Verilog Coding Tips and Tricks: division
Showing posts with label division. Show all posts
Showing posts with label division. Show all posts

Tuesday, November 17, 2015

Synthesisable Verilog code for Division of two binary numbers

For doing division, Verilog has an operator, '/' defined. But this operator has some limitation when it comes to certain synthesis tools such as Xilinx XST. The '/' operator is synthesisable only when the second operand is a power of 2. 

For division of generic numbers Xilinx returns the following error message during synthesis:
Can not simplify operator DIV
 Few year back, I wrote a VHDL function for implementing division which was synthesisable. The design was based on Restoring Division algorithmIn this article, I have converted the same design into Verilog.

Division code:

The size of operands to the division module are defined through a parameter named WIDTH. This way you can use the same code for implementing 8 or 16 or 32 or any sized division. Note that, both the input operands and output have the same size.

module division(A,B,Res);

    //the size of input and output ports of the division module is generic.
    parameter WIDTH = 8;
    //input and output ports.
    input [WIDTH-1:0] A;
    input [WIDTH-1:0] B;
    output [WIDTH-1:0] Res;
    //internal variables    
    reg [WIDTH-1:0] Res = 0;
    reg [WIDTH-1:0] a1,b1;
    reg [WIDTH:0] p1;   
    integer i;

    always@ (or B)
    begin
        //initialize the variables.
        a1 = A;
        b1 = B;
        p1= 0;
        for(i=0;< WIDTH;i=i+1)    begin //start the for loop
            p1 = {p1[WIDTH-2:0],a1[WIDTH-1]};
            a1[WIDTH-1:1] = a1[WIDTH-2:0];
            p1 = p1-b1;
            if(p1[WIDTH-1] == 1)    begin
                a1[0] = 0;
                p1 = p1 + b1;   end
            else
                a1[0] = 1;
        end
        Res = a1;   
    end 

endmodule

Testbench code:

module tb_division;
    parameter WIDTH = 8;
    // Inputs
    reg [WIDTH-1:0] A;
    reg [WIDTH-1:0] B;
    // Outputs
    wire [WIDTH-1:0] Res;

    // Instantiate the division module (UUT)
    division #(WIDTH) uut (
        .A(A), 
        .B(B), 
        .Res(Res)
    );

    initial begin
        // Initialize Inputs and wait for 100 ns
        A = 0;  B = 0;  #100;  //Undefined inputs
        //Apply each set of inputs and wait for 100 ns.
        A = 100;    B = 10; #100;
        A = 200;    B = 40; #100;
        A = 90; B = 9;  #100;
        A = 70; B = 10; #100;
        A = 16; B = 3;  #100;
        A = 255;    B = 5;  #100;
    end
      
endmodule

Simulation Waveform:

The codes were simulated in Xilinx ISE 13.1 to get the following waveform.



Synthesis Results:

The design was synthesised for Virtex 4 fpga and a maximum combinational path delay of 20 ns was obtained for 8 bit division.