Computer Programming as Baking Cookie

PowerPoint Presentation

Computer Programming as Baking Cookie

A Recipe for Computational Thinking

in the context of ITEC1001

(and beyond)

Informed and inspired by a STEM Grants Computational Thinking

research conducted and published in Fall 2012

by Dr. Sebastien Siva, Dr. Stella Smith, and Dr. David Kerven

By Jesse Huang ([email protected]))


1

1

Programming as Baking - TOC

Objectives

Notes on Delivery

Whats Computational Thinking?

Why flowchart? Picture worth thousand worlds.

Programming as Baking Evidences

Computational Thinking an Example

Computational Thinking the Evolution

Computational Thinking Vocabulary

Computational Thinking Reading

Computational Thinking Flowcharts

Computational Thinking Advanced Topic: Excel EMP()

Conclusion

Afterthought


2

Programming as Baking - Prolog

Objectives:

an integrated lecture/activity module designed

To promote Computational Thinking in the context of ITEC by giving a series of focused hands-on demonstrations on computer programming (primary) and on digital media and web technology (secondary.)

To introduce computer programming as a fun, useful, easy and delicious undertaking in the hope of inspiring a deeper appreciation of and stronger passion toward information technology in general and software engineering in particular.


3


Objectives:

an integrated lecture/activity module designed

With adequate level of complexity (i.e. non-trivial; thus, a challenge), to show students Whats possible with ITEC, not to bog down with implementation details hoping to achieve programming proficiency in a few hours of lecture and activity.


4


Notes on delivery:

Divide the lesson into a series of 15-20-minute mini lectures/activities to be sprinkled throughout one semester, starting at about week-6, after MS Word module on myitlab, in tandem with TIA Chapter 4. Application Software coverage

Stress the fact from the outset that well use the Number Conversion problem merely as a well-defined, non-trivial but manageable problem serving as a vehicle for illustrating the concept and learning the process of computational thinking and problem-solving .

Be sympathetic; deliver with humility and patience


5



6

Yummy Outcomes

Guaranteed!


First, let me clarify what do I mean by saying

Computational Thinking


7

Computational Thinking - Prolog


8

Confucius (550 BC - 479 BC,

revered by most Chinese people as the

Master of All Teachers after him

he was declared the "Extremely Sage Departed

Teacher" (). He is also known

separately as the "Great Sage" (),

"First Teacher" (), and "Model Teacher for Ten Thousand Ages"

(). ) said (regarding his pupils):

Give them fish, and for 3 days they may survive. Give them fishing nets and teach them how to fish instead, they will live and thrive until the pond is dry.


Here at SST, through the teaching of Computational Thinking, we, too, strive NOT to just give our students fishes (i.e. solutions to particular problems), but to teach them how to fish (i.e. general, algorithmic approaches to problem solving);

to give them recipes and show them how to make cookie cutters and bake cookies (i.e. computer programs, functions, procedures, etc.)


9

9


In the context of ITEC1001, for example, we will not stop at merely teaching our students a particular product such as MS Office productivity software for solving certain classes of problems (e.g. writing resume, PPT presentation),

but we will go further, through the introduction of computational thinking and algorithmic methodology, to also teach them a general, systematic approach to problem-solving.


10


In short, we are aspired to teach students

Not only How to Use software

e.g. MS Office productivity suites (fishes) in the context of general computing terminology

But also How to Make software

i.e. to apply computational thinking skill (fishing nets) to analyze problems and devise solutions; i.e. how to think like a programmer to overcome the learning curve when facing a given, unfamiliar software and/or technology


11


Loosely speaking, Computational Thinking may be viewed as a thought process for analyzing problems, recognizing patterns, and devising algorithmic solutions to the problems on hand. In other words, it is about the algorithmic way of thinking for analyzing problems and the systematic approach to the formation of solution.

http://www.voki.com/pickup.php?scid=8660682&height=267&width=200

More on Algorithmic Problem Solving at:

http://algorithmicproblemsolving.org/aps/


12


In the context of ITEC, I view


as:

