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_array_mult_joe_leighthardt (
    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;
    wire [3:0] pp0;
    wire [3:0] pp1;
    wire [3:0] pp2;
    wire [3:0] pp3;
    wire intsig1;
    wire intsig2;
    wire intsig3;
    wire intsig4;
    wire intsig5;
    wire intsig6;
    wire intsig7;
    wire intsig8;
    wire intsig9;
    wire intsig10;
    wire intsig11;
    wire intsig12;
    wire intsig13;
    wire intsig14;
    wire intsig15;
    wire intsig16;
    wire intsig17;
    

    
    
    assign pp0 = {m[3]&q[0],m[2]&q[0],m[1]&q[0],m[0]&q[0]};
    assign pp1 = {m[3]&q[1],m[2]&q[1],m[1]&q[1],m[0]&q[1]};
    assign pp2 = {m[3]&q[2],m[2]&q[2],m[1]&q[2],m[0]&q[2]};
    assign pp3 = {m[3]&q[3],m[2]&q[3],m[1]&q[3],m[0]&q[3]};
    assign p[0] = pp0[0];
    adder inst1(pp0[1],pp1[0],1'b0,p[1],intsig1);
    adder inst2(pp0[2],pp1[1],intsig1,intsig2,intsig3);
    adder inst3(pp0[3],pp1[2],intsig3,intsig4,intsig5);
    adder inst4(1'b0,pp1[3],intsig5,intsig6,intsig7);
    
    adder inst5(pp2[0],1'b0,intsig2,p[2],intsig8);
    adder inst6(pp2[1],intsig4,intsig8, intsig9, intsig10);
    adder inst7(pp2[2], intsig10, intsig6, intsig11, intsig12);
    adder inst8(pp2[3], intsig12, intsig7, intsig13, intsig14);
    
    adder inst9(pp3[0],1'b0,intsig9,p[3],intsig15);
    adder inst10(pp3[1],intsig15, intsig11, p[4],intsig16);
    adder inst11(pp3[2], intsig16, intsig13,p[5],intsig17);
    adder inst12(pp3[3],intsig17, intsig14, 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 adder(
input  x,
input y,
input carry,
output  z,
output carry_out
    );
// >>> Module Implementation Begin

// <<< Module Implementation End
endmodule




Reference solution:
rtl/generated.v:     
   
    wire int_sig1, int_sig2,int_sig3,int_sig4,int_sig5,int_sig6,int_sig7,int_sig8;
    assign int_sig1 = x & ~y;
    assign int_sig2 = ~x & y;
    assign int_sig3 = int_sig1 + int_sig2;
    assign int_sig4 = int_sig3 & ~carry ;
    
    assign int_sig5 = ~int_sig3 & carry;
    assign z = int_sig4 + int_sig5; 
    assign int_sig6 = x & y;
    assign int_sig7 = y & carry;
    assign int_sig8 = carry & x;    
    assign carry_out = int_sig6 | int_sig7 | int_sig8;