linear feedback shift register vhdl code

Implementing Linear Feedback Shift Registers (LFSRs) in VHDL Code

Linear Feedback Shift Registers (LFSRs) are a type of digital circuit that generates a sequence of random numbers using a finite state machine. They have numerous applications in various fields, including cryptography, coding theory, and random number generation.

One of the most significant advantages of LFSRs is their ability to generate a large number of unique states, making them ideal for generating high-quality random numbers. The effective length of an LFSR can be adjusted by choosing the tap feedback points, which determine how many bits are used in the feedback sequence.

To implement an LFSR in VHDL code, you need to design a shift register with a specified number of bits and choose the tap feedback points carefully. For example, if you want to generate a 5-bit random number each cycle, you would need a 31-bit LFSR and select 30 bits for your random number.

The last (tap) feedback point defines the effective length of the LFSR, after which it becomes simply a shift register with no bearing on the feedback sequence. It is essential to choose the order of the taps correctly, as the MSB will always be a feedback point.

VHDL Code Example:

```vhdl

module fibonacci_lfsr_nbit(input clk, input reset, output reg '31:0' out);

reg '30:0' stage;

always @(posedge clk) begin

if (reset) stage <= 31'd0;

else stage <= {stage'29:0', stage'30'^stage'29'};

end

assign out = stage;

endmodule

```

This VHDL code implements a 31-bit LFSR that generates a sequence of random numbers. The `always` block updates the `stage` register based on the clock signal, and the `assign` statement outputs the current state of the LFSR.

In conclusion, implementing an LFSR in VHDL code is relatively simple using a shift register with XOR operations for feedback terms. By choosing the correct tap feedback points, you can generate high-quality random numbers with varying bit widths. The code provided above demonstrates how to implement a 31-bit LFSR that generates a sequence of random numbers.

Linear feedback shift register vhdl code