mini project on 4 bit serial multiplier

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4 BIT SERIAL MULTIPLIER

A Project Based LAB Dissertation

LAB Title: Design with CPLDs and FPGAs

Submitted by

Mr. J.NAGA SAI (Reg. No. 150040317)

LAB Instructors

Mr. B.Kali vara Prasad (Section Instructor)

Mr. Narasimha Nayak

Dr.A. Kiran Kumar

Mr.M.Venkateswara rao

Department of ECE, KL University

Vaddeswaram, Guntur, AP – 522502

A.Y. 2016-17

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Department of Electronics and Communication Engineering KL

University

Vaddeswaram, Guntur, AP – 522502

CERTIFICATE

This is to certify that the project entitled "4-BIT SERIAL MULTIPLIER " is a

piece of work done by J.NAGA SAI(150040317) students of II B.Tech. (ECE),

during the First semester of academic year 2016-2017, of Department of

Electronics and Communication Engineering of KL University, Vaddeswaram,

Guntur, A.P.,

INDIA.

Course Coordinator Signature of the H.O.D

(Dr. Fazal Noorbasha) (Dr.ASCS Sastry)

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Declaration by the Students

We declare that the project entitled, “4-BIT SERIAL MULTIPLIER” is our own work

conducted under the esteemed guidance of Mr. B.Kali vara Prasad (Section Instructor)

Mr. Narasimha Nayak Dr.A. Kiran Kumar ,Mr.M.Venkateswara rao at the Department of

Electronics and Communication Engineering of KL University, Vaddeswaram, Guntur, A.P.,

INDIA.

J.NAGA SAI (Reg. No. 150040317)

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Acknowledgements

Working on this Project based Lab is certainly a memorable and enjoyable event in our life. We

have learned a lot of interesting new things that have broadened my view of the technology field.

In here, we would like to offer our appreciation and thanks to several grateful and helpful

individuals. Without them, this work could not have been completed and the experience would

not be so enjoyable.

We are very grateful to our esteemed Professors Dr. Fazal Noorbasha (Course Coordinator),

Mr.B.Kali vara Prasad (Section Instructor)Mr. Narasimha NayakDr.A. Kiran Kumar

Mr.M.Venkateswara raoDepartment of ECE, KL University, Vaddeswaram, Guntur, A.P.,

INDIA, for their valuable guidance and creative suggestions that helped us to complete this Lab

project.

Furthermore, we want to offer our thanks to Dr. ASCS Sastry, Professor & Head, Department

ECE, KL University, Vaddeswaram, Guntur, A.P., INDIA, for providing the required facilities to

carry out the project work successfully.

We would like to thank all those helped us directly or indirectly during this project work.

Mr. J.NAGA SAI (Reg. No. 150040317)

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4 BIT SERIAL MULTIPLIER

INDEX

Content Name Page no

1.ABSTRACT 6

2.INTRODUCTION 7

3. MULTIPLICATION ALGORITHM 8

4.PROCEDURE : 11

PROJECT VERILOG CODE 15

TEST BENCH 16

7.OUTPUT: 19

8.RESULT: 19

9. References : 19

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1.ABSTRACT

Bit-serial arithmetic is attractive in view of it is smaller pin count, reduced wirelength, and lower

floor space requirement in VLSI. In fact ,the compactness of the design may allow us to run a bit-

serial multiplier at a clock rate high enough to make the unit almost competitive with much more

complex designs with regard to speed. In addition, in certain application contexts inputs are

supplied bit-serially anyway. In such a case, using a parallel multiplier would be quite wasteful,

since the parallelism may not lead to any speed benefit. Furthermore, in applications that call for

a large number of independent multiplications, multiple bit-serial multiplier may be more cost-

effective than a complex highly pipelined unit.

Bit-serial multipliers can be designed as systolic arrays: synchronous arrays of processing

element that are interconnected by only short, local wires thus allowing very high clock rates. Let

us begin by introducing a semi systolic multiplier, so named because its design involves

broadcasting a single bit of the multiplier x to a number of circuit element, thus

violating the “short, local wires” requirement of pure systolic design.

