Programming Games

Formulas. Date. Representation in [computer] Storage. Credit Card.

Homework: Finish slide show.Upload application

Overview

• Representation of information. How is everything/anything represented 'in' the computer– Storage

• Formulas

– Simplified credit card calculation

Storage

• Everything (data and programs) is stored in the circuitry of 'the computer'.

• The circuitry includes transistors that are switches: on or off states, 0 or 1. Each switch is called a bit.

• So….numbers are stored using the binary (base 2) system

• Symbols (characters, letters, etc.) are stored using agreed upon systems of encoding– ASCII: 8 bits per character

– UNICODE: 16 bits per character

Why?

• Why not use circuits that can more easily represent numbers using the decimal (base 10) system?

• Answer: Easier to make on/off switches than something with 10 states. Easier to build circuitry for calculations for the base 2 addition and base 2 times tables than the ones you remember…

Recall base 10

• Recall 1s column, 10s column, 100s column

• Recall borrowing (re-grouping) and carrying

• Do problem(s)

Base 2

• Same principle

• 1s column, 2s column, 4s column, ????

• Do problem(s)

Joke

Explain joke on shirt

Base 16• Hexadecimal: used for quick way to

describe bits, mostly commonly for color coding

• Symbols used are 0, 1, 2, …, 9, A, B, C, D, E, F

• You may have seen color coding: RGB (red, green blue) FF0000 is red 00FF00 is green ??

Numbers with fraction partAka numbers with a decimal point• How to represent?• ANSWER: floating point numbers

aka scientific notation– 3.4521 * 102 is the same as 345.21 * 100

– Terminology: 3.4521 (or 345.21) is the mantissa or significand and the 2 (or 0) is the exponent.

• Computer format: use 2 or 16 in place of 10• Example using 32 bits:

– 1 bit for the sign (0 for +, 1 for -)– 8 bits for the exponent – 23 bits for the mantissa (width, i.e., 23, is the

precision)

Characters

• ASCII codingThe character A is represented by 01000001

The character a is represented by 01100001

The character 1 is represented by 00110001

The character 2 is represented by 00110010

….

• Unicode is a 16 bit format big enough (hopefully) for all the world's languages

String of characters

…such as a name or a label or a piece of text

• Fixed length: allocate 1 byte (8 bits) for each character– UNICODE 2 bytes

• Variable length: store string in two parts– One part holds length as a number and

pointer (address) of the whole string– String itself

Boolean

• Named after George Boole• True / False• Theoretically: 1 bit, 0 for false, 1 for true

but• The addressability requirement means it

could be 1 byte or even bigger• String of Booleans can be combined.

– A byte can represent the answer to 8 true/false questions.

Other information

• Programming generally requires encoding of information.

• The encoding CAN BE arbitrary, but does need to be defined– Later: My rock paper scissors game assigns 0 to rock,

1 to paper and 2 to scissors. The player NEVER sees this.

• Many systems of encodings start with 0– Arrays (sets of values) are indexed starting with 0.

Aside

• Representation somewhat analogous to issue of units?– Some number represents measurement of length or

distance or displacement or size. What unit?

• Numbers by themselves rarely convey information– Compared to what?– Out of what?– Definition, Denominator, Distribution, Difference

Instructions

• Computer storage holds– Instructions (the code)

• Instructions may be translation (compilation) of higher level instructions

• Machine code: Load Register, Store Register, Add, Multiply, Check value and jump, etc.

– Information

• Can't look at the bits and say what it is– 01001010 the letter J or the number 74 or ...

Reflect and Continue• Storage of standard things (e.g., numbers)

solved but representation of information for specific problems is / will be new challenge

• Now on to representation of formulas and logic.– Closed form – mathematical formula – easy to

represent in code– Algorithm, logic, may require use of conditionals,

more…

• Models: build computer model = representation of something, some phenomenon. NOT simple (closed form) formula, but involving programs…

Formulas

• Programming languages have features for expressing mathematical formulasdistance = velocity x time

Code, assume distance, velocity, time all variables

distance = velocity * time;

multiplication

Function expressing formula

function distance (velocity, time { return velocity * time;}Give me velocity and time and I'll [the

function] will return the distance.

