FPGA-BASED IMPLEMENTATION OF ELECTRONIC ABACUS...

FPGA-BASED IMPLEMENTATION OF ELECTRONIC ABACUS USING

ALTERA DE2 BOARD

AZMI BIN SIDEK

A project report submitted in partial

fulfilment of the requirement for the award of the

Degree of Master of Electrical Engineering

Faculty of Electrical and Electronic Engineering

Universiti Tun Hussein Onn Malaysia

JULY 2017

iii

For my beloved mother, my dearest wife and children.

iv

ACKNOWLEDGEMENT

Praise to Allah upon His blessing that granted me the guidance, strength and

knowledge to complete this project.

Special appreciation to my supervisor, Assoc. Prof. Dr. Abd. Kadir bin

Mahamad for the support and guidance throughout the duration of my study. Not

forgetting my fellow colleagues who gave me the friendly environment to work

within.

A very warm gratitude to my wife, children and family that gives me their

fullest support and understanding throughout the years upon completion of my study.

Last but not least, to everyone involved directly or indirectlytowards the compilation

of this thesis.

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ABSTRACT

The development of electronic abacus is to integrate the use of abacus along with

electronic devices which offers better visualisation of the abacus operations. The

main focus of this application is to assist the primary school students‟ in validating a

fundamental arithmetic operation by using an abacus. The electronic abacus is

developed by integrating an abacus, abacus decoder module and FPGA-based

processor. DE2 115 is chosen as the development module and VHDL as main

programming language. The arithmetic algorithm developed for the electronic abacus

is limited to the computational of whole numbers only. The electronic abacus is

operational in two modes, display mode and arithmetic mode. In the display mode,

the abacus beads position at column 1 until column 7is displayed as numerical

representation on the LCD screen. A computation of arithmetic operations with less

than three operatorsare available in the arithmetic modewith the capability

ofdisplaying the negative numerical and infinite value. The implementation of

integrating an abacus with electronic devices will hopefullycontribute in the

development of more lively and interesting teaching approach by using this ancient

apparatus.

vi

ABSTRAK

Penghasilan abakus elektronik yang menggabungkan abakus bersama peranti

elektronikdapatmenggambarkan operasi aritmetik abakus yang lebih jelas kepada

penggunanya. Digunakan sebagai alat bantuan bagi pelajar sekolah di peringkat

sekolah rendah dan sebagai pengesah operasi aritmetik bagi abakus. Abakus

elektronik dihasilkan dengan menggabungkan abakus, modul pengekodan serta

pemproses berasaskan FPGA. DE2 115 dipilih sebagai modul pembangunan dan

VHDL sebagai bahasa pengaturcaraan utama. Algoritma aritmetik yang dibangunkan

bagi abakus elektronik ini, bagaimanapun terhad kepada pengiraan untuk

nomborbulat sahaja. Abakus elektronik beroperasi dalam dua mod, iaitu mod

paparan dan mod aritmetik. Pada mod paparan, pengguna dapat melihat perwakilan

nombor pada paparan LCD yang mewakili kedudukan manik abakus pada lajur

pertama hingga lajur ke 7. Selain itu, pengiraan operasi aritmetik bagi kurang dari

tiga pengoperasi boleh dilaksanakan dalam mod aritmetik dengan keupayaan paparan

nilai negatif dan infiniti. Integrasi di antara peranti elektronik dengan abakus

diharapkan dapat membangunkanpenghasilan kaedah pembelajaran menggunakan

abakus yang lebih menarik dan bertenaga.

