1. CSE 111 Representing Nonnumeric Data in a Computer

2. Text American Code for Standard Information Interchange (ASCII)  7-bit  English  For codes, see  http://www.asciitable.com  http://en.wikipedia.org/wiki/File:ASCII_Code_Chart-Quick_ref_card.png  Examples  1000001 represents A  1001110 represents N  1100001 represents a  1110010 represents r

3. Text Unicode  16-bit  International  Windows ASCII vs. Unicode  Advantages  Disadvantages

4. Images A grid represents pixels in the image  The color of each pixel can be black or white  A bit represents the color of the pixel  Each bit can be a 0 (white) or a 1 (black) Example  Consider the following image

5. Images Example Con’t.

6. Images Example Con’t.  How many bits are required to render the letters UB as an image?  9,350 bits

7. Images Color  Each pixel is represented by multiple bits which indicate how much of each color is needed to create the desired color  Examples

8. Images Color  Example  Use 8-bits to represent red  Use 8-bits to represent blue  Use 8-bits to represent green  Result 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 Windows Low Medium High

9. Error Detection A code is said to be n-error detecting if the minimum of n errors that cannot be detected is n+1  Error defined as a bit being complemented erroneously Example  2-out-of-5 codes  Single error detecting  Example A 01010 transmitted as 01110 Error can be detected

10. Error Detection Example  Parity  A parity bit can be concatenated to a code word that does not incorporate error detection to make it a single error detecting code Detects an odd number of errors  Even Parity The code word (including the parity bit) has an even number of 1’s  Odd Parity The code word (including the parity bit) has an odd number of 1’s  Example The 7-bit ASCII code is often concatenated with a parity bit H (odd parity)  11001000

11. Error Correction It is possible to construct a code whereby a finite number of errors can be corrected

12. Error Correction POSTNET Example  Used by US Postal Service to encode ZIP codes  Check Sum Digits for Error Correction  2-out-of-5 code is used to encode each digit  A checksum digit is appended to ZIP code so that sum is a multiple of 10  If 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)

13. Error Correction POSTNET Example  Barcode sprayed on deliverable mail for automated mail processing

14. Error Correction POSTNET Example  Currently Used Formats  5 Digit ZIP Code A Code  9 Digit ZIP and ZIP + 4 Code C Code Allows 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 code Allows sorting to delivery point (address) sequence

15. Error Correction POSTNET Example  ZIP digits and checksum digit are encapsulated between two one’s  Example

16. Error Correction Another POSTNET Example  What ZIP Code is encoded by the following POSTNET code?

17. Error Correction Another POSTNET Example  What ZIP Code is encoded by the following POSTNET code?

18. Error Correction Another POSTNET Example  What ZIP Code is encoded by the following POSTNET code?  Sum up known (error-free) ZIP digits  1 + 6 + 0 + 9 = 16  Check digit  9  Solve  (16 + x + 9) mod 10 = 0 where x is the unknown digit  (16 + x + 9) = 30 since x must be 0  x  9  x = 5

19. Error Correction Another POSTNET Example  What ZIP Code is encoded by the following POSTNET code?

20. Error Correction Another POSTNET Example  What check sum digit must be included in the POSTNET encoding for the ZIP code 97121-1542?

21. Error Correction Another POSTNET Example  What check sum digit must be included in the POSTNET encoding for the ZIP code 97121-1542?  Sum ZIP Digits 9 + 7 + 1 + 2 + 1 + 1 + 5 + 4 + 2 = 32  Determine Check Digit Let x represent the check digit (32 + x) mod 10 = 0 (32 + x) = 40  since x must be 0  x  9 x = 8

22. References J. Glenn Brookshear, Computer Science - An Overview, 11 th 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, 3 rd Edition, Morgan Kaufmann Publishers, Inc., 2005 http://en.widipedia.org/wiki/Postnet http://www.asciitable.com http://en.wikipedia.org/wiki/File:ASCII_Code_Chart- Quick_ref_card.png