Gray Code Encoder and Decoder

test_gray_code.v

module test_gray_code;
  
  parameter DWIDTH = 10;
  
  function [DWIDTH-1:0] to_gray;
    input [DWIDTH-1:0] in;
    to_gray = in ^ (in >> 1);
  endfunction
  
  function [DWIDTH-1:0] to_binary;
    input [DWIDTH-1:0] in;
    integer i, j;
    begin
      for(i=0; i<DWIDTH; i=i+1) begin
        to_binary[i] = 1'b0;
        for(j=0; j<DWIDTH; j=j+1) begin
          if(j >= i) to_binary[i] = to_binary[i] ^ in[j];
        end
      end
    end
  endfunction

  reg [DWIDTH  :0] num;
  reg [DWIDTH-1:0] g;
  reg [DWIDTH-1:0] d;

  initial begin
    for(num=0; num<2**DWIDTH; num=num+1) begin
      g = to_gray(num);
      d = to_binary(g);
      $display("bin=%x gray=%x decode=%x match?=%b", num, g, d, num==d);
    end
    $finish;
  end
  
endmodule