In the diagram above, the bits shift from right to left, and the cells are numbered from 0 to \( N-1 \) (here we have a 5-bit shift-register, so \( N=5 \)).
The output of one cell is connected to the input of the next, so that the bits in the shift register propagate from left to right, or right to left, depending on how the shift register is set up. it has an output signal that is the state of the shift register - if the shift register contains a 1, then it outputs a 1 if it contains a 0, then it outputs a 0.it changes that state bit to the input signal, upon receiving a clock signal.it stores a single bit of state, either a 0 or a 1.We’ll start with the bitwise approach.Ī shift register is a series of bit cells, each of which is a flip-flop: There are at least three ways to describe the linear feedback shift register, or LFSR: a practical bitwise approach, and two theoretical approaches based on the algebra of finite fields, one using polynomials and the other using matrices. Linear Feedback Shift Registers: A Bitwise Approach
But part of the reason to understand the theory behind LFSRs is just because the math has an inherent beauty. You can use LFSRs to generate a pseudorandom bit sequence, or as a high-speed counter. Why study the LFSR? They have many practical applications in communications theory. This article is available in PDF format for easy printing