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2.INTRODUCTION

Multipliers play an important role in today’s digital signal processing and

various other applications. With advances in technology, many researchers have

tried and are trying to design multipliers which offer either of the following design

targets – high speed, low power consumption, regularity of layout and hence less

area or even combination of them in one multiplier thus making them suitable

for various high speed, low power and compact VLSI implementation.

The common multiplication method is “add and shift” algorithm. In parallel multipliers number

of partial products to be added is the main parameter that determines the performance of the

multiplier. To reduce the number of partial products to be added, Modified Booth algorithm is one

of the most popular algorithms. To achieve speed improvements Wallace Tree algorithm can be

used to reduce the number of sequential adding stages. Further by combining both Modified Booth

algorithm and Wallace Tree technique we can see advantage of both algorithms in one multiplier.

However with increasing parallelism, the amount of shifts between the partial products and

intermediate sums to be added will increase which may result in reduced speed, increase in silicon

area due to irregularity of structure and also increased power consumption due to increase in

interconnect resulting from complex routing. On the other hand “serialparallel” multipliers

compromise speed to achieve better performance for area and power consumption. The selection

of a parallel or serial multiplier actually depends on the nature of application. In this lecture we

introduce the multiplication algorithms and architecture and compare them in terms of speed, area,

power and combination of these metrics.

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3. MULTIPLICATION ALGORITHM

The multiplication algorithm for an N bit multiplicand by N bit multiplier is

shown below:

Y= Yn-1 Yn-2 ........................Y2 Y1 Y0 Multiplicand

X= Xn-1 Xn-2 ..................... X2 X1 X0 Multiplier

GENERALLY

Y= Yn-1 Yn-2 ........................Y2 Y1 Y0

X= Xn-1 Xn-2 ..................... X2 X1 X0

============================================================================

Yn-1X0 Yn-2X0 Yn-3X0 …… Y1X0 Y0X0

Yn-1X1 Yn-2X1 Yn-3X1 …… Y1X1 Y0X1

Yn-1X2 Yn-2X2 Yn-3X2 …… Y1X2 Y0X2

… … … …

…. …. …. …. ….

Yn-1Xn-2 Yn-2X0 n-2 Yn-3X n-2 …… Y1Xn-2 Y0Xn-2

Yn-1Xn-1 Yn-2X0n-1 Yn-3Xn-1 …… Y1Xn-1 Y0Xn-1

-----------------------------------------------------------------------------------------------------------------------------------------

-P2n-1 P2n-2 P2n-3 P2 P1 P0

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DIFFERENT TYPES OF MULTIPLIERS

Serial/Parallel Multiplier One operand is fed to the circuit in parallel while the other is serial. N partial

products are formed each cycle. On successive cycles, each cycle does the

addition of one column of the multiplication table of M*N PPs. The final results

are stored in the output register after N+M cycles. While the area required is N-

1 for M=N.

Shift and Add Multiplier Depending on the value of multiplier LSB bit, a value of the multiplicand is added and

accumulated. At each clock cycle the multiplier is shifted one bit to the right and its value is tested.

If it is a 0, then only a shift operation is performed. If the value is a 1, then the multiplicand is

added to the accumulator and is shifted by one bit to the right. After all the multiplier bits have

been tested the product is in the accumulator. The accumulator is 2N (M+N) in size and initially

the N, LSBs contains the Multiplier. The delay is N cycles maximum. This circuit has several

advantages in asynchronous circuits.

Array MULTIPLIER

Array multiplier is well known due to its regular structure. Multiplier circuit is based on add and

shift algorithm. Each partial product is generated by the multiplication of the multiplicand with

one multiplier bit. The partial product are shifted according to their bit orders and then added. The

addition can be performed with normal carry propagate adder. N-1 adders are required where N is

the multiplier length.

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EXAMPLE :

MULTIPLICATION IN DETAIL:

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4.PROCEDURE :

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Binary Multiplication :

In the binary number system the digits, called bits, are limited to the set. The result of multiplying

any binary number by a single binary bit is either 0, or the original number. This makes forming

the intermediate partial-products simple and efficient. Summing these partial- products is the time

consuming task for binary multipliers. One logical approach is to form the partial-products one at

a time and sum them as they are generated. Often implemented by software on processors that do

not have a hardware multiplier, this technique works fine, but is slow because at least one machine

cycle is required to sum each additional partial-product. For applications where this approach does

not provide enough performance, multipliers can be implemented directly in hardware.

