<< Chapter < Page Chapter >> Page >

Introduction

Often we want to represent data, e.g. characters, images, in a binary form. By binary form we mean representing by the symbols "0", and "1". Using binary representation allows us to conveniently store, retrieve, and manipulate them with a computer. To work with data in binary formwe must have a fixed way of encoding (representing) a fixed data stream. The set of all binary sequences in a representation of some data is called a code . (Note that this has nothing to do with cryptology). Usually we refer to the data that we want to represent by bits as a source .

Representing english characters

Let us consider a very practical example of the above ideas. Let our source be a stream of English characters. Now we want to represent this stream of characters as bits, say to store it on a computer or send it over the Internet. First we need to know the number of such characters,which is (traditonally) conveniently set to 128. The number 128 is obtained by summing upper case charachters (26), lower case (26), digits (10), brackets and punctuation (20), odd characters (14) (the "&" is an odd character), and control characters (32).

Obviously we need to have a unique representation of each of the 128 characters, this can e.g. be obtained by exhausting the 128 bit combinations which concatenating 7 bits give. Thus we have devised an 7-bit code. A well known 7-bit code is ASCII , short for "American Standard Code for Information Interchange". Adding a parity bit for error control to the ASCII code forms an 8-bit code. As anexample, the representation of an "A" in ASCII is 1000001.

Now, one can ask whether the 7-bit ASCII code is an optimal representation in terms of using, on average, the minimum number of bits representing the English characters? We will return to this question later (in example 3 ).

Got questions? Get instant answers now!

Minimal representation

When representing a source we want to use as few bits as possible, as this will imply that less disk space is required for storage or that transmission over the Internet is quicker. However, we do not want to use so few bits that the receiver cannot determine what was sent or stored.

So, for a given source what is the minimal representation? Here we consider the minimal representation as the representation that uses the minimum number of bits (on average) to encode the source without errors.According to Shannon's source coding theorem , a source that produces statistically independent outcomes, the minimum average number of bits per symbol is the entropy of the source! (A classical example of a source that produces statistically independent outcomes is throwing a die.)

Average indicates that the number of bits used for a specific symbol may be different from the number of bits representing another. E.g., as opposed to ASCII coding, we might represent an "A" with 7 bits, but an "E" with 3 bits.But it also implies that when you receive a series of symbols, the number you receive per time unit, say per second, will not be exactly the same, but averaged over a long term period, the rate is proportional to time with the rate per symbolas the proportionality constant.

Questions & Answers

what is mutation
Janga Reply
what is a cell
Sifune Reply
how is urine form
Sifune
what is antagonism?
mahase Reply
classification of plants, gymnosperm features.
Linsy Reply
what is the features of gymnosperm
Linsy
how many types of solid did we have
Samuel Reply
what is an ionic bond
Samuel
What is Atoms
Daprince Reply
what is fallopian tube
Merolyn
what is bladder
Merolyn
what's bulbourethral gland
Eduek Reply
urine is formed in the nephron of the renal medulla in the kidney. It starts from filtration, then selective reabsorption and finally secretion
onuoha Reply
State the evolution relation and relevance between endoplasmic reticulum and cytoskeleton as it relates to cell.
Jeremiah
what is heart
Konadu Reply
how is urine formed in human
Konadu
how is urine formed in human
Rahma
what is the diference between a cavity and a canal
Pelagie Reply
what is the causative agent of malaria
Diamond
malaria is caused by an insect called mosquito.
Naomi
Malaria is cause by female anopheles mosquito
Isaac
Malaria is caused by plasmodium Female anopheles mosquitoe is d carrier
Olalekan
a canal is more needed in a root but a cavity is a bad effect
Commander
what are pathogens
Don Reply
In biology, a pathogen (Greek: πάθος pathos "suffering", "passion" and -γενής -genēs "producer of") in the oldest and broadest sense, is anything that can produce disease. A pathogen may also be referred to as an infectious agent, or simply a germ. The term pathogen came into use in the 1880s.[1][2
Zainab
A virus
Commander
Definition of respiration
Muhsin Reply
respiration is the process in which we breath in oxygen and breath out carbon dioxide
Achor
how are lungs work
Commander
where does digestion begins
Achiri Reply
in the mouth
EZEKIEL
what are the functions of follicle stimulating harmones?
Rashima Reply
stimulates the follicle to release the mature ovum into the oviduct
Davonte
what are the functions of Endocrine and pituitary gland
Chinaza
endocrine secrete hormone and regulate body process
Achor
while pituitary gland is an example of endocrine system and it's found in the Brain
Achor
what's biology?
Egbodo Reply
Biology is the study of living organisms, divided into many specialized field that cover their morphology, physiology,anatomy, behaviour,origin and distribution.
Lisah
biology is the study of life.
Alfreda
Biology is the study of how living organisms live and survive in a specific environment
Sifune
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Information and signal theory. OpenStax CNX. Aug 03, 2006 Download for free at http://legacy.cnx.org/content/col10211/1.19
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Information and signal theory' conversation and receive update notifications?

Ask