As the LFSR is clocked a sequence of psuedo-random numbers is generated. This can be useful in applications such as direct-sequence spread spectrum radio applications, generating white noise or for scambling.Īlternatively, the entire state could be a considered as a binary number. The linear function for a LFSR is usually constructed by XOR'ing certain taps of the state together.īy taking the output bit (either the most or least significant bit of the state) of the LFSR a psuedo-random sequence of 1's and 0's is generated.

The missing value, either all zeros or all ones depending on how the linear function is constructed, will never change so the LFSR should never be initialized to this value. For a shift register of m bits the longest sequence has $2^m−1$ discrete states.

An appropriately designed linear function can lead to a very long sequence of unique states, however, after some time it will eventually repeat. A linear feedback shift register is a shift register whose input is a linear function of the previous state.