module inv (A, Y);
  input A;
  output Y;
  assign Y = (~A); // "A'"
endmodule
module tri_inv (A, S, Z);
  input A;
  input S;
  output Z;
  assign Z = (~A); // "A'"
endmodule
module buffer (A, Y);
  input A;
  output Y;
  assign Y = A; // "A"
endmodule
module nand2 (A, B, Y);
  input A;
  input B;
  output Y;
  assign Y = (~(A&B)); // "(A * B)'"
endmodule
module nor2 (A, B, Y);
  input A;
  input B;
  output Y;
  assign Y = (~(A|B)); // "(A + B)'"
endmodule
module xor2 (A, B, Y);
  input A;
  input B;
  output Y;
  assign Y = ((A&(~B))|((~A)&B)); // "(A *B') + (A' * B)"
endmodule
module imux2 (A, B, S, Y);
  input A;
  input B;
  input S;
  output Y;
  assign Y = (~((A&S)|(B&(~S)))); // "( (A * S) + (B * S') )'"
endmodule
module dff (D, CLK, RESET, PRESET, Q, QN);
  reg IQ, IQN;
  input D;
  input CLK;
  input RESET;
  input PRESET;
  output Q;
  assign Q = IQ; // "IQ"
  output QN;
  assign QN = IQN; // "IQN"
  always @(posedge CLK, posedge RESET, posedge PRESET) begin
    if ((RESET) && (PRESET)) begin
      IQ <= 0;
      IQN <= 0;
    end
    else if (RESET) begin
      IQ <= 0;
      IQN <= 1;
    end
    else if (PRESET) begin
      IQ <= 1;
      IQN <= 0;
    end
    else begin
      // "D"
      IQ <= D;
      IQN <= ~(D);
    end
  end
endmodule
module latch (D, G, Q, QN);
  reg IQ, IQN;
  input D;
  input G;
  output Q;
  assign Q = IQ; // "IQ"
  output QN;
  assign QN = IQN; // "IQN"
  always @* begin
    if (G) begin
      IQ <= D;
      IQN <= ~(D);
    end
  end
endmodule
module aoi211 (A, B, C, Y);
  input A;
  input B;
  input C;
  output Y;
  assign Y = (~((A&B)|C)); // "((A * B) + C)'"
endmodule
module oai211 (A, B, C, Y);
  input A;
  input B;
  input C;
  output Y;
  assign Y = (~((A|B)&C)); // "((A + B) * C)'"
endmodule
module halfadder (A, B, C, Y);
  input A;
  input B;
  output C;
  assign C = (A&B); // "(A * B)"
  output Y;
  assign Y = ((A&(~B))|((~A)&B)); // "(A *B') + (A' * B)"
endmodule
module fulladder (A, B, CI, CO, Y);
  input A;
  input B;
  input CI;
  output CO;
  assign CO = (((A&B)|(B&CI))|(CI&A)); // "(((A * B)+(B * CI))+(CI * A))"
  output Y;
  assign Y = ((A^B)^CI); // "((A^B)^CI)"
endmodule