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AIM: To design Fibonacci Sequence using Verilog.
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SOFTWARES USED: Xilinx Synthesis Tool ISE 9.2i
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INTRODUCTION
Hardware description language (HDL) is a general-purpose language intended to describe circuits textually, for a computer to read. In electronics, a hardware description language or HDL is a specialized computer language used to describe the structure, design and operation of electronic circuits, and most commonly, digital logic circuits. A hardware description language enables a precise, formal description of an electronic circuit that allows for the automated analysis, simulation, and simulated testing of an electronic circuit. It also allows for the compilation of an HDL program into a lower level specification of physical electronic components, such as the set of masks used to create an integrated circuit. Hardware description languages such as Verilog HDL and VHDL are very popular today. Verilog HDL originated in 1983 at Gateway Design Automation. Later, VHDL was developed under contract from DARPA. Initially a proprietary language, but became open standard in early 1990s, then IEEE standard ("1364") in 1995, revised in 2002, and again in 2005. Today Verilog HDL is an accepted IEEE standard. A Verilog HDL is a general-purpose hardware description language similar to C programming language. It is a textual description consisting of expressions, statements and control structures. One important difference between most programming languages and HDLs is that HDLs explicitly include the notion of time. HDLs form an integral part of Electronic design automation systems, especially for complex circuits, such as microprocessor.
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3.1.TYPICAL DESIGN FLOW OF HDL
Fig. Typical design flow of Hdl A Verilog design consists of a hierarchy of modules. Modules encapsulate design hierarchy, and communicate with other modules through a set of declared input, output, and bidirectional ports. Internally, a module can contain any combination of the following: net/variable declarations (wire, reg, integer, etc.), concurrent and sequential statement blocks, and instances of other modules (sub-hierarchies). Sequential statements are placed inside a begin/end block and executed in sequential order within the block. However, the blocks themselves are executed concurrently, making Verilog a dataflow language.
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3.2.FIBONACCI SEQUENCE The Fibonacci Series is a sequence of numbers first created by Leonardo Fibonacci in 1202. It is a deceptively simple series, but its ramifications and applications are nearly limitless. It has fascinated and perplexed mathematicians for over 700 years, and nearly everyone who has worked with it has added a new piece to the Fibonacci puzzle, a new tidbit of information about the series and how it works. By definition, the first two numbers in the Fibonacci sequence are 0 and 1, and each subsequent number is the sum of the previous two. By definition of fibonacci, the first two numbers are : Fibonacci(0)= 0 Fibonacci(1)=1 The next number is always the sum of the previous two. Fibonacci(n)=Fibonacci(n-1)+Fibonacci(n-2) Fibonacci(2)=0+1=1 Fibonacci(3)=1+1=2 Fibonacci(4)=1+2=3 Fibonacci(5)=2+3=5 Fibonacci(6)=3+5=8 Fibonacci(7)=5+8=13 Fibonacci(8)=8+13=21 Fibonacci(9)=13+21=34 Fibonacci(10)=21+34=55 Fibonacci(11)=34+55=89 Fibonacci(12)=55+89=144
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4. APPLICATION OF FIBONACCI SEQUENCE The Fibonacci numbers are an example of a complete sequence. This means that every positive integer can be written as a sum of Fibonacci numbers, where any one number is used once at most. Specifically, every positive integer can be written in a unique way as the sum of one or more distinct Fibonacci numbers in such a way that the sum does not include any two consecutive Fibonacci numbers. This is known as Zeckendorf's theorem, and a sum of Fibonacci numbers that satisfies these conditions is called a Zeckendorf representation. The Zeckendorf representation of a number can be used to derive its Fibonacci coding. . Fibonacci mathematics is a constantly expanding branch of number theory, with more and more people being drawn into the complex subtleties of Fibonacci's legacy. Fibonacci numbers are found in branching plants as they grow. There is one stem which branches into two. Then one of the new stems branches into two while the other one waits. This pattern of one branching while the other waits is repeated for each of the new stems. An example would be the sneezewort although some trees, root systems and algae exhibit this type of branching pattern. Fibonacci numbers are used by some pseudorandom number generators. A special value, closely related to the Fibonacci series, is called the golden section. This value is obtained by taking the ratio of successive terms in the Fibonacci series. If a graph of these values are plotted it is seen that they seem to be tending to a limit. This limit is actually the positive root of a quadratic equation and is called the golden section, golden ratio or sometimes the golden mean. The golden section is normally denoted by the Greek letter phi.
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5. VERILOG CODE 5.1.VERILOG MODULE module fibonacci(clock,reset,value); input clock,reset; output [31:0]value; reg [31:0]previous,current; reg [5:0]counter; //Reset the circuit always@(posedge reset) begin previous<=32’d0; current<=32’d1; count<=6’d1; end always@(posedge clock) begin //increment current index counter=counter+1; current=current+previous; previous=current-previous; end //Read the value of the nth fibonacci number assign value=previous; endmodule
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5.2.TEST BENCH module fibtb(); reg clock,reset; wire [31:0]value; fibonacci f1(value,clock,reset); initial begin reset=1; #10 reset=0; end initial begin clock=0; forever #10 clock=~clock; end initial begin #500 $finish; end endmodule
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6. SIMULATION OUTPUT
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7. CONCLUSION This report is a conceptual review of how to generate Fibonacci sequence in Verilog HDL. This report aims at providing layman’s understanding to the function of Fibonacci sequence. Fibonacci numbers are the the members of the Fibonacci series, which grows up accord to Fibonacci rule. The rule states, the present number in the series is the sum of past number and and the number before past, with the initial condition that, series starts from 0, and the second term is 1. 8. REFERENCES [1]. Samir Palnitkar, “Verilog HDL: Digital Design and Synthesis”, Prentice Hall, 2nd edition,2003. [2]. B.Bala Tripura Sundari,”Design through Verilog HDL”, John Wiley & Sons Publishers, 1st edition,2004 [3]. http://www.mathsisfun.com/numbers/fibonacci-sequence.html [4]. http://www.leonardo-fibonacci-numbers.com/
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