However, both of the LFSRs shown in Fig 2 are said to be of maximal length because they sequence through every possible value (excluding all of the bits being 0) before returning to their initial values.Ī binary field with ‘n’ bits can assume 2^n unique values, but a maximal-length LFSR with ‘n’ register bits will only sequence through (2^n – 1) values. In some cases an LFSR will end up cycling round a loop comprising a limited number of values. Comparison of alternative tap selections.īoth LFSRs start with the same initial value but, due to the different taps, their sequences rapidly diverge as clock pulses are applied. For example, consider two 3-bit XOR based LFSRs with different tap selections ( Fig 2).Ģ. The sequence of values generated by an LFSR is determined by its feedback function (XOR versus XNOR) and tap selection. The data input to the LFSR is generated by XOR-ing or XNOR-ing the tap bits the remaining bits function as a standard shift register. All of the register elements share a common clock input, which is omitted from the symbol for reasons of clarity. The taps in this example are at bit 0 and bit 2, and can be referenced as.
