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.

//////////////////////////////////////////////////////////////////////////////////
// TOP
//////////////////////////////////////////////////////////////////////////////////
/*
 * Copyright (c) 2024 Your Name
 * SPDX-License-Identifier: Apache-2.0
 */
`default_nettype none

module tt_um_digital_playground (
    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 (1=drive, 0=input/hi-Z)
    input  wire       ena,      // always 1 when the design is powered
    input  wire       clk,      // clock
    input  wire       rst_n     // reset_n - low to reset
);

  // Mode select (exclusive)
  wire [2:0] mode = ui_in[2:0];
  localparam MODE_GATES = 3'b000;
  localparam MODE_CNT   = 3'b001; // was MODE_MXD
  localparam MODE_PWM   = 3'b010;
  localparam MODE_HEX7  = 3'b011;
  localparam MODE_ALU   = 3'b100;
  localparam MODE_FDC   = 3'b101;
  localparam MODE_RAM   = 3'b110;
  localparam MODE_DIR   = 3'b111;

  // 000: Basic logic gates
  wire g_and, g_or, g_xor, g_nand, g_nor, g_not_a;
  gates_basic u_gates (
    .a(uio_in[0]), .b(uio_in[1]),
    .y_and(g_and), .y_or(g_or), .y_xor(g_xor),
    .y_nand(g_nand), .y_nor(g_nor), .y_not_a(g_not_a)
  );

  // 001: 8-bit counter (enable on ui_in[3])
  wire [7:0] cnt8_q;
  counter8 u_cnt8 (
    .clk (clk),
    .rst_n(rst_n),
    .en  (ui_in[3]),
    .q   (cnt8_q)
  );

  // 010: PWM
  wire pwm_o;
  pwm #(.N(8)) u_pwm (
    .clk    (clk),
    .rst_n  (rst_n),
    .duty   (uio_in[7:0]),
    .pwm_out(pwm_o)
  );

  // 011: HEX to 7-seg
  wire [6:0] seg7;
  hex7seg u_hex (.x(uio_in[3:0]), .seg(seg7));

  // 100: Mini ALU4
  wire [3:0] alu_y; wire alu_flag;
  mini_alu4 u_alu (
    .a (uio_in[3:0]),
    .b (uio_in[7:4]),
    .op(ui_in[5:3]),
    .y (alu_y),
    .carry_or_borrow(alu_flag)
  );

  // 101: Synchronous FDC
  wire [4:0] fdc_y;
  fdc_sincronico u_fdc (
    .VCO  (uio_in[0]),
    .clk  (clk),
    .reset(~rst_n),
    .D_out(fdc_y)
  );

  // 110: 16x4 RAM
  wire [3:0] ram_q;
  RAM u_ram (
    .clk     (clk),
    .we      (ui_in[7]),
    .add     (ui_in[6:3]),
    .data_in (uio_in[3:0]),
    .data_out(ram_q)
  );

  // 111: Direccionales
  wire [2:0] dir_izq, dir_der;
  direccionales u_dir (
    .clk (clk),
    .dir (ui_in[4:3]),
    .izq (dir_izq),
    .der (dir_der)
  );

  // Outputs
  reg [7:0] uo_out_r, uio_out_r, uio_oe_r;
  always @* begin
    uo_out_r  = 8'h00;
    uio_out_r = 8'h00;
    uio_oe_r  = 8'h00;
    case (mode)
      MODE_GATES: uo_out_r = {2'b00, g_not_a, g_nor, g_nand, g_xor, g_or, g_and};
      MODE_CNT  : uo_out_r = cnt8_q;                       // <- counter on outputs
      MODE_PWM  : uo_out_r = {uio_in[7:1], pwm_o};
      MODE_HEX7 : uo_out_r = {1'b0, seg7};
      MODE_ALU  : uo_out_r = {3'b000, alu_flag, alu_y};
      MODE_FDC  : uo_out_r = {3'b000, fdc_y};
      MODE_RAM  : uo_out_r = {4'b0000, ram_q};
      MODE_DIR  : uo_out_r = {1'b0, dir_der, 1'b0, dir_izq};
      default   : uo_out_r = 8'h00;
    endcase
  end