Abstract thinking

Step-by-step procedural thinking

Divide-and-conquer thinking

Iterative thinking


13


Computational Thinking in K12 Education, teacher resources second edition

(as it appears on D2L Computational Thinking community)

Operational Definition

CT (Computational Thinking) is a problem-solving process that includes

(but is not limited to) the following characteristics:

Formulating problems in a way that enables us to use a computer and other tools to help solve them

Logically organizing and analyzing data

Representing data through abstractions such as models and simulations

Automating solutions through algorithmic thinking (a series of ordered steps)

Identifying, analyzing, and implementing possible solutions with the goal of achieving the most efficient and effective combination of steps and resources

Generalizing and transferring this problem-solving process to a wide variety of problems

These skills are supported and enhanced by a number of dispositions or attitudes that are essential dimensions of CT. These dispositions or attitudes include:

Confidence in dealing with complexity

Persistence in working with difficult problems

Tolerance for ambiguity

The ability to deal with open-ended problems

The ability to communicate and work with others to achieve a common goal or solution


14

15

S4. Understanding Your Computer Computer System (Hierarchy) Overview

An example of abstract thinking:

Distilling the content of a one-semester course into a single flowchart

15


In the context of ITEC, I have come to the following humble conclusions:


is

Computer Programming

The task of programming is very much like that of baking/cooking: take in a set of input (ingredients), follow the directions of recipes or cookbooks to process the ingredients, and produce output (e.g. cookies.)


16


As demonstrated by researches conducted by Drs. Siva, Smith, et al., computational thinking is a way of thinking and approach to solution, and it is best manifested by flowcharts.

Thus, we will use flowchart and a real computer program, Number Converter, to illustrate the application of algorithmic computational thinking process to solve a real-life problem,


17

i.e. to convert numeral representation of a numeric value from one arbitrary base to another.


Again, we want to stress the fact that well use the Number Conversion problem merely as a well-defined, non-trivial (reasonably complex), but manageable problem serving as a vehicle for illustrating the concept and learning the process of computational thinking and problem-solving

The lesson will be delivered as a series of 15-20-minute mini lectures/activities sprinkled throughout the semester

By the end of this lesson, students will not only learn or reinforce some valuable skills in problem-solving, but also get a glimpse of some fundamentals in computer programming


18

Introduction

A flowchart is a type of diagram that represents an algorithm or process.

Shows the steps as boxes of various kinds, and their order with connecting arrows.

Flowcharts are used in analyzing, designing, documenting or managing a process or program in various fields.

(reused Dr. Sebastien Sivas slide)

A Sample Loop

Most students will need a C or better to complete the GGC Freshman Math Sequence.

Start

MATH 0099

MATH 1111

Stop

Is compass score above 36?

No

Yes

Is grade C or better?

Yes

No


Blackjack Exercise

The card game Blackjack requires the dealer to follow very specific rules for dealing cards to himself. He must deal one card face down, and then deal face up cards until his hand has a total score greater than 16. If his final score is greater than 21, then the dealer busts, else the dealer stands. Either way, his deal is complete.

Create a flow chart on the right hand side depicting the dealer process described above. Note, for this exercise, you do not need to know how a total score is calculated, simply include a step called calculate score.


Blackjack SolutionRemove fromStudent Copy

Start

Deal Face Down Card

Deal Face Up Card

Stop

Is score greater than 16

Yes

No

Is score greater than 21

BUST

Yes

STAND

No

Calculate Score




23

Why flowchart?

A picture is worth thousand words!

- By Hogben, Lancelot T., 1895 Mathematics for the Million

In mathematics, a percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%. Ex.: 6% means 6 parts/boxes out of (over) 100 parts/boxes.



