Count the number of 1's in a Binary number - Verilog Implementation with Testbench

Suppose you have a binary number, how do you count the number of one's in it? There are more than one way to do it. We will see two ways to do it and compare their performances.

Let's take a 16 bit binary number. The output of our design will have a width of 5 bits, to include the maximum value of output, which is 16("10000").

For example,

Input = "1010_0010_1011_0010" =>  Output = "00111" ( 7 in decimal)

Input = "1110_1010_1001_1010" =>  Output = "01001" ( 9 in decimal)

Input = "0011_0110_1000_1011" =>  Output = "01000" ( 8 in decimal)

Design 1 - A simple Verilog code can be written to achieve this:

module num_ones_for(
    input [15:0] A,
    output reg [4:0] ones
    );

integer i;

always@(A)
begin
    ones = 0;  //initialize count variable.
    for(i=0;i<16;i=i+1)   //check for all the bits.
        if(A[i] == 1'b1)    //check if the bit is '1'
            ones = ones + 1;    //if its one, increment the count.
end

endmodule

The code isn't that big and the logic is easy to understand. But it's less efficient and uses much more resources than the customized design I will present next.

Another way to achieve our purpose, would be to add all the bits in our input. Think of it as a sequence of 16 one bit-adders. The zeros in the input vector will not change the sum, and effectively we get the sum as the number of ones in the vector.

***Design 2 -See the Verilog code below to get what I meant:

module num_ones_for(
    input [15:0] A,
    output reg [4:0] ones
    );

integer i;

always@(A)
begin
    ones = 0;  //initialize count variable.
    for(i=0;i<16;i=i+1)   //for all the bits.
        ones = ones + A[i]; //Add the bit to the count.
end

endmodule

Testbench(same for both the designs):

module tb;

    // Inputs
    reg [15:0] A;

    // Outputs
    wire [4:0] ones;

    // Instantiate the Unit Under Test (UUT)
    num_ones_for uut (
        .A(A), 
        .ones(ones)
    );

    initial begin
        A = 16'hFFFF;   #100;
        A = 16'hF56F;   #100;
        A = 16'h3FFF;   #100;
        A = 16'h0001;   #100;
        A = 16'hF10F;   #100;
        A = 16'h7822;   #100;
        A = 16'h7ABC;   #100;   
    end
      
endmodule

Well, design 2 looks much more simpler than design 1 and the synthesis results showed that its much more faster and uses less number of LUT's. See the table below to see how the performance have improved.

Comparison:-

Name of Design	Combination delay	Number of Slice LUT’s used
Design 1	5.632 ns	47
Design 2	2.597 ns	20

As you can see Design 2 is much better than Design 1.