CSE 111

Representing Nonnumeric Data in a Computer

Text

American Code for Standard Information Interchange (ASCII)7-bitEnglishFor codes, see

http://www.asciitable.comhttp://en.wikipedia.org/wiki/File:ASCII_Code_Chart-Quick_ref_card.png

Examples1000001 represents A1001110 represents N1100001 represents a1110010 represents r

Text

Unicode16-bitInternationalWindows

ASCII vs. UnicodeAdvantagesDisadvantages

Images

A grid represents pixels in the imageThe color of each pixel can be black or whiteA bit represents the color of the pixel

Each bit can be a 0 (white) or a 1 (black)

ExampleConsider the following image

Images

Example Con’t.

Images

Example Con’t.How many bits are required to render the letters UB

as an image? 9,350 bits

11 0

8 5

Images

ColorEach pixel is represented by multiple bits which

indicate how much of each color is needed to create the desired color

Examples

R ed G reen

Ye llo w (1 0 0 % R e d , 1 0 0 % G ree n , 5 0 % B lu e )O ran g e (1 0 0 % R e d , 4 0 % G reen )

L ig h t B lu e (6 0 % R e d , 6 0 % G ree n , 1 0 0 % B lu e )G rey (5 0 % R ed , 5 0 % B lu e , 5 0 % G ree n )

B ro w n (5 0 % R ed , 2 5 % G reen , 2 5 % B lu e )B lu e

P u rp le (5 0 % R ed , 5 0 % B lu e )

Images

ColorExample

Use 8-bits to represent redUse 8-bits to represent blueUse 8-bits to represent greenResult

Each pixel can take on 16,777,216 possible colors

Using this scheme, the previous example (UB) would require 224,400 bits 24-fold increase over black & white

Colors in Microsoft WindowsLowMediumHigh

Error Detection

A code is said to be n-error detecting if the minimum of n errors that cannot be detected is n+1Error defined as a bit being complemented

erroneously

Example2-out-of-5 codes

Single error detectingExample

A 01010 transmitted as 01110Error can be detected

Error Detection

ExampleParity

A parity bit can be concatenated to a code word that does not incorporate error detection to make it a single error detecting codeDetects an odd number of errors

Even ParityThe code word (including the parity bit) has an even number of

1’s

Odd ParityThe code word (including the parity bit) has an odd number of

1’s

ExampleThe 7-bit ASCII code is often concatenated with a parity bitH (odd parity) 11001000

Error Correction

It is possible to construct a code whereby a finite number of errors can be corrected

Error Correction

POSTNET ExampleUsed by US Postal Service to encode ZIP codesCheck Sum Digits for Error Correction2-out-of-5 code is used to encode each digitA checksum digit is appended to ZIP code so that

sum is a multiple of 10If a single digit is in error (number of 1’s 2) the

checksum can be used to correct check digit

Entire code is encapsulated between an initial and a guard bit (logic-1)

Z IP D ig it

S u m+

C h eck S u m

D igitm o d 1 0

0

Error Correction

POSTNET ExampleBarcode sprayed on deliverable mail for automated

mail processing

1234567890

Error Correction

POSTNET ExampleCurrently Used Formats

5 Digit ZIP CodeA Code

9 Digit ZIP and ZIP + 4 CodeC CodeAllows sorting to individual delivery carrier and in some cases,

sequencing

11 Delivery Point Bar Code (DPBC)Consists of 5 digit ZIP, ZIP + 4, and delivery point codeAllows sorting to delivery point (address) sequence

Error Correction

POSTNET ExampleZIP digits and checksum digit are encapsulated

between two one’sExample

1 7

4 2Z IP C o d e

6 0

Error Correction

Another POSTNET ExampleWhat ZIP Code is encoded by the following

POSTNET code?

Error Correction

Another POSTNET ExampleWhat ZIP Code is encoded by the following

POSTNET code?

196

Z IP C o d e? 0 9

Error Correction

Another POSTNET ExampleWhat ZIP Code is encoded by the following POSTNET

code?

Sum up known (error-free) ZIP digits1 + 6 + 0 + 9 = 16

Check digit9

Solve(16 + x + 9) mod 10 = 0

where x is the unknown digit

(16 + x + 9) = 30since x must be 0 x 9

x = 5

196

Z IP C o d e? 0 9

Z IP D ig it

S u m+

C h eck S u m

D igitm o d 1 0

0

Error Correction

Another POSTNET ExampleWhat ZIP Code is encoded by the following

POSTNET code?

196

Z IP C o d e5 0 9

Error Correction

Another POSTNET ExampleWhat check sum digit must be included in the

POSTNET encoding for the ZIP code 97121-1542?

Error Correction

Another POSTNET ExampleWhat check sum digit must be included in the

POSTNET encoding for the ZIP code 97121-1542?

Sum ZIP Digits9 + 7 + 1 + 2 + 1 + 1 + 5 + 4 + 2 = 32

Determine Check DigitLet x represent the check digit(32 + x) mod 10 = 0

(32 + x) = 40

since x must be 0 x 9x = 8

Z IP D ig it

S u m+

C h eck S u m

D igitm o d 1 0

0

References

J. Glenn Brookshear, Computer Science - An Overview, 11th edition, Addison-Wesley as an imprint of Pearson, 2012

W. Daniel Hillis, The Pattern on the Stone, Basic Books (Perseus Books Group), 1998

Donald D. Givone, Digital Principles and Design, McGraw-Hill, 2003

John L. Hennessy and David A. Patterson, Computer Organization and Design, The Hardware/Software Interface, 3rd Edition, Morgan Kaufmann Publishers, Inc., 2005

http://en.widipedia.org/wiki/Postnethttp://www.asciitable.comhttp://en.wikipedia.org/wiki/File:ASCII_Code_Chart-

Quick_ref_card.png