24

- By Hogben, Lancelot T., 1895 Mathematics for the Million

Another examples:

Square of Sum of two quantities

Square of Difference of two quantities



25

Lessons to be learned (Variable vs. Content; Abstract vs. Concrete ):

Learn to think in general/abstract terms (from concrete to abstract):

Square of Sum of two quantities

Learn to translate general/abstract terms back into concrete representations (i.e. pictures, flowcharts)

An example from MyITlab Excel module -

Using the formula rate = amount of increase/base, insert a formula in cell C7 that will calculate the percentage that the population has increased between 1970 and 1980.

Programming as Baking - Evidences


26

(Evidences: we call programming manuals as cookbooks)



27

(How many bits makes one bite ? Java refers to both a type of coffee and a programming language!)



28

(Thus why weve produced)



29

(But, if done right)


Jelly Sandwich Cookies Recipe

Ingredients

2 cups Basic Cookie Dough

Assorted jellies or jams

Directions

On a lightly floured surface, roll out dough to 1/8-in. thickness. Cut with a 2-1/2-in. round cookie cutter. using a 1-1/2-in. cookie cutter of your choice, cut out the center of half of the cookies (discard centers).

Place whole cookies 2 in. apart on greased baking sheets. spread with 1 teaspoon jelly or jam; top with cutout cookies. Pinch edges with a fork to seal. Bake at 375 for 10-12 minutes or until edges are golden brown. Remove to wire racks to cool.

Yield

24 yummy Jelly Sandwich Cookies


30

(To demonstrate, here is a recipe )


Jelly Sandwich Cookies App

Ingredients (Input)

$Basic_Cookie_Dough = 2-cups ;

$jellies _or_jams = 1-p0rtion;

Directions (Process, Function/Method)

$Cookie_Sheet = Roll_out ( $Basic_Cookie_Dough , 1/8-in. thickness ); $Cookie_2-1/2 = CookieCutter.Cut ( 2-1/2-in, $Cookie_Sheet ); $Cookie_1-1/2 = CokkieCutter.Cut( 1-1/2-in., $Cookie_2-1/2, half at-enter); Discard ( $Cookie_1-1/2 );

Place ( $Cookie_2-1/2, 2 in. apart , on greased baking sheets); Spread ( 1 teaspoon jelly or jam, on $Cookie_2-1/2; top (with cutout cookies); Pinch (edges with a fork to seal.) Bake (at 375 for 10-12 minutes or until edges are golden brown.) Remove (to wire racks to cool.)

Yield (Output; eventually goes to our tummy for storage)

24 yummy Jelly Sandwich Cookies


31

( converted to an app in PHP )


All evidences point to one conclusion:


32

Programming

Is

Baking/Cooking!


making Cookie Cutters


33

(Alright, maybe programming is not strictly making cookies but ...)

To automate, to enhance, to change the world and make it better, easier, faster (and make a lot of $money while doing it.)


Number Converter

A web-based cookie cutter (i.e. program) that is built upon three basic ingredients to demonstrate the essence & power of computer programming (i.e. computational thinking.)


34

Transforming

manual labor

Into

automation


S.E.A.L. Challenge - Number Conversion

A guided learning expedition through a series of three S.E.A.L. (Student Engagement toward Active Learning) Challenges to illustrate the process of , and develop the skill in, computational thinking to solve a non-trivial but well-defined and manageable problem: to convert numbers from an arbitrary base to another.


35

Ex. decimal to binary/hexadecimal, and back to decimal; binary to Base-80 and back, etc.

S.E.A.L. Challenges - Number Conversion

Challenge 04: Manual Approach to Number Conversion - with pencil & paper

Numeral versus Number (Value)

Convert numeral representation between various bases using pencil and paper to analyze the problem, and to devise or learn a solution

Challenge 05: Semi-computational Approach to Number Conversion - using Excel spreadsheet

Using Excel spreadsheet formulas to solve the problem

Expand the spreadsheet to support 32-bit number and extend the base to 80 using VLOOKUP() function

Challenge 06: Computational Approach to Number Conversion - with computer programming

Using the Number Converter program (cookie cutter)

Study the functionality, source code,

Draw flowcharts (reverse engineering) on the three major functions: Main driver, ConverToDecimal(), ConvertTo()


36




Work through the above activity/assignment to achieve the following learning objectives:

S.E.A.L. Challenge 04: Manual Approach to Number Conversion - with pencil & paper

Concepts & skills developed: Numeral versus Number(Value), Computational Thinking/Approach

Objectives:

To introduce, clarify, and/or illuminate the concept of Computational Thinking as an algorithmic approach or generalized procedure to problem-solving.

