Factorial of positive integer 

Theory:The factorial of a positive integer n, denoted as n!, is the product of all positive integers from n down to 1.

n!=n×(n−1)×(n−2)×⋯×1n! = n \times (n-1) \times (n-2) \times \cdots \times 1n!=n×(n−1)×(n−2)×⋯×1 

Block diagram:

Verilog code:

module factorial_calculator (

    input wire [2:0] n,

    output reg [12:0] factorial

);

    integer i;

    always @(*) begin

        factorial = 1;

        i = n;

        while (i > 0) begin

            factorial = factorial * i;

            i = i - 1; // Decrement i

        end

    end

endmodule

 Test bench:

module factorial_tb;

    reg [2:0] n;

    wire [12:0] factorial;

    factorial_calculator uut (

        .n(n),

        .factorial(factorial)

    );

      initial begin

        $monitor("Time=%t, n=%d, fact=%d", $time, n, factorial);

        n = 3; #10;

        n = 4; #10;

        n = 5; #10;

        $finish;

    end

endmodule

Output:

Device utilization:

Time analysis: