8.2 FEEDBACK SHIFT REGISTERS

A finite state machine (FSM) [Mealy, 1955] consists of finite sets of (internal) states {s}, input and output alphabets {a} and {b}, an output function T determining the output

image

and a state function Σ determining the successor state.

image

Given an initial internal state s0, and sequence of input states a0, a1, …, the functions T and Σ determine the output sequence b0, b1, …, according to the recursion

image

image

Figure 8.1 Feedback shift register.

Figure 8.1 depicts a feedback shift register (FSR) with feedback function f, an FSM with null input consisting of N stages (each capable of storing one bit), a feedback register, and a single output port, where

  • The content of Stage i at time t is si(t) = 0 or 1,
  • The output s0(t) is the content of Stage 0 at time t,
  • The state of the FSR at time t is the N-vector s(t) = (s0(t), s1(t), …, sN−1(t)) image (where image is the set of 2N vectors ...

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