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A checksum is a method of determining whether an error has occurred in the transmission of data. There an numerous different algorithms. Essentially you send an extra piece of data that is used to validate the previous block.
The most common are the CRC checks. These usually involve XORing the incoming data with a seed value. There is alot of math behind it, but the key is to me able to catch whether any of the bits were received incorrectly.
Usually when the CRC or checksum indicates a failure, all you can do is request a retransmission. The checksum only gives a yes-no answer to an indication of where in the block of data the error is.
Check sums are even used on compresses files or on software programs in embedded systems so that the integrity of the files can be checked before execution. In systems where personal safety is concerned, you do not want to operate if the ROM is corrupted.
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