vii

TABLE OF CONTENTS

ACKNOWLEDGEMENT iv

ABSTRACT v

ABSTRAK vi

LIST OF TABLES x

LIST OF FIGURES xi

LIST OF SYMBOLS AND ABBREVIATIONS xiv

LIST OF APPENDICES xv

CHAPTER 1 1

INTRODUCTION 1

1.1 Introduction 1

1.2 Problem Statement 2

1.3 Objectives 2

1.4 Project Scope 3

1.5 The Organisation of Thesis 3

CHAPTER 2 5

LITERATURE REVIEW 5

2.1 Introduction 5

2.2 Abacus Historical Review 5

2.3 Abacus Architecture 8

2.4 Abacus Arithmetic Operation 9

2.4.1 Addition 10

viii

2.4.2 Subtraction 12

2.4.3 Multiplication 12

2.4.4 Division 14

2.5 Previous Related Works 16

2.6 Summary of Previous Related Works 18

CHAPTER 3 20

METHODOLOGY 20

3.1 Introduction 20

3.2 Project Activities 20

3.3 Hardware Design 21

3.4 Abacus Numerical Display and Arithmetic Algorithm 27

3.5 Experimental Configuration 30

CHAPTER 4 33

DATA ANALYSIS AND RESULTS 33

4.1 Introduction 33

4.2 Bead Sensor Circuitry and DE2 Interface Board Evaluation 33

4.3 Bead Sensor Decoder 37

4.4 Binary to ASCII Conversion 38

4.5 LCD Controller 39

4.6 Arithmetic Algorithm 40

4.6.1 Two Variables Arithmetic Operation 41

4.6.2 Three Variables Arithmetic Operation 42

4.6.2.1 Combinations of Additional Operators 43

4.6.2.2 Combinations of Subtraction Operators 46

4.6.2.3 Combinations of Multiplication Operators 47

4.6.2.4 Combinations of Division Operators 47

4.7 VHDL Evaluations 49

ix

4.8 Complete System Evaluations 51

4.8.1 Display Mode 53

4.8.2 Arithmetic Mode 53

4.8.2.1 Two Variables Mode 54

4.8.2.2 Three Variables Mode 57

CHAPTER 5 67

DISCUSSION AND CONCLUSIONS 67

5.1 Introduction 67

5.2 Discussion 67

5.3 Conclusions 70

5.4 Future Works 71

REFERENCES Error! Bookmark not defined.