To develop, practice, and/or reinforce skills needed for further exploration of the discipline of Computational Thinking while setting the stage for developing a deeper appreciation for computer programming as an application of such thinking, which will be covered through a series of two separate but related exercises: 1.) Semi-Computational Approach to Number Conversion - using Excel spreadsheet and 2.) Computational Approach to Number Conversion - with computer programming.

To serve as a benchmark for contrasting the levels of effort needed between manual and computational approaches for problem-solving, thus highlight the benefit of efficiency and effectiveness gained by the latter.

By the conclusion of this assignment, students should demonstrate heightened appreciation regarding Computational Thinking as an iterative procedure that, like a good novel, has a begin, middle, and end, and by which certain process(es) can be repeated again and again until certain condition(s) is(are) met. It is this iterative nature of the procedure that lends itself nicely to be carried out by computer programming, thus lies in the heart of computational thinking.


37



https://www.youtube.com/watch?v=qWxiXU02ZQM

(Non-computational/Limited approach)

https://www.youtube.com/watch?v=unYy2xRDm0o

(Non-computational/Limited approach)

https://www.youtube.com/watch?v=ZR0pC6_iW5Q

(Computational/Algorithmic/General approach)


38


Challenge 05: Semi-computational Approach to Number Conversion - using Excel spreadsheet


39
Decimal to Binary:$QuotientDecimal -->$Base34567$Remainder02172831128641122432013221600421080052540062270072135082671923311021611128012240132201421015201


Challenge 06: Computational Approach to Number Conversion - with computer programming (cookie cutter)


40

But, wait, wait, dont tell me: what is a cookie cutter?



41

Simply put:

To learn computer programming (NOT software design/development/engineering) is to learn how to read, write, and think in a foreign language; its all about vocabulary & grammar

(Ex. An esoteric programming language INTERCAL)

It takes only patience and dedication to learn vocabulary & grammar in a foreign language.

Make clear about this point can encourage students to ask questions (there will be no stupid question) to promote true learning

41

What is Programming?

THREE

Basic

Ingredients

A computer program is a cookie cutter to make the world go faster and easier

To program is to write a series of computer instructions (recipe) to process (bake) certain input (data; ingredients) into some useful output (information; cookies)

Only THREE basic ingredients to make up a computer program:

Data & Structure: primitive data, record, array.

Operators : + -, *, /, etc.

Control Flow:sequence, selection, iteration


Ingredients #1: Data & Data Structure

Primitive Data

Variables that hold a single piece of data, such as

A number, e.g. $course_number = 1001; $credit_hour = 4;

A character, e.g. $initial = C; $grade = A;

A string, e.g. $cource_subject = ITEC;

Record (Class)

A group of variables containing Primitive Data to form a logical entity, such as

$course = {$course_subject, $course_number, $credit_hour, };

$contact_info = {$name, $address, $phone, $email, );

Array (Table)

A collection of Primitive Data or Record, such as

$base_10_numeral = {0, 1, 2, 3, , 9};

$base_2_numeral = {0, 1};

$course_catalog = {$course, $course,, $course};

$yellow_page = {$contact_info, $contact_info, , $contact_info};


42

42


an important data structure: Array


43

Google image Array of Dishes:

