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Published byLynn Julia Mills Modified over 9 years ago
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CSE 111 Representing Nonnumeric Data in a Computer
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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
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Text Unicode 16-bit International Windows ASCII vs. Unicode Advantages Disadvantages
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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
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Images Example Con’t.
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Images Example Con’t. How many bits are required to render the letters UB as an image? 9,350 bits
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Images Color Each pixel is represented by multiple bits which indicate how much of each color is needed to create the desired color Examples
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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
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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
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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
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Error Correction It is possible to construct a code whereby a finite number of errors can be corrected
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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)
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Error Correction POSTNET Example Barcode sprayed on deliverable mail for automated mail processing
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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
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Error Correction POSTNET Example ZIP digits and checksum digit are encapsulated between two one’s Example
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Error Correction Another POSTNET Example What ZIP Code is encoded by the following POSTNET code?
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Error Correction Another POSTNET Example What ZIP Code is encoded by the following POSTNET code?
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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
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Error Correction Another POSTNET Example What ZIP Code is encoded by the following POSTNET code?
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Error Correction Another POSTNET Example What check sum digit must be included in the POSTNET encoding for the ZIP code 97121-1542?
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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
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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
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