APPENDIX A 76

APPENDIX B 78

APPENDIX C 80

APPENDIX D 81

APPENDIX E 82

APPENDIX F 106

x

LIST OF TABLES

2.1 Summary of previous related works 17

4.1 Binary logical levels 32

4.2

Bead position binary representation with respect

to numeral value

33

4.3 Experimental result for abacus column 7 33







4.10 Combinational of addition operators 42

4.11 Combinational of subtraction operators 44

4.12 Combinational of multiplication operators 45

4.13 Combinational of division operators 46

4.14 DE2 hardware and pin allocations 49

xi

LIST OF FIGURES

2.1 Salamis Tablet 6

2.2 Replica of Roman Abacus 6

2.3 Chinese abacus (2/5 suan pan) 7

2.4 Japanese abacus (soroban) 8

2.5 The evolution of counting devices 8

2.6 Japanese abacus construction and notations 9

2.7

Japanese abacus beads position and numerical

value

9

2.8 Additional Operation 10

2.9 Subtraction Operation 12

2.10 Multiplication Operation 14

2.11 Division Operation 15

3.1 Project flowchart 20

3.2 Abacus model used in hardware design 21

3.3 Abacus modification 21

3.4 DE2Interface board 22

3.5 Bead sensor board elevation 22

3.6

Multistage board configuration with respect to

abacus bead

23

3.7

Proximity sensor grid configuration on bead

sensor board

23

3.8 Proximity sensorcontrol circuitry 24

3.9 Configuration of alternate column triggering 25

3.10 Configuration of I2C interconnection 26

3.11

Flowchart for display and two variables

arithmetic mode

27

xii

3.12 Flowchart for three variables arithmetic mode 28

3.13 Experimental setup configuration 30

4.1

Beads position with respective to its resistor

value

32

4.2 Simulation output of a single column 36

4.3 Simulation output of binary to ASCII conversion 37

4.4 LCD controller state machine 38

4.5 Simulation of two variables arithmetic 39

4.6 Simulation output of addition combinations 42

4.7 Simulation output of subtraction combinations 43

4.8

Simulation output of multiplication

combinations

45

4.9 Simulation output of division combinations 46

4.10 Flow Summary 47

4.11 Power Analyser Summary 48

4.12 Display mode 50

4.13 Addition mode 51

4.14 Subtraction mode 52

4.15 Multiplication mode 53

4.16 Division mode 53

4.17 Division mode of infinite value 54

4.18 Arithmetic function of two (2) additions 56

4.19 Arithmetic function of addition and subtraction 56

4.20

Arithmetic function of addition and

multiplication

57

4.21 Arithmetic function of addition and division 57

4.22 Arithmetic function of subtraction and addition 58

4.23 Arithmetic function of two (2) subtractions 58

4.24

Arithmetic function of subtraction and

multiplication

59

4.25 Arithmetic function of subtraction and division 59

4.26

Arithmetic function of multiplication and

addition

60

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4.27

Arithmetic function of multiplication and

subtraction

60

4.28 Arithmetic function of two (2) multiplications 61

4.29 Arithmetic function of multiplication and

division

61

4.30 Arithmetic function of division and addition 62

4.31 Arithmetic function of division and subtraction 62

4.32 Arithmetic function of division and

multiplication

63

4.33 Arithmetic function of two (2) divisions 63

5.1 Row spacer 65

5.2 Sensing error 66

xiv

LIST OF SYMBOLS AND ABBREVIATIONS

Ω - Resistance

A.D - Anno Domini

ASCII - American Standard Code for Information Interchange

B.C - Before Christ

CMOS - Complementary Metal Oxide Semiconductor

DE2 - Development and Education board version 2

FPGA - Field-programmable gate array

GPIO - General-purpose input/output

LCD - Liquid Crystal Display

I2C - Inter-Integrated Circuit

RTL - Register Transfer Level

SDA - Serial Data

SCL - Serial Clock

TTL - Transistor-Transistor Logic

USB - Universal Serial Bus

V - Volt

VCC - Collector Supply Voltage

VDD - Drain Supply Voltage

VHDL - Very High Speed Integrated Circuit Hardware Description Language

xv

LIST OF APPENDICES

APPENDIX TITLE PAGE

A Bead sensor design 73

B DE2 interface design 75

C Abacus bead decoder source code 77

D Binary to ASCII decoder source code 78

E

Abacus numerical display and arithmetic

functions source code

79

F Arithmetic algorithm source code 103

CHAPTER 1

INTRODUCTION

1.1 Introduction

Arithmetic operation is a process of adding and subtracting numbers. The

advancement of these operation produce multiplication and division operations. The

invention of counting apparatus is major step in human civilisation and influenced by

continuous development of these mathematical process. Abacus is a counting

apparatus which undergo multiple evolutions, is believed to be initiated by the

Babylonian, popularise in ancient Chinese and perfected by the Japanese. As

automatic counting machine such as calculator become more common these day, the

traditional counting machine such as abacus still plays an important role in the

development of children intellectual. The uses of abacus in Malaysian early

education, proves that this ancient counting machine is far from being forgotten. The

fingers manipulation during operating of the abacus, develop a mental calculator for

the users thus integrate active process on both side of the brain.Furthermore, the uses

of abacus will boost up children mathematical confidence level thus preparing the

younger generation to be more confident in facing the future challenges[1] and

develop active attitude toward study[2].

2

1.2 Problem Statement

The practiseof traditional abacus as brain stimuli has been acknowledge worldwide

and proven to be an effectivemethod in mathematical learning process. Learning a

traditional abacus without the presence of a teacher is proven to be a hassle, as it

requires different technique for different mathematical operation.This drawback has

been acknowledged by the researcher, and the development of computerised module

related to abacus usage for the young and old, has filled the gap. The virtual abacus

or software based application thus provide better visualisation of operation and

technique used, but missing out on the physical experience perspective.

The development of electronic abacus is an approach to validate the

mathematical operation conducted by an abacus, without missing the physical

experience of using it. It is design as additional apparatus which can be detached

while not in use, thus preserving its authenticity.The electronic abacus algorithm can

be developed using various programming language. The development of electronic

abacus algorithm using VHDL programming language is chosen as its offers better

digital design flexibility and synthesizable register transfer level (RTL), which later

can be used to develop its specific function of integrated circuit. Furthermore, VHDL

programming offers precision simulation for complex algorithm compared to other

microprocessor simulations. The development of electronics abacus could promote a

better understanding and active learning process in mathematical courses for

kindergarten, schools‟ studentas well asadult learners.

1.3 Objectives

Objective of this projects are as follows:

a) To develop an electronic abacus validator for the use of learning

mathematical through arithmetic operation.

b) To develop a concise apparatus with detachable standard size abacus.

c) To evaluate the implementation of VHDL programming in DE2 thus validate

electronic abacus application.

3

1.4 Project Scope

There are several scopes for this project as listed below.

a) The abacus used is a wooden standard size Japanese abacus which is

commonly used as educational tools in primary schools.

b) The arithmetic operations are limited to fundamental operation such as

addition, subtraction, multiplication, division and combination of two

operators.

c) The decimal notation for multiplication and division is excluded as the

reference of unit rod is varied for these operations.

d) Arithmetic operations can be conducted with two or three variables with

various arithmetic combinations.

e) Arithmetic processes involved in division operation or combination of

division operations, will produced a whole number result without the

remainder.

f) The arithmetic process is limited to only whole numbers operations and

capable of displaying numerical representation up until 107 (0 to 9999999).

1.5 The Organisation of Thesis

This thesis consists of five chapters:

Chapter 1: This chapter deals with the basic introduction of abacus, problem

statement, objectives and project scope.