The function header indicates the [incoming] parameters (aka arguments). NOTE: in ActionScript and some other languages, the function header also indicates datatypes of the parameters and the returned value.

Temperature conversion

Tempfahrenheit = Tempcentigrade*(9/5)+32;

Check by putting in points

for boiling:

212 Fahrenheit and 100 Centigrade

For freezing

32 Fahrenheit and 0 Centigrade

What is formula for… the other direction?

Caution• Recall: Programming systems store whole

numbers (0, 1, 2, -10, etc.) differently than numbers with fractions (0.5, 10.23, -2.3333333, etc.)

• Need to make sure that none of the intermediate steps are truncated to whole numbers!– One approach: write 9.0 and 5.0 and 32.0– Note: problem occurs with the division, not

multiplication or addition

Precedence

• Many programming courses start off with rules of precedencea*b+cIs evaluated as (a*b)+c. The multiplication is

done first

• Recommendation: put in parentheses!

• MAYBE: avoid long statements—use multiple lines

Conditionals

• Suppose a formula (for ticket price or score or …) involves a conditional test:– One Tuesdays, drinks are half priceLogic: if it is Tuesday, dcost = .5*dcost;

• Implementation: use if statement– Alternative: conditional operator. Show later.

• But how do we know if it is Tuesday?• Implementation: use Date

– Remember from first HTML example!

Date code

today = new Date();

dayofweek = today.getDay();

//encoding is 0 for Sunday, 1 for Mon.,

// 2 for Tuesday

if (dayofweek==2) {

dcost = .5 * dcost;

}

Conditional operator

• Operator with 3 operands condition ? value_if_true : value_if_false

…

dcost = (dayofweek==2) ? (.5*dcost) : dcost;

Comfortable_with_conditional ? Use_It : if_statement

Credit card: Simplified

• Make purchases• Receive monthly bill• If you pay up (do NOT have a balance), no credit

charges• If you do not pay anything, fee + interest• If you pay the minimum, interest• Next month, balance is remaining balance, fee,

interest, new purchases• Demonstrate

Credit card

• Multiple purchases

• Do not 'get the float' if you don't pay up

• Compounding may be DAILY

• Advice: pay up—never have a balance– Read the small print

Problems• Slide show

– There is one <img> element. Its src is changed, producing the slide show.

• The code is in the <script> element. This includes 3 function definitions: startss, stopss, change. The change function changes the sn variable (the pointer into the slides array) and changes the src of the img element, displaying a new picture.

• The <body> element has the buttons, made using <a> elements and the <img> element. You can put in other stuff into the <body>

File structure on server

• You may have an index.html file for each folder, including the WEB folder

• If you have an html file in Folder A, and have a folder named pictures in folder A containing a file named bird.gif, the html file can refer to "pictures/bird.gif"

Scaling up

• … making an application bigger / big enough after testing a smaller version

• The slide show can be scaled up to hold more slides by adding names to the array

• Note: the code refers to slides.length

• Scaling up can be more difficult…

Virtual Dog

• Discrete event simulation: Model of a phenomenon

• My model of a dog's behavior• Represent (keep track of) dog's state

– Weight, divided into ranges for purposes of the display

– Time since last feeding• Player actions

– Feed– Pet

• Stochastic (probalistic) effect

Your virtual something

• Start out with small number of states (pictures) and

• 2 actions by the player

• You may build on this application for your final project.

• This scaling up may be / will be more complex since you will be adding more conditions and buttons

Homework

• Review (will be on the midterm!)– Binary, hexadecimal, ASCII– Credit card application

• Finish slide show• Upload application(s)

– Make index.html file

• Look ahead: virtual something– Plan first (states, pictures, player moves)