*(This code was contributed by Jeff Cassidy at Isophase Computing
(jeff@isophase-computing.ca, https://github.com/isophase), with edits
by myself.)*

Converts an unsigned binary number to the corresponding Reflected Binary Gray Code.

A Reflected Binary Gray Code starts from a simple 1-bit sequence 0,1 and can be constructed recursively for larger bit widths N. The sequence for N bits is build as follows:

- The sequence of N-1 bits with 0 prepended to each element, concatenated with
- the sequence of N-1 bits
*reversed*with 1 prepended to each element

For example:

- N=1 bit: 0, 1
- N=2 bits: 00, 01, 11, 10
- N=3 bits: 000, 001, 011, 010, 110, 111, 101, 100

The resulting Reflected Binary Gray Code has two useful properties:

- It is cyclic with length 2
^{N}, so it can represent or index the same number of items as a binary coded number of the same length. - Each Gray code word differs by exactly 1 bit from the previous and the next code in sequence, which makes it behave nicely if a word may be read inaccurately from a mechanical indicator or a Clock Domain Crossing. Missing the changed bit means you are off by 1 step, not some variable number of steps as with a binary code.

The reverse function also exists.

`default_nettype none module Binary_to_Gray_Reflected #( parameter WORD_WIDTH = 0 ) ( input wire [WORD_WIDTH-1:0] binary_in, output reg [WORD_WIDTH-1:0] gray_out ); localparam ZERO = {WORD_WIDTH{1'b0}}; initial begin gray_out = ZERO; end function [WORD_WIDTH-1:0] binary_to_gray ( input [WORD_WIDTH-1:0] binary ); integer i; reg [WORD_WIDTH-1:0] gray; begin for(i=0; i < WORD_WIDTH-1; i=i+1) begin gray[i] = binary[i] ^ binary[i+1]; end gray[WORD_WIDTH-1] = binary[WORD_WIDTH-1]; binary_to_gray = gray; end endfunction always@(*) begin gray_out = binary_to_gray(binary_in); end endmodule