$numeral_map = array(

'0', '1', '2', '3', '4', '5', '6', '7', '8', '9',

'A', 'B', 'C', 'D', 'E', 'F', 'G', 'H', 'I', 'J',

'K', 'L', 'M', 'N', 'O', 'P', 'Q', 'R', 'S', 'T',

'U', 'V', 'W', 'X', 'Y', 'Z', 'a', 'b', 'c', 'd',

'e', 'f', 'g', 'h', 'i', 'j', 'k', 'l', 'm', 'n',

'o', 'p', 'q', 'r', 's', 't', 'u', 'v', 'w', 'x',

'y', 'z', '!', '@', '#', '^', '&', '*', '(', ')',

'~', '[', ']', '{', '}', '|', '', '/', '?'

);
Index/Value0123101112131415676869777879Numeral0123ABCDEF*()>/?
$numeral_map array looks like this:

To access an array element: $x = $numeral_map[0]; $y = $numeral_map[10]; etc.


Ingredients #2: Basic Operators


44
SymbolOperation MeaningExampleStatement: Instruction or command to tell the computer what to do; e.g. $x = 100 + 10; means add 100 and 10 together and put the result into the memory location designated as $x. 123Numeric literalDefines a numeric value (i.e. can be computed)$x = 100 ;123String literalDefines a string value composed of characters (i.e. cant be computed(Hello World ; Bill Gate $xVariableDefines a memory (RAM) location (bucket) to hold value$x = 100; Assignment Operators:=AssignmentMoves the value on the right to the variable on the left$x = 100; Arithmetic Operators:+AdditionAdd two operands, returns the sum$x = 100 + 10; $x = $x + 20; (what is $x ?) SubtractionSubtract the right operand from the left, returns the difference$x = 100 10; $x = $x 20 (what is $x ? )*MultiplicationMultiplies two operands, returns the product$x = 100 * 10; $x = $x * 20 (what is $x ? )/DivisionDivide the left operand by the right, returns the quotient$x = 100 / 10; $x = $x / 20 (what is $x ? )%ModulusSame as Division, but return remainder instead$x = 105 % 10; $x = $x % 2 (what is $x ? )

44


Ingredients #2: Basic Operators (continued)


45
SymbolOperation MeaningExampleComparison and Conditional Operators:==Equal Is the left operand equal to the right operand? Return TRUE if yes$x = 100; $y = 30 + 70; if ($x == $y) {echo yes;} else {echo no;}!= Or Not equalReturn TRUE if NOT equal$x = 100; $y = 30 + 70; if ($x != $y) {echo yes;} else {echo no;}>Greater thanReturn TRUE if left operand is greater than the right$x = 10;While ($x > 5) {Print $x;$x = $x 1;} (What numbers get printed?)=Greater than OR equal toReturn TRUE if left operand is greater than OR equal to the right$x = 10;While ($x >= 5) {Print $x;$x = $x 1;} (What numbers get printed?) 0 ) {
$remainder = (int)($quotient % $to_base);

$quotient = (int)($quotient / $to_base);

$numeral = $numeral_map[$remainder];

$to_numeral_arr[] = $numeral ;

}

$to_number = implode("",array_reverse($to_numeral_arr)); return $decimal_value;

}


49

Ingredients #3: Control Flow (continued)


4. Function Call (GoTo) :


50

Validate( $from_base, $from_number, $to_base );

if (empty($errors)) {

$to_number = ConvertTo( $from_base, $from_number, $to_base, $to_basex_steps );

}

For a function to work, it must first be defined, and then be called to execute. It usually returns values.



A function in computer programming is like a cookie cuter in cookie baking; it involves two steps

Step 1: Define a function (or design and make a cookie cutter):

mySuperDuperCookieCutter (shape) {

Cut a cookie in the shape as specified by the shape input parameter.

Return the cut cookie;

}

Step 2: Call (i.e. use ) the service of a function:

Cookie_basket = mySuperDuperCokkieCutter(star); // cut a star-shaped // cookie

Cookie_basket = mySuperDuperCookieCuter(round); // cut a round-shaped // cookie

, etc.


