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_a_4_array_multiplier (
    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,      
    input  wire       clk,      
    input  wire       rst_n     
);

    wire [3:0] m = ui_in[7:4]; 
    wire [3:0] q = ui_in[3:0]; 
    wire [7:0] p;              

    wire [3:0] pp0, pp1, pp2, pp3;
    wire [4:0] sum1, sum2, sum3;
    wire [4:0] carry1, carry2, carry3;

    assign pp0 = m & {4{q[0]}};
    assign pp1 = m & {4{q[1]}};
    assign pp2 = m & {4{q[2]}};
    assign pp3 = m & {4{q[3]}};

    assign p[0] = pp0[0];
    half_add ha1 (pp0[1], pp1[0], p[1], carry1[0]);
    full_add fa1 (pp0[2], pp1[1], carry1[0], sum1[0], carry1[1]);
    full_add fa2 (pp0[3], pp1[2], carry1[1], sum1[1], carry1[2]);
    full_add fa3 (1'b0, pp1[3], carry1[2], sum1[2], carry1[3]);

    half_add ha2 (sum1[0], pp2[0], p[2], carry2[0]);
    full_add fa4 (sum1[1], pp2[1], carry2[0], sum2[0], carry2[1]);
    full_add fa5 (sum1[2], pp2[2], carry2[1], sum2[1], carry2[2]);
    full_add fa6 (carry1[3], pp2[3], carry2[2], sum2[2], carry2[3]);

    half_add ha3 (sum2[0], pp3[0], p[3], carry3[0]);
    full_add fa7 (sum2[1], pp3[1], carry3[0], p[4], carry3[1]);
    full_add fa8 (sum2[2], pp3[2], carry3[1], p[5], carry3[2]);
    full_add fa9 (carry2[3], pp3[3], carry3[2], p[6], p[7]);

    assign uo_out = p;
    assign uio_out = 0;
    assign uio_oe  = 0;

    wire _unused = &{ena, clk, rst_n, uio_in, 1'b0};

endmodule

module half_add (
    input a, b,
    output sum, cout
);
// >>> Module Implementation Begin

// <<< Module Implementation End
endmodule



module full_add (
    input a, b, cin,
    output sum, cout
);
    assign sum = a ^ b ^ cin;
    assign cout = (a & b) | (cin & (a ^ b));
endmodule


Reference solution:
rtl/generated.v:     assign sum = a ^ b;
    assign cout = a & b;