When information is transferred back and forth among the various parts of a computer, or transmitted from the earth to the moon and back, or, for that matter, merely left in storage, a chance exists that the bit pattern ultimately retrieved may not be identical to the original one. Particles of dirt or grease on a magnetic recording surface or a malfunctioning circuit may cause data to be incorrectly recorded or read. Static on a transmission path may corrupt portions of the data. And, in the case of some technologies, normal background radiation can alter patterns stored in a machine’s main memory. To resolve such problems, a variety of encoding techniques have been developed to allow the detection and even the correction of errors. Today, because these techniques are largely built into the internal components of a computer system, they are not apparent to the personnel using the machine. Nonetheless, their presence is important and represents a significant contribution to scientific research. It is fitting, therefore, that we investigate some of these techniques that lie behind the reliability of today’s equipment.
• Parity Bits
A simple method of detecting errors is based on the principle that if each bit pattern being manipulated has an odd number of 1s and a pattern with an even number of 1s is encountered, an error must have occurred. To use this principle, we need an encoding system in which each pattern contains an odd number of 1s. This is easily obtained by first adding an additional bit, called a parity bit, to each pattern in an encoding system already available (perhaps at the high-order end).
In each case, we assign the value 1 or 0 to this new bit so that the entire resulting pattern has an odd number of 1s. Once our encoding system has been modified in this way, a pattern with an even number of 1s indicates that an error has occurred and that the pattern being manipulated is incorrect.
• Error-Correcting Codes...
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