Binary to Gray Code Converter

October 3, 2025

Solving Approach

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MSB of the Gray output is identical to the MSB of the binary input. Each subsequent Gray bit is obtained by performing a bitwise XOR between the corresponding binary bit and its immediate higher-order binary bit.

Code

module bin2gray4(
    input [3:0] bin_in,
    output [3:0] gray_out
);

    assign gray_out = {bin_in[3],bin_in[3]^bin_in[2],bin_in[2]^bin_in[1],bin_in[1]^bin_in[0]};

endmodule

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Testbench Code

`timescale 1ns/1ps

module tb_bin2gray4;
    // Input
    reg  [3:0] bin_in;

    // DUT output
    wire [3:0] gray_out;

    // Expected output
    reg  [3:0] expected_gray_out;

    // Mismatch signal
    wire mismatch = (gray_out !== expected_gray_out);

    integer TOTAL_TEST_CASES = 0;
    integer TOTAL_PASSED_TEST_CASES = 0;
    integer TOTAL_FAILED_TEST_CASES = 0;

    // Instantiate DUT
    bin2gray4 dut (
        .bin_in(bin_in),
        .gray_out(gray_out)
    );

    // VCD dump (Inputs -> Outputs -> Expected -> mismatch)
    initial begin
        $dumpfile("tb_bin2gray4.vcd");
        $dumpvars(0,
            tb_bin2gray4.bin_in,             // input
            tb_bin2gray4.gray_out,           // output
            tb_bin2gray4.expected_gray_out,  // expected
            tb_bin2gray4.mismatch            // mismatch flag
        );
    end

    // Golden model (same vector formula)
    task compute_expected;
        input [3:0] t_bin;
        begin
            expected_gray_out = t_bin ^ (t_bin >> 1);
        end
    endtask

    task run_one;
        input [3:0] t_bin;
        begin
            bin_in = t_bin;
            compute_expected(t_bin);
            #1; // settle

            TOTAL_TEST_CASES++;
            if (!mismatch) begin
                TOTAL_PASSED_TEST_CASES++;
            end else begin
                TOTAL_FAILED_TEST_CASES++;
                $display("FAILED: bin=%b | gray=%b expected=%b mismatch=%b",
                         bin_in, gray_out, expected_gray_out, mismatch);
            end
        end
    endtask

    integer i;
    initial begin
        // Exhaustive: cover all 16 input values
        for (i = 0; i < 16; i = i + 1)
            run_one(i[3:0]);

        // Print full truth table (≤ 16 lines)
        $display("bin  -> gray");
        $display("------------");
        for (i = 0; i < 16; i = i + 1) begin
            bin_in = i[3:0];
            compute_expected(i[3:0]);
            #1;
            $display("%b -> %b (exp=%b mismatch=%b)",
                     bin_in, gray_out, expected_gray_out, mismatch);
        end

        // Summary
        $display("======================================");
        $display("TOTAL_TEST_CASES=%0d", TOTAL_TEST_CASES);
        $display("TOTAL_PASSED_TEST_CASES=%0d", TOTAL_PASSED_TEST_CASES);
        $display("TOTAL_FAILED_TEST_CASES=%0d", TOTAL_FAILED_TEST_CASES);
        $display("ALL_TEST_CASES_PASSED=%s",
                 (TOTAL_FAILED_TEST_CASES==0) ? "true" : "false");
        $display("======================================");
        $finish;
    end
endmodule