COMPONENTS IN A 4 BIT SERIAL MULTIPLIER :

1. AND GATE

2. HALF ADDER

3. FULL ADDER

1. AND GATE :

The AND gate is a basic logic that implements logical conjunction – It behaves according

to the truth table

Logic Diagram

TRUT H TABLE :

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Workinng :

In this gate if either of the inputs is low (0), then the output is also low, but if

all the inputs are high (1) the output will also be high (1).

2.HALF ADDER

Half adder is a combinational arithmetic circuit that adds two numbers and produces a sum bit (S)

and carry bit (C) as the output. If A and B are the input bits, then sum bit (S) is the X-OR of A

and B and the carry bit (C) will be the AND of A and B.

Logic Diagram :

TRUTH TABLE :

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Working :

The half adder adds two one-bit binary numbers (AB). The output is the sum of the two bits (S)

and the carry (C). Note how the same two inputs are directed to two different gates. The inputs to

the XOR gate are also the inputs to the AND gate.

VERILOG CODE FOR HALF ADDER

module HalfAdder(a,b,s,c);

input a,b;

output s,c; xor

a1(s,a,b); and

a2(c,a,b);

endmodule

3.FULL ADDER :

The full adder circuit adds three one – bit binary numbers(C A B) and outputs two one – bit binary

numbers, a sum(S) and a carry(C)

Block Diagram :

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Truth Table :

VERILOG CODE FOR FULL ADDER

module FullAdder(a,b,c,s,ca );

input a,b,c; output s,ca; wire

s1,c1,c2;

HalfAdder h1(a,b,s1,c1);

HalfAdder h2(s1,c,s,c2); or

o1(ca,c1,c2);

endmodule

PROJECT VERILOG CODE

module Multiplier(

A,

B,

Product_out ); input [3:0] A;

input [3:0] B; output [7:0]

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Product_out; assign Product_out[0] =

A[0] & B[0];

HalfAdder u0 (A[0]&B[1], A[1]&B[0], Product_out[1], C0);

FullAdder u1 (A[1]&B[1], A[2]&B[0], C0, sum_u1, C1);

FullAdder u2 (A[2]&B[1], A[3]&B[0], C1, sum_u2, C2);

HalfAdder u3 (A[3]&B[1], C2, sum_u3, C3);

HalfAdder u4 (A[0]&B[2], sum_u1, Product_out[2], C4);

FullAdder u5 (A[1]&B[2], sum_u2, C4, sum_u5, C5);

FullAdder u6 (A[2]&B[2], sum_u3, C5, sum_u6, C6);

FullAdder u7 (A[3]&B[2], C3, C6, sum_u7, C7);

HalfAdder u8 (A[0]&B[3], sum_u5, Product_out[3], C8);

FullAdder u9 (A[1]&B[3], sum_u6, C8, Product_out[4], C9);

FullAdder u10 (A[2]&B[3], sum_u7, C9, Product_out[5], C10); FullAdder

u11 (A[3]&B[3], C7, C10, Product_out[6], Product_out[7]);

endmodule

TEST BENCH

module

multitb;

// Inputs

reg [3:0] A;

reg [3:0] B;

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// Outputs

wire [7:0] Product_out;

// Instantiate the Unit Under Test (UUT)

Multiplier uut (

.A(A),

.B(B),

.Product_out(Product_out)

); initial begin

// Initialize Inputs

A = 8;

B = 8;

// Wait 100 ns for global reset to finish

#100;

// Add stimulus here


A = 1;

B = 1;


#100;


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A = 2;

B = 2;


#100; // Initialize Inputs

A = 0;

B = 0;


#100;

end

endmodule

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7.OUTPUT:

8.RESULT:

We had performed the ‘4 BIT SERIAL MULTIPLIER’code in the xilinx,and we tested

the output with some values and got the output which we had expected

9. References :

1.www.allaboutcircuits.com

2.www.google.com/applications+of+shift+register

3.http://en.wikipedia.org/wiki/Shift_register

4.www.elektor.com

http://www.allaboutcircuits.com/

http://www.allaboutcircuits.com/

http://www.google.com/applications+of+shift+register

http://www.google.com/applications+of+shift+register

http://en.wikipedia.org/wiki/Shift_register

