Computation of cyclic redundancy checks may use whichever form is more convenient. Parallel update for a byte or a word at a time can also be done explicitly, without a table. This is normally used in high-speed hardware implementations. For each bit an equation is solved after 8 bits have been shifted in. The following tables list the equations for some commonly used polynomials, using following symbols: As the CRC-32 polynomial has a large number of terms, when computing the remainder a byte at a time each bit depends on several bits of the previous iteration. In byte-parallel hardware implementations this calls for either multiple-input
Zero-byte file be zero bytes (a common convention terminates text files with a one- or two-byte newline, however). Conversely, zero-byte files must use some disk space to be indexed by a filesystem (though none for content, in most cases). In some cases, zero-byte files may be used to convey information like file metadata (for example, its filename may contain an instruction to a user viewing a directory listing such as documents-have-been-moved-to-partition-D, etc.); or to put in a directory to ensure that it is nonempty, since some tools such as backup and revision control software may ignore the empty directories. There are many