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
Type-in program such as "Byte" and "Popular Computing" printed them less frequently, often as a test program to illustrate a technical topic covered in the magazine rather than an application for general use. Consumer-oriented publications such as "Compute!" and "Family Computing" ran several each issue. The programs were sometimes specific to a given home computer and sometimes compatible with several computers. Entirely platform-specific magazines such as "Compute!'s Gazette" (Commodore) and "Antic" (Atari), since they only had to print one version of each program, were able to print more, longer listings. Although type in programs were usually copyrighted, like the many games in