51

For a function to work, it must first be defined, and then be called to execute. It usually returns values.

A special note about function -



Now, lets dissect this number-converter

cookie cutter

My Computational Thinking supplement site


52

PHP/Java Source



53

Number Converter code: main driver

$convert = isset( $_REQUEST['convert'] ); //has user submitted input form via //either GET or POST?

if ( $convert ) { //if yes...

//get user inputs

$from_base = $_REQUEST['from_base'];

$from_number = $_REQUEST['from_number'];

$to_base = $_REQUEST['to_base'];

Validate( $from_base, $from_number, $to_base );

if ( empty( $errors ) ) { //if no error

$to_number = ConvertTo( $from_base, $from_number, $to_base, $to_basex_steps );

} //else, fall through to display the page and error message at the bottom and //ask user to try again

} //else, this must be initial page hit;

//fall through to display the page at the bottom to ask use to submit input

PHP/Java Source



54

Number Converter flowchart: Main() driver

PHP/Java Source



55

Number Converter flowchart: ConvertTo() Function

PHP/Java Source



56

Number Converter flowchart: ConvertToDecimalValue() Function

PHP/Java Source

Computational Thinking Advanced Topics

Alternatively or additionally, the class may dissect these programs:

Challenge 07: Dissecting Programs Implementing MS Excel Functions

My Computational Thinking supplement site


57

Source

Computational Thinking Advanced Topics


58

A Demo Implementation of Excel PMT() Function

What is a

Programmer?

It is not like these


59

Computational Thinking Conclusion

2:30 AM

a Programmer is:

a

strives to recognize the challenges, the opportunities, the repetitive pattern of certain manual processes, and devises solutions to them

an

trained to construct programs (recipe, cookie cutter, computational solutions) to instruct computers to automate those manual processes

and, most of all


60


Computational-thinker

Software Engineer


a Programmer, like a Chef, is:

a

who makes cookies (or cookie cutter; output) out of ingredients (input) following a set recipe (process, algorithm, procedure, method), to make the world faster, easier, and better.


61

Problem-solver

and making a lot of $money

while doing it.

Chapter 1 Review:

Think about How we shop,

research, entertain, socializenowadays? None of these is possible without programmers.


As a

a Chef relives the problem of hunger

a Programmer provides faster, easier, and better way to satisfy humankinds thirst for knowledge (e.g. Google, Wiki), entertainments (e.g. YouTube, games), connection & communication (e.g. Facebook, iPhone, email), and the infrastructure to support all of the above (i.e. Operating System, e.g. MS Window, Apple Mac OS, Unix/Linux), and much more


62

Computational-thinker & Problem-solver


Programming, like baking, is:


63

Fun, Easy,

(a piece of cookie)

Useful,

& very Yummy indeed.

a potential gravy (or icing on a cookie?) of teaching Computer Programming as Baking Cookie is perhaps to attract more female ITEC majors to strengthen the representation of WIT (?)



64

Computer Programming as Playing Football

To encourage Men In Technology, perhaps we can present to our students that a programmer is like a quarterback in a football game


65

Computer Programming as Playing Football

instead of talking about cookbook, well talk about playbook (so much more like flowchart or Entity-Relationship diagram?)


66


To program is to cook according to cookbooks (or to play according to playbooks, in order


67

(Either way, it brings us to the same conclusion)

To automate, to enhance, to change the world and make it better, easier, faster (and make a lot of $money while doing it.)


The End

Thank You for Your Indulgence.

Question?


68

https://www.youtube.com/watch?v=vUEXMnBj-qY

Love Me With All Your Heart Engelbert H. Karaoke.mp4


Results from pilot implementation:

Students have developed deeper appreciation for information technology in general and for ITEC1001 course in particular; many expressed that those S.E.A.L challenges focused on the theme of computational thinking have enhanced their ITEC1001 learning experience.