Chapter 2: This describe the history of abacus, the construction of abacus used,

arithmetic operational technique and previously related works associated with this

project.

Chapter 3: This chapter discussed the methodological aspect of the project. The

planning of the project is demonstrated and the hardware design and configuration is

discussed. Moreover, the software development method and implementation is

explained.

4

Chapter 4: This chapter deals with the result and analysis obtained both from the

experiment and simulation.

Chapter 5: The final chapter concludes the outcome of the project and few

discussions regarding future work or recommendation to further improvementof the

future design.

CHAPTER 2

LITERATURE REVIEW

2.1 Introduction

Abacus is a calculating apparatus used to perform various arithmetic calculations.

The abacus evolution is influenced by the development of arithmetic operations

andthe use of various numeral notations. The modern day abacus has gone through

various adaptation and developed to comply with the modern numeral notation,

which is based upon Arabic numbering system. The development of electronic based

abacus is a step forward in utilising this ancient apparatus alongside with an

electronic device to promote more interesting and conducive mathematical learning

process for the early education.

2.2 Abacus Historical Review

The abacus is generally defined as an ancient calculating tools which used in trade to

solve arithmetic problems[3]. The first counting tablet was introduced in Sumer

dated somewhere in period of 4000 B.C[4]. Abacus terminology originated from

Arabic word of „abq‟ which means dust or fine sand, later adapted to Latin word as

abacus, which means the sand tray[5]. It reflects the uses of clay or wood tray filled

with sands for writing symbol in the early age its usage. It eventually evolved into

stone counting boards with parallel grooves and pebbles. Known as „abax‟ or

„abakon‟to the Greek,which defined as table or tablet. The last surviving of ancient

counting board was discovered in Salamis Island on 1846, named the Salamis tablet.

Believed to be used during Babylonians circa 300 B.C[5].

6

The Roman invented the first hand held abacus named calculus which later

renamed as calculi, consists of parallel slits representing Roman numerical

notations[5][6]. The idea of dividing each slits into decimal position,give birth to the

implementation of such characteristics in Chinese and Japanese abacus. Figure 2.1

and 2.2 illustrate the configurations of Salamis tablet and Roman Abacus.

Figure 2.1: Salamis Tablet [6]

Figure 2.2: Replica of Roman Abacus[6]

In mid-century, the abacus is further evolved by introducing more counting

columns and the replacement of pebbles to printed „jeton‟. Each „jeton‟ is a

representation of seven pebbles. At the end of 12th

century, the design further

evolved into nine vertical columns, with each „jeton‟ representing one to nine

digits[6].The European version of abacus is further developed in 14th

century, but the

7

use of abacus became diminished after the counting with written numbers

(arithmetic) gains it popularity.

The invention of Chinese abacus or „suan-pan‟ dated back from the period of

1200 A.D[7][8]. The configuration of Chinese abacusis illustrated in Figure 2.3. The

Chinese abacus is built upon a frame construction of wood and metal reinforcement,

consists of upper deck and lower deck. Each column represented by a rod, consists of

two beads on the upper deck and five beads on the lower deck; such configuration is

also known as 2/5 abacus[7][8].Each columnis representing decimal points according

to Arabic numerical notations.This configuration remains unchanged until 1850

where 1/5 abacus with a single bead in upper columns was introduced. Awarded as

Fifth Invention of Ancient China, the abacus is able to conduct arithmetic operation

such as addition, subtraction, multiplication and division; it also has the ability to

perform square roots and cubic roots[9].

Figure 2.3: Chinese abacus (2/5 suan pan)

The wide application of abacus in ancient China, gain its worldwide

impact.The invention of Japanese abacusin 16th

century isstrongly influenced by 1/5

Chinese abacus. The present day soroban, or Japanese abacus consists only one bead

on upper deck and four beads on the lower deck. This configuration remains

unchanged since 1930. The 1/4 abacus configuration is the most suitable for decimal

calculation, thus abandoned hexadecimal calculation applied by the Chinese

abacus[10]. Mathematical operation perform by Japanese abacus does not limit the

user of using only round numbers but also in decimal points, as well as negative

numbers[4]. A modern day Japanese abacus is as depicted in Figure 2.4.

8

Figure 2.4: Japanese abacus (soroban)

Figure 2.5 illustrate the evolution of counting boards from the earliest of its

existence until the present day. The development of counting boards in Western

Europe is at a standstill since the introduction of Arabic numbering system[7]. The

modern day abacus is constructed based on Japanese abacus as it is uses common

Arabic numerical system, provide multiple variation of arithmetical operation and

much preferred worldwide compared to traditional Chinese abacus.

