The math involved in analyzing the properties of a LFSR uses Galois fields:Ī simple simulation of a LFSR with two taps: lfsrsim.zipĪ complete list of all dual tap LSFRs up to 42 bit in length and their periods: lfsrperiods. 24 Stage Linear Feedback Shift Register (LFSR) This circuit can be used to generate a pseudo-random sequence of 0's and 1's - that is 'white noise' or 'static.

If you need a counter and it does not have to count in a linear way then a LFSR is faster and requires less hardware resources. Feedback around an LFSRs shift register comes from a selection of points (taps) in the register chain and constitutes XORing these taps to provide tap(s). Only some combinations of taps and lengths will generate a sequence with a period of 2 n-1 cycles. There are many possible configurations, the one presented here is very simple and has the property that it will start from an input of all 0's and is very easy to implement in software and hardware.Ī LFSR of this type will never contain only 1's and would stall if loaded with that value. It is demonstrated that the coefficients of the feedback function and the characteristic polynomial of a linear feedback shift register can be deduced from.

A LFSR (linear feedback shift register) is a shift register where the input is a linear function of two or more bits (taps).

Taps for linear feedback shift register