The feedback tap numbers shown correspond to a primitive polynomial in the table, so the register cycles through the maximum number of 65535 states excluding the all-zeroes state. However, other methods, that are less elegant but perform better, should be considered as well.Ī 16-bit Fibonacci LFSR. One can produce relatively complex logics with simple building blocks. In general, the arithmetics behind LFSRs makes them very elegant as an object to study and implement. The mathematics of a cyclic redundancy check, used to provide a quick check against transmission errors, are closely related to those of an LFSR. Both hardware and software implementations of LFSRs are common. However, an LFSR with a well-chosen feedback function can produce a sequence of bits that appears random and has a very long cycle.Īpplications of LFSRs include generating pseudo-random numbers, pseudo-noise sequences, fast digital counters, and whitening sequences. Likewise, because the register has a finite number of possible states, it must eventually enter a repeating cycle. The initial value of the LFSR is called the seed, and because the operation of the register is deterministic, the stream of values produced by the register is completely determined by its current (or previous) state. Thus, an LFSR is most often a shift register whose input bit is driven by the XOR of some bits of the overall shift register value. The most commonly used linear function of single bits is exclusive-or (XOR). In computing, a linear-feedback shift register ( LFSR) is a shift register whose input bit is a linear function of its previous state. JSTOR ( March 2009) ( Learn how and when to remove this template message).Unsourced material may be challenged and removed.įind sources: 'Linear-feedback shift register' – news Please help improve this article by adding citations to reliable sources.

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Linear feedback shift register masks