Figure 2.5: The evolution of counting devices[7]

2.3 Abacus Architecture

This section is dedicated to elaborate the fundamental notation and bead values.The

application is focused on theJapanese abacus as it is the main instrument used in this

project.Japanese abacus is constructed with a slider rod that hold five beads in each

column. A horizontal separator divides a single bead on the upper deck which

represent five points and four beads on the lower deck representing a single point for

each beads. The four notations specified by a dot on the horizontal separator,

indicated the thousandth, unit, thousands and millions decimal locations. The

illustration in Figure 2.6 displays the common Japanese abacus constructions and it

notifications.

9

Each columns configuration represents decimal numeral value, ranges from 0

to 9 according to its decimal position. Figure 2.7 shows the beads configuration with

respect to equivalent decimal numbers. Calculations of round number shall begin at

the second dot from the right. The initial value of 0 is achieved when no beads is

touching the bar and value of beads are counted otherwise. The addition of value 5

and 1‟s concludes the possibilities of achieving numeral representation of 0 to

9.These principles are applied for all the columns, providing various possibilities of

numeral representation.

Figure 2.6: Japanese abacus construction and notations

Figure 2.7: Japanese abacus beads position and numerical value

2.4 Abacus Arithmetic Operation

Abacus is able to emulate multiple arithmetic operations, the imminent discussion

covers the fundamental arithmetic operations such as addition, subtraction,

multiplication and division. The abacus does not compute the arithmetic functions

10

like calculator, but providing the process of achieving the same goal as a counting

machine. Each arithmetic operation requires different technique and will be

discussed further.

The important rules of arithmetic operation using abacus is, to begin the

process from left bead rods to the right and the use of complementary numbers of 5‟s

or 10‟s. Each technique of complementary numbers is grouped into itstotal sum such

as combination of 4 and 1 or 3 and 2 for complementary number of 5‟s. The rules is

also applied for complementary of 10‟s which group into five possible combinations.

2.4.1 Addition

The following procedure perform an addition operation of 45.7 + 4.5. The method of

complementary numbers is demonstrated.

4 5 . 7

Step 1

4 5 . 7

4

4 9 . 7

Step 2

4 5 . 7

-5

4 9 . 2

-9

4 0 . 2

+1

5 0 . 2

Step 3

Step 4

Step 5

11

Figure 2.8: Additional Operation

12

Figure 2.8 illustrate the complete additional operation which is summarized

into the following step. First step is to set the initial value of the arithmetic operation.

45.7 is set according to its decimal places. Second step is by adding value of 4 to unit

rod without its decimal values. Followed by adding 0.5 to the rod of tenth, this

achieved by subtracting the value of complement 10‟s (5). Then, value of 1 is carried

into the unit rod. Adding the value of carry is by subtracting it with the

complementing value of carry (complement of 1 is 9). The carry value on unit rod is

bring forward to the tens rod. Addition of the last carry value to the tens rod resulting

the final value at 50.2.

2.4.2 Subtraction

An arithmetic operation of 22.3-2.8 require different procedure compared to addition

operation. Illustration in Figure 2.9 shows detail steps of conducting subtraction

using abacus.

First step is to set the initial value of 22.3. Next, is to subtract the second

value without its fractional value, giving the subtraction of initial value with 2. This

result in a new value of 20.3. Subtract its factional value according to its decimal

places, hence subtracting 8 from the tenth rod. The subtraction of 3 to 8 on the tenth

rod is not possible, as the minuend is larger than subtrahend. This require borrowing

from the unit rod but no value in the unit column. The unit column is borrowing form

the tens column, thus subtracting 1 from the tens column, hence adding 9 to unit

column. The borrowing from unit column resulting the complement of value 8 to +2.

This event produces an addition of 3 on tenth column, resulting the final value of

19.5.

2.4.3 Multiplication

Arithmetic multiplication on abacus requires the user to set the multiplicand in the

central part of the abacus, while the multiplier is set to the left, leaving two empty

rods in between[5]. The product is later added to the right of the multiplicand. If

multiple multiplicand is required, the first multiplicand is cleared before the second

multiplicand is inserted.

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2 2 . 3

Step 1

2 2 . 3

-2

2 0 . 3

Step 2

2 0 . 3

-1

1 0 . 3

+9

1 9 . 3

+2

1 9 . 5

Step 3

Step 4

Step 5

Figure 2.9: Subtraction Operation

An arithmetic operation of 2.3×17 on abacus will be explained by the

following procedures. In this operation, it processes the total of three whole numbers

which contributed by two whole number on the multiplier and a single unit on the

multiplicand. The position of multiplier or multiplicand is set by the user, but must

be separated by at least two empty columns.