  assign uo_out  = uo_out_r;
  assign uio_out = uio_out_r;
  assign uio_oe  = uio_oe_r;

  wire _unused = &{ena, 1'b0};
endmodule


`timescale 1ns / 1ps
//////////////////////////////////////////////////////////////////////////////////
// 000 Basic logic gates (bundle)
//////////////////////////////////////////////////////////////////////////////////
module gates_basic(
  input  wire a, b,
  output wire y_and, y_or, y_xor, y_nand, y_nor, y_not_a
);
  assign y_and  = a & b;
  assign y_or   = a | b;
  assign y_xor  = a ^ b;
  assign y_nand = ~(a & b);
  assign y_nor  = ~(a | b);
  assign y_not_a= ~a;
endmodule
//////////////////////////////////////////////////////////////////////////////////
// 001 Replaced block: 8-bit counter
//////////////////////////////////////////////////////////////////////////////////
module counter8 #(
  parameter N = 8
)(
  input  wire clk,
  input  wire rst_n,   // active-low reset
  input  wire en,      // count enable
  output reg  [N-1:0] q
);
  always @(posedge clk or negedge rst_n) begin
    if (!rst_n) q <= {N{1'b0}};
    else if (en) q <= q + 1'b1;
  end
endmodule
//////////////////////////////////////////////////////////////////////////////////
// 010 PWM (counter + comparator)
//////////////////////////////////////////////////////////////////////////////////
module pwm #(parameter N=8)(
  input  wire clk, rst_n,
  input  wire [N-1:0] duty,
  output reg  pwm_out
);
  reg [N-1:0] cnt;
  always @(posedge clk or negedge rst_n) begin
    if (!rst_n) cnt <= {N{1'b0}};
    else        cnt <= cnt + 1'b1;
  end
  always @(*) pwm_out = (cnt < duty);
endmodule

//////////////////////////////////////////////////////////////////////////////////
// 011 HEX to 7-Segment (active-low segments option)
//////////////////////////////////////////////////////////////////////////////////
module hex7seg(
  input  wire [3:0] x,
  output reg  [6:0] seg // {a,b,c,d,e,f,g}, 1=ON (set invert if needed)
);
// >>> Module Implementation Begin

// <<< Module Implementation End
endmodule


//////////////////////////////////////////////////////////////////////////////////
// 100 Mini-ALU (4-bit)
//////////////////////////////////////////////////////////////////////////////////
module mini_alu4(
  input  wire [3:0] a, b,
  input  wire [2:0] op,   // 000 add,001 sub,010 AND,011 OR,100 XOR,101 NOTA,110 PASSA,111 PASSB
  output reg  [3:0] y,
  output wire       carry_or_borrow
);
  wire [4:0] addv = {1'b0,a} + {1'b0,b};
  wire [4:0] subv = {1'b0,a} + {1'b0,~b} + 5'b00001;
  assign carry_or_borrow = (op==3'b000) ? addv[4] :
                           (op==3'b001) ? ~subv[4] : 1'b0;
  always @(*) begin
    case (op)
      3'b000: y = addv[3:0];
      3'b001: y = subv[3:0];
      3'b010: y = a & b;
      3'b011: y = a | b;
      3'b100: y = a ^ b;
      3'b101: y = ~a;
      3'b110: y = a;
      3'b111: y = b;
      default:y = 4'h0;
    endcase
  end
endmodule
//////////////////////////////////////////////////////////////////////////////////
// 101 Synchronous FDC
//////////////////////////////////////////////////////////////////////////////////
module fdc_sincronico(
    input wire VCO, clk, reset,
    output reg [4:0] D_out
);
    wire [4:0] count, q1, q2;

    counter counter_1(.clk(VCO), .reset(reset), .count(count));
    register register_1(.clk(clk), .reset(reset), .d(count), .q(q1));
    register register_2(.clk(clk), .reset(reset), .d(q1), .q(q2));

    always @* 
        D_out = q1 - q2;
endmodule
module counter(
    input wire clk, reset,
    output reg [4:0] count
);
    always @(posedge clk) begin
        if (reset) 
            count <= 5'd0;
        else 
            count <= count + 1;
        end
endmodule

module register(
    input wire clk, reset,
    input wire [4:0] d,
    output reg [4:0] q
);
    always @(posedge clk) begin
        if (reset) 
            q <= 5'd0;
        else 
            q <= d;
    end
endmodule

