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_tt09_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 [8:0] p;

    wire [3:0] partial[3:0];
    wire [4:0] sum1, sum2, sum3;
    wire [3:0] c1, c2, c3, c4;
    
    assign partial[0][0] = m[0] & q[0];
    assign partial[0][1] = m[1] & q[0];
    assign partial[0][2] = m[2] & q[0];
    assign partial[0][3] = m[3] & q[0];
    assign partial[1][0] = m[0] & q[1];
    assign partial[1][1] = m[1] & q[1];
    assign partial[1][2] = m[2] & q[1];
    assign partial[1][3] = m[3] & q[1];
    assign partial[2][0] = m[0] & q[2];
    assign partial[2][1] = m[1] & q[2];
    assign partial[2][2] = m[2] & q[2];
    assign partial[2][3] = m[3] & q[2];
    assign partial[3][0] = m[0] & q[3];
    assign partial[3][1] = m[1] & q[3];
    assign partial[3][2] = m[2] & q[3];
    assign partial[3][3] = m[3] & q[3];
    
    fulladder inst1_1(partial[0][1], partial[1][0], 1'b0, sum1[0], c1[0]);
    fulladder inst1_2(partial[0][2], partial[1][1], c1[0], sum1[1], c1[1]);
    fulladder inst1_3(partial[0][3], partial[1][2], c1[1], sum1[2], c1[2]);
    fulladder inst1_4(partial[1][3], 1'b0, c1[2], sum1[3], sum1[4]);
    
    fulladder inst2_1(sum1[1], partial[2][0], 1'b0, sum2[0], c2[0]);
    fulladder inst2_2(sum1[2], partial[2][1], c2[0], sum2[1], c2[1]);
    fulladder inst2_3(sum1[3], partial[2][2], c2[1], sum2[2], c2[2]);
    fulladder inst2_4(sum1[4], partial[2][3], c2[2], sum2[3], sum2[4]);
    
    fulladder inst3_1(sum2[1], partial[3][0], 1'b0, sum3[0], c3[0]);
    fulladder inst3_2(sum2[2], partial[3][1], c3[0], sum3[1], c3[1]);
    fulladder inst3_3(sum2[3], partial[3][2], c3[1], sum3[2], c3[2]);
    fulladder inst3_4(sum2[4], partial[3][3], c3[2], sum3[3], sum3[4]);
    
    assign p[0] = partial[0][0];
    assign p[1] = sum1[0];
    assign p[2] = sum2[0]; 
    assign p[3] = sum3[0];
    assign p[4] = sum3[1];
    assign p[5] = sum3[2];
    assign p[6] = sum3[3];
    assign p[7] = sum3[4];
  
  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 fulladder(
    input a,
    input b,
    input c,
    output y,
    output z
    );
// >>> Module Implementation Begin

// <<< Module Implementation End
endmodule




Reference solution:
rtl/generated.v:     
// Internal Signals
    wire int_sig1;
    wire int_sig2;
    wire int_sig3;
    wire int_sig4;
    wire int_sig5;
    wire int_sig6;
    wire int_sig7;
    wire int_sig8;
        
    assign int_sig1 = a & ~b;
    assign int_sig2 = ~a & b;
    assign int_sig3 = int_sig1 + int_sig2;
    assign int_sig4 = int_sig3 & ~c;
    assign int_sig5 = ~int_sig3 & c;
    assign y = int_sig4 + int_sig5; 
    assign int_sig6 = a & b;
    assign int_sig7 = b & c;
    assign int_sig8 = c & a;    
    assign z = int_sig6 | int_sig7 | int_sig8;