5-bit LFSR

A linear feedback shift register is a shift register usually with a few XOR gates to produce the next state of the shift register. A Galois LFSR is one particular arrangement where bit positions with a "tap" are XORed with the output bit to produce its next value, while bit positions without a tap shift. If the taps positions are carefully chosen, the LFSR can be made to be "maximum-length". A maximum-length LFSR of n bits cycles through 2n-1 states before repeating (the all-zero state is never reached).

The following diagram shows a 5-bit maximal-length Galois LFSR with taps at bit positions 5 and 3. (Tap positions are usually numbered starting from 1). Note that I drew the XOR gate at position 5 for consistency, but one of the XOR gate inputs is 0.

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module top_module(
    input clk,
    input reset,    // Active-high synchronous reset to 5'h1
    output [4:0] q
); 
    always@(posedge clk)begin
        if(reset)begin
            q<=5'h1;
        end
        else begin
            q[4]<=1'b0^q[0];
            q[3]<=q[4];
            q[2]<=q[3]^q[0];
            q[1]<=q[2];
            q[0]<=q[1];
        end
    end
endmodule

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