//////////////////////////////////////////////////////////////////////////////////
// 110 16 x 8 RAM, synchronous read, 2-cycle pipelined WE
//////////////////////////////////////////////////////////////////////////////////

module RAM (
  input        clk,
  input        we,
  input  [3:0] add,
  input  [3:0] data_in,
  output reg [3:0] data_out
);
  reg [3:0] mem [0:15];
  reg we_s, we_ss;
  always @(posedge clk) begin
    data_out <= mem[add];
    we_s     <= we;
    we_ss    <= we_s;
  end

  always @(posedge clk) begin
    if (we_ss)
      mem[add] <= data_in;
  end
endmodule

//////////////////////////////////////////////////////////////////////////////////
// 111 Single-module version of direccionales 
//////////////////////////////////////////////////////////////////////////////////

// ========================== controller (fixed) =========================
module controller (
  input  [1:0] dir,   // 00=off, 01=left, 10=right, 11=both
  input        clk,
  output reg [1:0] left,
  output reg [1:0] right
);
  // state cycles: 01 -> 10 -> 11 -> 01 ...
  reg [1:0] state;

  // pequeño generador de secuencia cíclica de 3 pasos
  always @(posedge clk) begin
    if (dir == 2'b00) begin
      state <= 2'b00;               // apagado
    end else if (state == 2'b00) begin
      state <= 2'b01;               // arranque en 01
    end else if (state == 2'b01) begin
      state <= 2'b10;
    end else if (state == 2'b10) begin
      state <= 2'b11;
    end else begin
      state <= 2'b01;
    end
  end

  // routing según dirección
  always @* begin
    left  = 2'b00;
    right = 2'b00;
    case (dir)
      2'b01: begin left  = state; right = 2'b00; end // solo izquierda
      2'b10: begin left  = 2'b00; right = state; end // solo derecha
      2'b11: begin left  = state; right = state; end // ambos (hazard progresivo)
      default: begin left = 2'b00; right = 2'b00; end
    endcase
  end
endmodule

// ============================ decoder ==========================
module decoder (
  input  [1:0] in,
  output reg [2:0] out
);
  always @* begin
    case (in)
      2'b00: out = 3'b000;
      2'b01: out = 3'b001;
      2'b10: out = 3'b011;
      2'b11: out = 3'b111;
      default: out = 3'b000;
    endcase
  end
endmodule


// ======================= direccionales ===================
module direccionales (
  input        clk,
  input  [1:0] dir,
  output [2:0] izq,
  output [2:0] der
);
  wire [1:0] node2;   // left  state after controller
  wire [1:0] node3;   // right state after controller

  controller controller1(.dir(dir), .clk(clk), .left(node2), .right(node3));
  decoder    decoder1  (.in(node2), .out(izq));
  decoder    decoder2  (.in(node3), .out(der));
endmodule

Reference solution:
rtl/generated.v:   always @(*) begin
    case (x)
      4'h0: seg=7'b1111110;
      4'h1: seg=7'b0110000;
      4'h2: seg=7'b1101101;
      4'h3: seg=7'b1111001;
      4'h4: seg=7'b0110011;
      4'h5: seg=7'b1011011;
      4'h6: seg=7'b1011111;
      4'h7: seg=7'b1110000;
      4'h8: seg=7'b1111111;
      4'h9: seg=7'b1111011;
      4'hA: seg=7'b1110111;
      4'hB: seg=7'b0011111;
      4'hC: seg=7'b1001110;
      4'hD: seg=7'b0111101;
      4'hE: seg=7'b1001111;
      4'hF: seg=7'b1000111;
      default: seg=7'b0000000;
    endcase
  end