Lesson 2

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Computational◦ problems involving some kind of mathematical

processing Logical

◦ Problems involving relational or logical processing Repetitive

◦ Problems involving repeating a set of mathematical and/or logical instructions.

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The building blocks of equations and expressions◦ Constants◦ Variables◦ Operators◦ Functions

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A value◦ a specific alphabetical and/or numeric value ◦ Does not change during the processing of all

the instructions in a solution Can be of any data type

◦ Numeric, alphabetical or special symbols Examples

◦ 3, 5, 10, “Mulder”, “Scully”, “+”, “-”, “/”◦ Note: “” indicates datum rather than variable

name

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In some programming languages, constants can be named◦ Provides protection to the constant value and

other areas of the program.◦ Cannot be changed once given initial value

Example◦ SalesTaxRate = 6◦ Commission_Rate = 6◦ Note: no spaces within variable names

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May change during processing A name is assigned to each variable used in

a solution.◦ The name references the memory area where the

value is stored. May be of any data type Examples

◦ Age, LastName, Address, PayRate

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Use mnemonic terms, that is, the name means something◦ Use PayRate not Z

Do not use spaces◦ Either combine terms (PayRate) or include an

underscore to separate (Pay_Rate) Do not use special symbols Be consistent!

◦ Some languages are case sensitive◦ PayRate, Pay_Rate, PAYRATE, or PAY_RATE

Use appropriate naming convention

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Data◦ Raw, organized facts

Information◦ Meaningful output

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Most common types◦ Numeric◦ Character◦ Logical

Most languages include other data types◦ Date◦ Currency◦ User-defined

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Data Type Data Set ExamplesInteger All whole numbers 3456

-43

Real All real numbers (whole + decimal)

3456.78

0.000123

Character (uses quotation marks)

All letters, numbers, and special symbols

“A”, “a”, “1”, “5”, “+”, “%”

String (uses quotation marks)

Combinations of more than one character

“Mulder”“Scully”“123-45-6789”

Logical True or False TrueFalse

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Include all types of numbers◦ Integers

3, 5, -5, 0, -1 and 32,767◦ Real numbers (floating point numbers)

3.1459, -5745 Scientific Notation

2.3E5 or 5.4E-3, where E stands for the Power of 10

◦ Can be Positive or Negative

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Alphanumeric data set◦ Consists of

all single-digit numbers, letters, and special characters available to the computer

◦ contained within quotation marks

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EBCDIC – Extended Binary Coded Decimal Information Code◦ Used on IBM mainframes

ASCII - American Standard Code for Information Interchange◦ 256 characters (1 byte)

First 128 – standard Second 128 – specific to computer

Unicode (2 bytes)◦ Replacing ASCII as standard on PC’s

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See Appendix C

Made up of one or more characters. Contained within quotation marks Cannot be used within calculations

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“123” is not the same thing as 123◦ The first one is a string◦ The second one is a number

Becomes important when deciding when a piece of data is a string or a number◦ Ex. Social Security Numbers

The first one contains 11 characters and is left aligned whereas the second contains 9 numbers and is right aligned

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The computer’s particular coding scheme (ASCII, Unicode, or EBCDIC) converts the character to its associated ordinal number◦ Note: Uppercase letters have a smaller ordinal

values than lowercase letters “A” = 193 whereas “a” = 129 (Unicode 16-bit) “A” = 65 whereas “a” = 97 (ASCII 8-bit)

Once converted, each character, one at a time, can be compared

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Joins character data or string data together

Operators: + and &◦ Dependent on programming language◦ & can mix data types◦ + cannot mix data types (also known as Join)

Examples◦ FName & “ ” & MI & “ ” & LName◦ “James” + “ ” + “T.” + “ ” + “Kirk” = “James T. Kirk”◦ “James” & “ ” & “T.” & “ ” & “Kirk” = “James T. Kirk”

Note the space at the end of the T.

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Consists just two pieces of data◦ True and False◦ Different programming languages also allow

Yes and No 1 (True) and 0 (False) On and Off

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Dependent on programming language, numerous other pre-defined data types are available.◦ Examples

Dates 01/01/1900 January 1, 1900 Times 03:35:05 PM 15:35:05 Currency 3000.00

◦ Note: This is how the data will be stored, not how it is formatted.

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User-defined Data types◦ Defined by the user as a new data type

Examples Records

Employee_RecordFnameLnameSSN

End

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Programmer designates the data type Data types cannot be mixed

◦ Called data typing All data to be used in calculations must be

declared as a numeric data type Each data type uses a data set or domain

◦ Integers – typically -32768 -> 0 -> 32767 but is programming language dependent

◦ Characters – all alphanumeric characters included in the computer’s coding scheme

◦ Logical – the words “true” and “false”

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Small sets of instructions that perform specific tasks and return values.

