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Understanding Nonnumeric Data Representation in Computers

Explore ASCII and Unicode encoding, color representation, error detection, correction techniques like parity and POSTNET encoding. Learn about the utilization of bits in images and ZIP code correction.

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Understanding Nonnumeric Data Representation in Computers

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  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, 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/Postnet • http://www.asciitable.com • http://en.wikipedia.org/wiki/File:ASCII_Code_Chart-Quick_ref_card.png

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