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 Stochastic computing is a collection of techniques that represent continuous values by streams of random bits. Complex computations can then be computed by simple bit-wise operations on the streams. Stochastic computing is distinct from the study of randomized algorithms. Suppose that formula_1 is given, and we wish to compute formula_2. Stochastic computing performs this operation using probability instead of arithmetic. Specifically, suppose that there are two random, independent bit streams called "stochastic number"s (i.e. Bernoulli processes), where the probability of a one in the first stream is formula_3, and the probability in the second stream is formula_4. We