You are an expert Verilog hardware designer working on a complete FPGA or ASIC project. You are given the full source code of a Verilog project. One of the modules in the project is incomplete — its implementation is missing and marked with:

// >>> Module Implementation Begin

// <<< Module Implementation End

Your task is to complete the missing implementation so that the entire project functions correctly. You must infer what the missing module or logic is supposed to do by analyzing the rest of the codebase: module names, signal connections, instantiations, comments, and usage patterns.

Follow these rules:

1. Only generate Verilog code to go between the `// >>> Module Implementation Begin` and `// <<< Module Implementation End` comments.
2. Use Verilog-2001 syntax. Ensure the code is synthesizable.
3. Assume the goal is a working, integrated hardware design — your code must make the whole system function as intended.
4. Analyze the naming, I/O ports, and how the module is instantiated or used in other parts of the project.
5. Implement correct behavior based on design context. Do not guess randomly — reason it out.
6. Avoid vendor-specific features unless explicitly required.
7. Do not output comments, explanation, or anything outside the required code region unless explicitly asked.

Your output should contain **only the Verilog code** that fits inside the marked region.

/*
 * Copyright (c) 2024 Your Name
 * SPDX-License-Identifier: Apache-2.0
 */

`default_nettype none

module tt_um_four_bit_multiplier_nasan016_npham2003 (
    input  wire [7:0] ui_in,    // Dedicated inputs
    output wire [7:0] uo_out,   // Dedicated outputs
    input  wire [7:0] uio_in,   // IOs: Input path
    output wire [7:0] uio_out,  // IOs: Output path
    output wire [7:0] uio_oe,   // IOs: Enable path (active high: 0=input, 1=output)
    input  wire       ena,      // always 1 when the design is powered, so you can ignore it
    input  wire       clk,      // clock
    input  wire       rst_n     // reset_n - low to reset
);

    wire [3:0] m = ui_in [3:0];
    wire [3:0] q = ui_in [7:4];
    wire [12:0]temp_carry;
    wire [12:0]temp_adds;
    wire [7:0] p;
    
    assign p[0] = m[0] & q[0];

    full_adder f1((m[1] & q[0]), (m[0] & q[1]), 0, p[1], temp_carry[0]);
    full_adder f2((m[2] & q[0]), (m[1] & q[1]), temp_carry[0], temp_adds[0], temp_carry[1]);
    full_adder f3((m[3] & q[0]), (m[2] & q[1]), temp_carry[1], temp_adds[1], temp_carry[2]);
    full_adder f4(0, (m[3] & q[1]), temp_carry[2], temp_adds[2], temp_carry[3]);
    
    
    full_adder f5(temp_adds[0], (m[0] & q[2]), 0, p[2], temp_carry[4]);
    full_adder f6(temp_adds[1], (m[1] & q[2]), temp_carry[4], temp_adds[3], temp_carry[5]);
    full_adder f7(temp_adds[2], (m[2] & q[2]), temp_carry[5], temp_adds[4], temp_carry[6]);
    full_adder f8(temp_carry[3], (m[3] & q[2]), temp_carry[6], temp_adds[5], temp_carry[7]);
    
    full_adder f9(temp_adds[3], (m[0] & q[3]), 0, p[3], temp_carry[8]);
    full_adder f10(temp_adds[4], (m[1] & q[3]), temp_carry[8], p[4], temp_carry[9]);
    full_adder f11(temp_adds[5], (m[2] & q[3]), temp_carry[9], p[5], temp_carry[10]);
    full_adder f12(temp_carry[7], (m[3] & q[3]), temp_carry[10], p[6], p[7]);
    assign uo_out = p;
      assign uio_out = 0;
  assign uio_oe  = 0;

  // List all unused inputs to prevent warnings
  wire _unused = &{ena, clk, rst_n, uio_in, 1'b0};
endmodule



module full_adder (a, b, c, dout, carry);
// >>> Module Implementation Begin

// <<< Module Implementation End
endmodule




Reference solution:
rtl/generated.v:     input a;
    input b;
    input c;
    output dout;
    output carry;

    assign dout = a ^ b ^ c;   
    assign carry = (a &b ) | (c & (a^b));