Set multiplier 17 at the far most left hand side with an empty column at the

beginning. Set the multiplicand of 23, at two columns spacingafter the last multiplier

value. This step is as illustrated in Figure 2.10,Step 1. Further to the right, leave an

empty column after the multiplier and set the next column (1/T) as the unit rod.

The product of 3×1 (actual multiplication of 0.3×10) is added to reference

unit column (column 1/T) and product of 3×7 (actual multiplication of 0.3×7) is

14

added to reference unit tenth (column 1/H). Clear the value of 3 in multiplicand

column,indicating that this process section is completed. The current value of this

operation is as illustrated in Figure 2.10, Step 4.

The similar operation is applied to the balance multiplicand. The product of

2×1 (actual multiplication of 2×10) is added to reference tens column (column U)

and the product of 2×7 (actual multiplication of 2×7) is added to the reference unit

tens (column U). Clearing the multiplicand value (2) at its respective column is

necessary to acquire the final value. The final product of the multiplication is 391. As

the reference unit is at column 1/T, the actual value become 39.1. This multiplication

process detailsis as illustrated in Figure 2.10.

2.4.4 Division

The application of division operation took different approach. The abacus committee

agreed to separate dividend and divisor by four empty rods, but the consideration

must be given for a smaller sized abacus[5].

A division operation of 144 ÷ 3 on the abacus is as illustrated in Figure 2.11.

The dividend (144) has three whole numbers, whereas the divisor has only a single

whole number but additional a single spacing givenresulting two columns for the

divisor. Set the divisor at far most left column, leaving two empty consecutive

columns,giving the divisor at rod position thousands to tens. This configuration is

depicted on Figure 2.11, Step 1.

The divisor value of 3, has larger value to the most significant value of

dividend (1). To overcome this issue set the second number of the dividend (4) to the

first empty column to the left. The number placed on the previously empty columns

is called a quotient. Next is multiply divisor value by the quotient number, resulting

3×4 = 12. Subtract this result at its reference column (same columns as dividend

value 14). This procedure is shown as Step 2 in Figure 2.11.

15

0 1 7 0 0 2 3 0 0 0 0 Step 1

0 1 7 0 0 2 3 0 0 0 0

+ 0 3 Step 2

0 1 7 0 0 2 3 0 3 0 0

+ 2 1 Step 3

0 1 7 0 0 2 3 0 5 1 0

clear (-3) Step 4

0 1 7 0 0 2 0 0 5 1 0

0 1 7 0 0 2 0 0 5 1 0

+ 0 2 Step 5

0 1 7 0 0 2 0 2 5 1 0

+ 1 4 Step 6

0 1 7 0 0 2 0 3 9 1 0

clear (-2) Step 7

0 1 7 0 0 0 0 3 9 1 0

Figure 2.10: Multiplication Operation

16

The partial quotient value of 4 and the remainder dividend of 4 is added

(4+4=8), and positionedat the lower column compared to the previous quotient. The

current quotient value of 8 is multiplied by 3 (8×3=24), and the multiplication

product is subtracted from the current value at the lower reference points from the

previous step. Illustrated as Step 3 in Figure 2.11, the final value is 48. The last

quotient column indicates the decimal point notation.

Step 1

0 3 0 0 1 4 4 0 0

Step 2

0 3 0 0 1 4 4 0 0

(4)

- 1 2

0 3 0 4 0 2 4 0 0

Step 3

0 3 0 4 0 2 4 0 0

(8)

- 2 4

0 3 0 4 8 0 0 0 0

Figure 2.11: Division Operation

2.5 Previous Related Works

Previous works play an important role of providing preliminary information for the

researcher related to the project. These information is a composition of patent,

journal, articles, thesis or papers. A traditional abacus has evolved into different

configuration and construction due to adaptation of arithmetic teaching technique.

The patented abacus filed by Andrew F. Schott[11] suggesting the invention of 2/9

abacus is to facilitate the arrangement of counters while another pattern by Shlomo

Ruvane Frieman [3] which uses 18 beads without horizontal separators. The

invention by Shlomo is centred upon introducing new method of mathematical

17

teaching by using his invention. These mechanical inventions however require

different arithmetic solving technique compared to the well-established Chinese or

Japanese abacus.

Electronic abacus develop by KLN KLEIN Production Development

Inc.[12], features five columns of optical switches that resemble the abacus bead.

