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
Walkie bits Walkie bits Walkie Bits are little plastic toy turtles that sing, dance and walk (they can walk in the rhythm which you tap on their shell). They are made by Takara, a Japanese toy company in June 2005. Walkie Bits are very small, only about five centimeters, and come in a variety of different colors and "flavors" like "blue soda" and "green pineapple". The Walkie Bits turtles are very popular in Japan, with 300,000 units sold within just a few months of their release. Many Japanese people collect them because there are so many colors and they are relatively inexpensive.