Two types:◦ Pre-defined

Built into a computer language or application.◦ User-defined

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Benefits◦ Reduces the amount of code that needs to be

written, thus reducing errors of repetition◦ Shortens the development time◦ Improves readability

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Data usually placed within parentheses that the function uses without altering the data◦ In Sqrt(n), the n represents the parameter, in this

case a number◦ In Value(s), the s represents a string

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Mathematical String Conversion Statistical Utility Specific to each programming language…a

partial list follows

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Function Form Example Result

Square Root Sqrt(n) Sqrt(4) 2

Absolute Abs(n) Abs(-3), Abs(3) 3

Rounding Round(n,n1) Round (3.7259,2) 3.73

Integer Integer(n) Integer(5.7269) 5

Random Random Random 0.239768

Sign of a number Sign(n) Sign(7.39) 1

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Function Form Example Result

Middle String Mid(s, n1, n2)Mid(S,3,2) where S = "Thomas" "om"

Left String Left(s, n)Left(S,3) where S = "Thomas" "Tho"

Right String Right(s, n)Right(S, 3) where S = "Thomas" "mas"

Length String Length(s)Length(S) where S = "Thomas" 6

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Function Form Example Result

Valued Conversion Value(s) Value("-12.34") -12.34

String Conversion String(n) String(-12.34) "-12.34"

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Function Form Example Result

Average Average(list) Average(5, 3, 8, 6) 5.5

Maximum Max(list) Max(5, 3, 8, 6) 8

Minimum Min(list) Min(5, 3, 8, 6) 3

Summation Sum(list) Sum (5, 3, 8, 6) 22

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Function Form Example Result

Date Date Date 9/14/02

Time Time Time 9:22:38

Error is a special function that appears in most languages and upon execution return control to the program when (not if) system errors occur.

The data connectors within expressions and equations.

Two types of operations◦ Unary

Negation◦ Binary

Addition, Subtraction, Multiplication, Floating Point Division and Integer Division

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Mathematical◦ +, -, *, /◦ \, Mod ◦ ^, and ◦ functions

Relational◦ <, >, <=, >=, =, <>

Logical◦ And, Or, Not, XOR, EQV

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Integer Division (\)◦ Regular Floating Point Division, except only the

whole number part of the answer is returned.◦ If given a Floating Point number, the number is

rounded—first—before division occurs. Modulo Division (Mod) or Modulus

◦ The remainder part of the answer is returned.

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Returns either the keywords True or False or

Returns a non-zero or zero value.◦-9, -1, 1, 2 are equivalent to True◦0 is equivalent to False

Is stored in two bytes

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Perform comparisons variable - relational operator - variable

◦Ex.If Y > Z then ...

◦ = equal◦ <> not equal◦ < less than◦ > greater than ◦ <= less than or equal to◦ >= greater than or equal to

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And, Or, XOR, Not, EQV Boolean Expressions are used

◦ To create more complicated Boolean Expressions.◦ If a = b AND c < d Then …

They are defined by using Truth Tables…◦ Know the significance of each!

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Significance: The only time the result is True is if both A and B are True.

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A = B = then A AND BTrue True TrueTrue False FalseFalse True FalseFalse False False

Significance: The only time the result is False is if both A and B are False.

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A = B = then A OR BTrue True TrueTrue False TrueFalse True TrueFalse False False

Also called the “logical complement” or “logical negation”

Significance: Whatever the value of A is, NOT A will be the opposite.

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A = NOT A

True FalseFalse True

Significance: The only time the result is True is if A and B are different and False if both A and B are the same.

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A = B = then A XOR BTrue True FalseTrue False TrueFalse True TrueFalse False False

Significance: The only time the result is True is if A and B are the same and False if both A and B are the different.

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A = B = then A EQV BTrue True TrueTrue False FalseFalse True FalseFalse False True

Data and Operators are combined to form expressions and equations

To evaluate these in the proper order, a hierarchy of operations, or Order of Precedence, is used.◦ Note: Whenever you want to clarify an equation,

use the parentheses!

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OPERATOR TYPE NAME ( ) Parentheses Parentheses ^ Arithmetic Exponent (Powers) * / Arithmetic Multiplcation, floating-point division

\, Mod Arithmetic Integer division, Modulus + - Arithmetic Addition, subtraction

= <> <= >=

> <

Comparison (all have same level of precedence

Equal to, not equal to, less than or equal to, greater than or equal to, greater than, less than

NOT Logical Logical Negation AND Logical Logical And OR Logical Logical Or

XOR Logical Logical Exclusive Or EQV Logical Logical Equivalent

ORDER OF PRECEDENCE

Evaluate the following: A = True, B = False, C = True, D = False

A or B or C and D and A and B and (not C) or (not D) To do this, we create what’s called an

Evaluation Tree…

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A or B or C and D and A and B and (not C) or (not D)

False True

False False False FalseTrue

True True

Expressions◦ Process the data and the operands, through the

use of the operators◦ Does not store the resultant (answer)◦ Examples

Price * SalesTaxRate(Hours – 40) * Wage * 1.5

Length * Width

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Same as an expression, except the equation stores the resultant (answer) in a memory location

“takes on the value of” not equals◦ Examples

SalesTax = Price * SalesTaxRateOvertimePay = (Hours – 40) * Wage * 1.5

Area = Length * Width◦ SalesTax is the memory location where the

answer will be stored Often called Assignment Statements

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Destructive Read-In◦The value stored

in the variable on the left-hand side of the equals sign is replaced by the result of the expression on the right-hand side.

Non-Destructive Read-In◦Values used on the

right-hand side are protected from being changed.

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SalesTax = Price * SalesTaxRate

D R-I ND R-I ND R-I

Algebraic Expressions cannot be represented in the computer.

They must be converted to a form the computer will recognize.

Thus, Straight Line Form

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2

2

)(

)(

)(

YX

YX

YXY

= (X – Y) / ( (X + Y)^2 / (X – Y )^2 )

straight line form

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