This device however, does not have the display feature included. An invention by

Junji Hiromori[13]combined both electronic calculator and abacus thus provide

simultaneous function of traditional counting machine and modern computation. The

utilization of numerical keypad as dual function of abacus beads and keypad is an

advancement to traditional abacus,however the movement of abacus bead must be

done independently to avoid operational errors. The invention of Indian

Abacus[14]by Naina Mohamed and Basheer Ahamed is a hardware based electronic

abacus. The function of abacus is emulated by a 13×5 grid of sliding switches.The

operational result is later displayed on LCD screen or sent via USB,in order for the

result to be posted through the internet. This capability enables the Indian Abacus to

be used in primaryand secondary abacus competition, thus emphasised as educational

tools. The Digicus[15] is a combination of traditional Japanese abacus with a

calculator. Developed by Sharp Inc., this invention operates independently. The

calculator is attached as a component of the whole system and does not integrated

with each other, hence not categorised as electronic abacus. Even though most of

these design features enhance the function of the abacus which enables better

understanding of mathematical operations, the authenticity is not well preserved.

Software oriented abacus by Suzana Baharudin etal.[16], emphasized on

interactive learning of abacus for primary one students and offers addition and

subtraction up until numeral of 20. This interactive and attractive application thus

provide motivational emotion to the primary students in learning mathematics but

physical experience using the real abacus in more crucial. Computer-based abacus

training system, developed by Steven N. Long et al.[17],provide the interactive

practice of abacus on computer. Arithmetic operations is demonstrated by graphic

movement of the abacus bead thus provide visual learning process without the

presence of a teacher. Replicating the function of abacus in screen with list of

features, suggesting that this training system is a potential to be applied as

educational teaching tools. Software approach in [16][17] however provide only

virtual abacus experience.

18

Electronic abacus proposed by Alison Barker[18] is equipped with electronic

sensors which detect the abacus bead position.The data is transmitted through USB

and displayed on the computer screen. The additional features of audible capabilities

and magnified text enable this prototype to be used by visually impaired personnel

and normal person as well. The development of E-Abacus by Mohamad Solehin

Robian [19] and Abd Kadir Mahamad et al.[20], demonstrate the integration of

traditional abacus with the use of sensors and microcontroller. This integration

produces flexible application, and enabling the abacus to be operated individually or

with the aid of microcontroller computation.The ability of displaying the arithmetic

representation according to abacus bead positions and result from arithmetic

operation on LCD screen is the distinctive features of this invention. Complex

circuitry and bulky size are the major drawback for this design due to the use of two

separate processors, each for bead sensor circuitry and LCD display.

2.6 Summary of Previous Related Works

The listed previous related works in Table 2.1 is summarized based on the

configuration that features electronic element thus excluding the inventions that uses

only mechanical features.

Table 2.1: Summary of previous related works

Title Author Summary

Electronic abacus KLN KLEIN

Production

Development Inc.

Custom abacus with five columns bead representation.

Uses optical switches to represent abacus bead.

Display feature is not included on the device.

Combined

Electronic

Calculator and

Abacus with

Deflective Guide

Bars

Junji Hiromori Custom abacus with slider features of calculator

keypad.

The movement of abacus bead must be done

independently to avoid operational errors.

Indian Abacus -

Digital

Basheer Ahamed,

Naina Mohamed

13×5 custom abacus, uses slider switch as abacus bead

representation.

Can be used as standalone device or connected to the

computer.

Arithmetic result is displayedon LCD and computer

screen.

Interconnection module to internet, providing data

analysis online.

Designing an

Interactive

Abacus Learning

Suzana Baharudin,

Riaza Mohd Rias,

Mariam Farida

Virtual abacus, software based.

Interactive abacus learning application for primary

students.

19

Application for

Beginners: A

Prototype

Ahmad Limited arithmetic operation until numeral of 20.

Table 2.1 (continued)

Title Author Summary

Computer-based

Abacus Training

Steven N. Long et al. Virtual abacus, software based application.

Emphasized as abacus training module.

Feature realistic graphical movement of abacus bead

during arithmetic operation.

Lots of detailed notation and menu selection for

interactive learning.

Designing

Accessible

Software for the

Electronic Abacus

Alison Barker Detection of abacus bead using electronic sensors.

Able to display result on LCD or computer screen.

Abacus module integrated with computer to visualise

the data with adjustable font size and audible result.

Suitable for normal and visually impaired personnel.

E-Abacus Mohamad Solehin

Robian, Abd Kadir

Mahamad, Sharifah

Saon

Detachable abacus unit from module.

Uses electronic sensors and microcontrollers as

processing unit.

