The member functions Load, Read, Clear and ShiftLeft of class _8bitShiftRegister constitute a straightforward implementation of the behavioral specification of the register. To reduce the complexity of the division operation, subtractions are performed in a bitwise fashion and without borrow. The check bits are obtained as the remainder of the division of a data bit-vector and a generator bit-vector. A burst is defined to be a large chunk of data transferred at high speed.Ī CRC code consists of \(k\) data bits (or message bits) and \(r < k\) check bits. Lang Digital Systems and Hardware/ Firmware Algorithms. Computation of Cyclic Redundancy Check (CRC) CodesĬRC codes are used in data transmission both between computers over communications lines, and between hard drives and the CPU to detect burst errors (cf. Knuth has noted that for keys consisting of 15 bits, the 10 th-degree divisor polynomial yields different remainders for any pair of keys that differ in fewer than seven bit positions. In the case of hashing by polynomial division, the divisor polynomial determines the effectiveness of the method. The most difficult problem to address in hashing is the avoidance of collisions, and a judicious choice of the hashing function is of prime importance. The remainder is equal to 10001 and the integer equivalent (17) is the index into the hash table for the key in question.
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