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 Hanyuan (Bob) Huang
 * SPDX-License-Identifier: Apache-2.0
 */

`default_nettype none

module tt_um_b_8_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,      // 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
);

  // All output pins must be assigned. If not used, assign to 0.

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




//partial products 
    //partial digit 0 
    wire p00 = m[0] & q[0];
    wire p01 = m[0] & q[1];
    wire p02 = m[0] & q[2];
    wire p03 = m[0] & q[3];
    
    //partial digit 1 
    wire p10 = m[1] & q[0];
    wire p11 = m[1] & q[1];
    wire p12 = m[1] & q[2];
    wire p13 = m[1] & q[3];   
    
    //partial digit 2 
    wire p20 = m[2] & q[0];
    wire p21 = m[2] & q[1];
    wire p22 = m[2] & q[2];
    wire p23 = m[2] & q[3];
    
    //partial digit 3 
    wire p30 = m[3] & q[0];
    wire p31 = m[3] & q[1];
    wire p32 = m[3] & q[2];
    wire p33 = m[3] & q[3];
    
    
    //wiring internal signals for adders 
    wire s1, s2, s3, s4, s5, s6, s7, s8, s9;
    wire c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12;
    
    //row 1
    assign p[0] = p00;
    
    //row 2 
    fullad fa1(.cin(1'b0), .x(p01), .y(p10), .sum(p[1]), .cout(c1));
    fullad fa2(.cin(c1), .x(p02), .y(p11), .sum(s1), .cout(c2));
    fullad fa3(.cin(c2), .x(p03), .y(p12), .sum(s2), .cout(c3));
    fullad fa4(.cin(c3), .x(1'b0), .y(p13), .sum(s3), .cout(c4));
    
    //row 3 
    fullad fa5(.cin(1'b0), .x(s1), .y(p20), .sum(p[2]), .cout(c5));
    fullad fa6(.cin(c5), .x(s2), .y(p21), .sum(s4), .cout(c6));
    fullad fa7(.cin(c6), .x(s3), .y(p22), .sum(s5), .cout(c7));
    fullad fa8(.cin(c7), .x(c4), .y(p23), .sum(s6), .cout(c8));
    
    //row 4 
    fullad fa9(.cin(1'b0), .x(s4), .y(p30), .sum(p[3]), .cout(c9));
    fullad fa10(.cin(c9), .x(s5), .y(p31), .sum(s7), .cout(c10));
    fullad fa11(.cin(c10), .x(s6), .y(p32), .sum(s8), .cout(c11));
    fullad fa12(.cin(c11), .x(c8), .y(p33), .sum(s9), .cout(c12));
    
    //rest of digits 
    assign p[4] = s7;
    assign p[5] = s8;
    assign p[6] = s9;
    assign p[7] = c12;


    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, 1'b0};

  endmodule


module fullad(cin, x, y, sum, cout);
// >>> Module Implementation Begin

// <<< Module Implementation End
endmodule






Reference solution:
rtl/generated.v:     input x, y, cin;
    output sum, cout;
    wire z1, z2, z3;
    
    xor(sum,x,y,cin);
    and(z1,x,y);
    and(z2,x,cin);
    and(z3,y,cin);
    
    or(cout,z1,z2,z3);