Able to display abacus beads representation and

arithmetic result on LCD.

Complex circuitry and bulky in size.

Computation is limited to the use of whole numbers

only.

CHAPTER 3

METHODOLOGY

3.1 Introduction

A procedure of outlining the research methodology is crucial in achieving the

research objectives. A well-planned methodology could be used as a documented

guideline prior to conducting of any experiment which leads to the reduction of

complications. The following project methodology is focused on the abacus sensor

circuitry design, hardware interface to DE2 board, source code flow chart, simulation

method and operational procedures. The synchronism of hardware setup and VHDL

programming is essential for an orderly operated Electronic Abacus.

3.2 Project Activities

This project is sectioned into two parts, hardware design and VHDL programming.

Hardware design feature two separate design, the abacus sensor beads and DE2

interface board. VHDL programmingwillprovide the arithmetic and bead

representation algorithmas well as displayingthe resultonto the LCD screen.

Multiple aspects must be considered in designing the hardware and algorithm used in

translating bead placement into decimal numbers. Figure 3.1 illustrate the flow chart

of overall project planning, inclusive of hardware design to software integration for

the whole system of Electronic Abacus.

21

Start

Study the Abacus

operational procedures

Selecting Abacus

model to be used

End

Study the suitable

sensors for Abacus bead

Selecting suitable

sensors (with Abacus

dimension limitation)

Abacus bead sensor

(hardware) design

Comply?

NoFitting and bead position

alignment.

Assembling and Testing

Comply?

Yes

No

A

Yes

Development of source

code

A

Interfacing hardware to

DE2

Functional testing

Comply?

Operational testing

Comply?

Yes

Yes

Source code amendment

No

No

Figure 3.1: Project flowchart

3.3 Hardware Design

Selecting the proper abacus by considering the dimension constraint, as well as the

most suitable sensor for the application is a major step in hardware design. The most

suitable choice of the abacus is that it offers the least amount of modification to its

original structure in order for the sensors to be placed underneath the abacus beads.

As abacus comes with various configurations, the most common abacus used by

primary school student which is readily available in the market is selected. A wooden

22

abacus with the dimensions as illustrated in Figure 3.2 is chosen due to its medium

size that offers flexibility of sensors used.

Figure 3.2: Abacus model used in hardware design

This model consists of thirteen columns with a single bead on the top and

four beads at the bottomof the abacus separator. As sensor board will be placed

inside the abacus inner dimension, thus minor modification is required. Figure 3.3

illustrate the comparison between the original states of abacus with the modified

version.

Original condition of abacus

Modified abacus with back panel, reset bar and support bar removed

23

Figure 3.3: Abacus modification

Two parts of boardare required to position the sensor as close as possibleto

the respective beadensuring proper sensor triggering. The first board(bead sensor) is

dimensioned respective to the abacus hollow inner dimension, served as the locking

mechanism to ensure the abacus is stationary during operation. The second board

(DE2 interface) serves as an interface to DE2 board thus providing an elevation in

order to position the sensor beads with minimal distance to it respective abacus

beads. Figure 3.4 shows the DE2 interface board design, whereas Figure 3.5 illustrate

the elevation provided by DE2 interface board. Figure 3.6 shows the positioning of

bead sensor and interfaceboard respective to abacus bead.The average spacing from

abacus base to the abacus beads is approximately at 7.45mm. Total elevation given

by the abacus sensor board is 4.6mm, and with an additional height of abacus sensor

of 1.5mm, giving the total distance from PCB base to the sensor at 6.1mm. So, the

distance between abacus beads and its respective sensor is approximately at 1.35mm.

Figure 3.4: DE2Interface board

4.6 mm 3 mm

24

Figure 3.5: Bead sensor board elevation

The main function of using proximity sensor in this design is to detect the

presence of abacus bead without any physical contact, while keeping distance

between the sensors with abacus bead to minimal. Reflective interrupter SH9206 is

used as the abacus proximity bead sensor. The packaging of this device allows a

precision fitting in a concise space and due to the use of surface mount component,

the position of the sensors will be uniform. The sensors are aligned into 13×5 matrix

grid, and positioned precisely according to the centre of bead position in each rows

and columns. Figure 3.7 depicted the positioning of each sensoron the bead sensor

board. The abacus reset mechanism is removed as the reset bar is located at the same

height of the abacus bead, assuring accuracy of bead position detection.

Figure 3.6: Multistage boardconfiguration with respect to abacus bead

Abacus beads

Proximity Sensor Bead sensor board

DE2 Interface board

Proximity sensors Current limiting resistors

72

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