Grey encoder and decoder

Author: Rui
Reference from the website and wikipedia

Something to mention:

1.$display always to display the last sampled value,may cause some mismatch in the screen output

2.parameterized module design help to scaling 

Grey encoder

// grey encoder, from binary input to grey output
// algorithm:
// from rightmost, x[i] xor x[i+1], keep the leftmost bitmodule grey_encoder#(parameter WIDTH = 4)

    (input [WIDTH - 1 : 0] bin,
    output [WIDTH - 1 : 0]grey);
wire [WIDTH-2 : 0] temp;

assign temp =  bin[WIDTH -1:1];
assign grey = {bin[WIDTH-1], temp ^ bin[WIDTH -2 :0]};
endmodule

Grey decoder 

//algorithm
//keep the leftmost bit
//b[n] = g[n], b[i] = b[i+1] xor g[i] i:0~n-2
//pretty simple to understand, use xor 0 to keep the bit, xor 1 to invert bit
module grey_decoder#(parameter WIDTH=4)
    (input [WIDTH-1:0] grey,
    output reg [WIDTH-1:0] bin);
integer i;
always@(grey) begin
    bin[WIDTH-1] = grey[WIDTH-1];
    for (i=(WIDTH-2); i>=0; i=i-1)
        bin[i] = bin[i+1] ^ grey[i];
end
endmodule

Testbench

// testbench for grey encoder
// Author Rui Chen

`include "grey.v"
module grey_top;
parameter WIDTH = 4;
reg [WIDTH-1 : 0] bin, grey2;
wire [WIDTH-1 : 0] grey, bin2;

grey_encoder #(.WIDTH(WIDTH)) encoder (.bin(bin), .grey(grey));
grey_decoder #(.WIDTH(WIDTH)) decoder (.grey(grey2), .bin(bin2));

always@(grey) grey2 = grey;

initial begin
    $display("debug output");
    repeat(10) begin
    #3 bin = $random;
    $display("encoder part");
    $display("binary input: %b, grey output: %b", bin, grey);
    $display("decoder part");
    $display("grey input: %b, binary output: %b", grey2, bin2);
    end
    #3 $finish;
end

initial begin
    $dumpfile("grey.vcd");
    $dumpvars;
end
endmodule

Simulation result