Reply
cell is the smallest unit of life
Fauziya
cell is the smallest unit of life
Akanni
ok
Innocent
cell is the structural and functional unit of life
Hasan
is the fundamental units of Life
Musa
what are emergency diseases
Micheal Reply
There are nothing like emergency disease but there are some common medical emergency which can occur simultaneously like Bleeding,heart attack,Breathing difficulties,severe pain heart stock.Hope you will get my point .Have a nice day ❣️
_Adnan
define infection ,prevention and control
Innocent
I think infection prevention and control is the avoidance of all things we do that gives out break of infections and promotion of health practices that promote life
Lubega
Heyy Lubega hussein where are u from?
_Adnan
en français
Adama
which site have a normal flora
ESTHER Reply
Many sites of the body have it Skin Nasal cavity Oral cavity Gastro intestinal tract
Safaa
skin
Asiina
skin,Oral,Nasal,GIt
Sadik
How can Commensal can Bacteria change into pathogen?
Sadik
How can Commensal Bacteria change into pathogen?
Sadik
all
Tesfaye
by fussion
Asiina
what are the advantages of normal Flora to the host
Micheal
what are the ways of control and prevention of nosocomial infection in the hospital
Micheal
what is inflammation
Shelly Reply
part of a tissue or an organ being wounded or bruised.
Wilfred
what term is used to name and classify microorganisms?
Micheal Reply
Binomial nomenclature
adeolu
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Source:  OpenStax, Fundamentals of electrical engineering i. OpenStax CNX. Aug 06, 2008 Download for free at http://legacy.cnx.org/content/col10040/1.9
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