Students have displayed heightened interest in software development and web technology; several students have approached me without solicitation for advises on future ITEC course and/or major; many have expressed wish to enroll into other ITEC courses taught by me.

Students have shown improvement in their computational / abstract thinking skill, and expressed desire to explore further.

It worked!


69

Afterthought

Student Engagement toward Active Learning

Success Factors of a S.E.A.L. lecture/activity:

Design complex (non-trivial) but manageable: design it with adequate level of difficulty and complexity; make it a challenge, preferably with concrete, manageable example(s); too simple would make it boring; too complicated would induce frustration.

Delivery rigor but with humility: be sympathetic; mindful that we may have spent the better part of our adult life studying/practicing IT, ITEC1001 to most of our students is perhaps their first formal encounter with the subject matter; intimidation, even without intention, is not a recipe for falling in love at the first sight.


70

Afterthought

Statement 1

Statement 2

...

Start

End

1. Sequence

If

Condition

true?

Statement(s)Statement(s)

...

...

Start

End

YesNo

2. Selection (Decision)

While

Condition

true?

Statement(s)

...

...

Start

End

YesNo

3. Iteration (Loop)

{ Definition& Invocation }

1Function in Computer Programming

Compiled by Jesse Huang, 10/05/2013

1.7 Construct

error message(s)

1.3

$convertbutton

pressed?

1.8 Draw the web page

1.1 Declare & initialize

variables, i.e.:

...

$errors= array();

...

$from_base = 10;

$from_number = "";

$to_base = 2;

$to_number = "";

...

Main Start

Main End

No(i.e. this is

initial page hit)

Yes(i.e. user has

submitted inputs)

1.2 Set up a $numeral_map

0.10.2

Initial

page

hit

$convert

button

pressed

HTML

HTML

Web browser

0.1

0.2

1.4Validate($from_base, $from_number,

$to_base)

i.e. user inputs

1.5

Any input error?

1.6 $to_number = ConvertTo($from_base,

$from_number, $to_base)

No(i.e. user input

are all valid)

Yes(e.g $from/$to_base

out of bound, invalid

numerals)

Number Converter Main()Driver (1)

2

2.3

$quotient > 0 ?


variables, i.e.:

...

global $numeral_map;

global $to_decimal_steps;

$to_numeral_arr = array();

$remainder = 0;

$quotient = 0;

...

Start

Return

No(i.e. $quotient reached zero)

2.2 $quotient =

ConvertToDecimalValue(

$from_base,

$from_number,

$to_decimal_steps);

2.4$remainder = ($quotient % $to_base);

Number ConverterConverTo()Function (2)

2

3

2.5$numeral = $numeral_map[$remainder];

2.6$quotient = (int)($quotient / $to_base);

Yes

2.7$to_numeral_arr[] = $numeral;

2.8 Assemble

$to_numeral_arrinto a

$to_numberstring with

correct most-significant-to-

least-significant order;

2

(functionreturn with

output $to_number)

(function call with 3 input

parameters: $from_base,

$from_number, $to_base)

3.3

$i >= 0 ?

(more digit to process ?)


variables, i.e.:

$decimal_value = 0;

$position_magnitude = 0;

$from_numeral_arr =

str_split($from_number);

$number_of_digit =

count($from_numeral_arr);

Start

Return

No(i.e. no more digit to process)

3.2 $i =highest position(defined as

$number_of_digit 1);

3.4 $exponent = $number_of_digit -$i 1;

Number Converter ConverToDecimalValue()Function (3)

3

3.5$multiplier = ToValue($from_numeral_arr[$i]);

3.6 $position_value = Power($from_base, $exponent);

3.7 $position_magnitude = ($multiplier * $position_value);

3

(functionreturn with

output $decimal_value)

(function call with 2 input

parameters: $from_base,

$from_number)

3.8 $decimal_value += $position_magnitude;

3.9 $i = $i -1;

Yes

For demo in computer programming class

Jesse Huang

Excel PMT() Implementation1

Documents

Computer Programming as Baking Cookie