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
Stochastic computing stochastic computing is robust against noise; if a few bits in a stream are flipped, those errors will have no significant impact on the solution. Furthermore, stochastic computing elements can tolerate skew in the arrival time of the inputs. Circuits work properly even when the inputs are misaligned temporally. As a result, stochastic systems can be designed to work with inexpensive locally generated clocks instead of using a global clock and an expensive clock distribution network. Finally, stochastic computing provides an estimate of the solution that grows more accurate as we extend the bit stream. In particular, it provides a