Compressed files are especially susceptible to corruption. While changing a bit from to 1 or vice versa in a text file generally only affects a single character, changing a single bit in a compressed file often makes the entire file unreadable. Therefore, it’s customary to store a checksum with the compressed file so that the recipient can verify that the file is intact. The zip format does this automatically, but you may wish to use manual checksums in other circumstances as well.

There are many different checksum schemes. A particularly simple example adds a parity bit to the data, typically 1 if the number of 1 bits is odd, if the number of 1 bits is even. This checksum can be calculated by summing up the number of 1 bits and taking the remainder when that sum is divided by two. However, this scheme isn’t very robust. It can detect single-bit errors, but in the face of bursts of errors as often occur in transmissions over modems and other noisy connections, there’s a 50/50 chance that corrupt data will be reported as correct.

Better checksum schemes use more bits. For example, a 16-bit checksum could sum up the number of 1 bits and take the remainder modulo 65,536. This means that in the face of completely random data, there’s only 1 in 65,536 chances of corrupt data being reported as correct. This chance drops exponentially as the number of bits in the checksum increases. More mathematically sophisticated schemes can reduce the likelihood of a false positive even further. ...

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