Data Communications Networking Devices - 4th Ed.pdf

58 _______________________________ FUNDAMENTAL WIDE AREA NETWORKING CONCEPTSFigure 1.30 The Hamming code encoding process. Using exclusive-OR arithmetic thethree equations yield P 1 ˆ 0, P 2 ˆ 1, P 3 ˆ 1Figure 1.31The Hamming code decoding processUsing the values obtained for each parity bit results in the transmitted messagebecoming 0111100. Now assume an error occurs in bit 5,resulting in the receivedmessage becoming 0111000. Figure 1.31 illustrates the Hamming code decodingprocess in which the received message is exclusive-ORed against a matrix of allpossible values of the three parity bits,yielding the sum 101 2 ,which is the binaryvalue for 5. Thus,bit 5 is in error and is corrected by reversing or resetting itsvalue.1.13 STANDARDS ORGANIZATIONS, ACTIVITIES AND THE OSIREFERENCE MODELThe importance of standards and the work of standards organizations have provedessential for the growth of worldwide communications. In the United States andmany other countries,national standards organizations have de®ned physical andoperational characteristics that enable vendors to manufacture equipmentcompatible with line facilities provided by communications carriers as well asequipment produced by other vendors. At the international level,standardsorganizations have promulgated several series of communications related recommendations.These recommendations,while not mandatory,have become highlyin¯uential on a worldwide basis for the development of equipment and facilitiesand have been adopted by hundreds of public companies and communicationscarriers.In addition to national and international standards a series of de facto standardshas evolved through the licensing of technology among companies. Such de factostandards,as an example,have facilitated the development of communications