Transcript Introduction

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
◦
◦
◦
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Constants
Variables
Operators
Functions
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A value

Can be of any data type
◦ a specific alphabetical and/or numeric value
◦ Does not change during the processing of all the
instructions in a solution
◦ 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
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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.
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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
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Do not use spaces
◦ Either combine terms (PayRate) or include an
underscore to separate (Pay_Rate)
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Do not use special symbols
Be consistent!
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Use appropriate naming convention
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◦ Some languages are case sensitive
◦ PayRate, Pay_Rate, PAYRATE, or PAY_RATE
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Data
◦ Raw, organized facts
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Information
◦ Meaningful output
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Most common types
◦ Numeric
◦ Character
◦ Logical
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Most languages include other data types
◦ Date
◦ Currency
◦ User-defined
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Data Type
Data Set
Examples
Integer
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
True
False
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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
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ASCII - American Standard Code for Information
Interchange
◦ 256 characters
(1 byte)
Unicode
(2 bytes)
 First 128 – standard
 Second 128 – specific to computer
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◦ Replacing ASCII as standard on PC’s
See Appendix C
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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
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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)
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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)
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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_Record
Fname
Lname
SSN
End
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Programmer designates the data type
Data types cannot be mixed
◦ Called data typing
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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)
Integer
Integer(n)
Integer(5.7269)
Random
Random
Random
Sign of a number Sign(n)
3.73
5
0.239768
Sign(7.39)
1
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Function
Middle String
Left String
Right String
Length String
Form
Example
Result
Mid(S,3,2) where
Mid(s, n1, n2) S = "Thomas"
"om"
Left(S,3) where S
Left(s, n)
= "Thomas"
"Tho"
Right(S, 3) where
Right(s, n)
S = "Thomas"
"mas"
Length(S) where S
Length(s)
= "Thomas"
6
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Function
Form
Example
Valued Conversion Value(s)
Value("-12.34")
String Conversion String(n)
String(-12.34)
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-12.34
"-12.34"
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Function
Form
Example
Result
Average
Average(list)
Average(5, 3, 8, 6)
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)
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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.
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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
◦
◦
◦
◦
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+, -, *, /
\, Mod
^, and
functions
Relational
◦ <, >, <=, >=, =, <>
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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.
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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
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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 …
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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.
A=
True
True
False
False
B=
True
False
True
False
then A AND B
True
False
False
False
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Significance: The only time the result is False is
if both A and B are False.
A=
True
True
False
False
B=
True
False
True
False
then A OR B
True
True
True
False
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Also called the “logical complement” or
“logical negation”
Significance: Whatever the value of A is, NOT A
will be the opposite.
A=
True
False
NOT A
False
True
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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.
A=
True
True
False
False
B = then A XOR B
True
False
False
True
True
True
False
False
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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.
A=
True
True
False
False
B = then A EQV B
True
True
False
False
True
False
False
True
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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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ORDER OF PRECEDENCE
OPERATOR
TYPE
NAME
( )
Parentheses
Parentheses
^
Arithmetic
Exponent (Powers)
*/
Arithmetic
Multiplcation, floating-point division
\, Mod
Arithmetic
Integer division, Modulus
+Arithmetic
Addition, subtraction
= <>
Comparison (all
Equal to, not equal to, less than or equal to,
<= >=
have same level of greater than or equal to, greater than, less
> <
precedence
than
NOT
Logical
Logical Negation
AND
Logical
Logical And
OR
Logical
Logical Or
XOR
Logical
Logical Exclusive Or
EQV
Logical
Logical Equivalent
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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)
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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
False
True
True
True
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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
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Often called Assignment Statements

◦ Examples
SalesTax = Price * SalesTaxRate
OvertimePay = (Hours – 40) * Wage * 1.5
Area = Length * Width
◦ SalesTax is the memory location where the
answer will be stored
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Destructive
Read-In
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◦ 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.
SalesTax = Price * SalesTaxRate
D R-I
ND R-I
ND R-I
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Algebraic Expressions cannot be represented
in the computer.
They must be converted to a form the
computer will recognize.
Thus, Straight Line Form
(X  Y)
Y
= (X – Y) / ( (X + Y)^2 / (X – Y )^2 )
2
(X  Y)
straight line form
(X  Y )2
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