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BEGINNING PROBLEM-SOLVING
CONCEPTS FOR THE COMPUTER
Chapter 2
1
3 Types of Problems that can be solved on
computers : 2
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.
Fundamental Concepts 3
The building blocks of equations and expressions
Constants
Variables
Operators
Functions
Expressions
equations
Constants 4
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, “Sara”, “+”, “-”, “/”
Constants 5
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
Variables 6
May change during processing
In many programming languages, variables are called identifiers.
The variable name should be consistent with what the
value of the variable represents
A name is assigned to each variable used in a solution.
The name references the memory area where the value is stored.
Variables 7
The computer uses the name as a reference to help it find that value in its memory .
May be of any data type
Examples
Age, LastName, Address, PayRate
Difference between name of a variable and
value of a variable
The rule for naming variable differ from language to
language .
there will be no character- length limitations for
variable .
The computer uses the variable name to find the
location; it uses the value found at the memory
location to do the processing.
8
Rules for Naming Variables 9
1- name variable according to what it represents
√ Hours for hours worked.
x H for hours worked (correct but not
recommended because it is not clear enough).
√ PayRate for rate of pay.
x P for rate of pay (correct but not
recommended because it is not clear enough).
Create as short a name as possible, but one that clearly represents the variable.
2- Do not use spaces √ HoursWorked for hours worked (correct).
x Hours Worked Incorrect because the space.
√ StudentName for student name (correct).
x Student Name Incorrect because the space.
3 - Start a variable name with a letter. √ Hours for hours worked (correct).
x 2hours Incorrect because starting by number 2.
√ Student for student name (correct).
x 8Student Incorrect because starting by number 8
4- Do not use a dash ( or any other symbol that is used as mathematical operator).
For example:
√ StudentName for student name (correct).
x Student-Name Incorrect because using a dash symbol.
13
4 - Be consistent when using upper-and lower case characters.
HOURS is different variable name than Hours
For example:
Age and AGE are two variables (not the same variable).
5 - Exact variable name must be used in all places where the data item is used . For example:
If the data item hours worked has the variable name of Hours, Hours must
be used consistently.
√ Hours hours worked
x Hrs or HoursWorked (Incorrect, it is a new variable).
Constant Name Variable Names
PI
KCONATANT
MULTIPLIER
PayRate
Rate
HoursWorked
Amount
Tempreature
StudentName
6 - Use the naming convention specified by the company
where you work. The naming convention is uppercase for the
first character in each of the words in the name, with no
spaces between words in the name.
Data type 16
Data
unorganized facts.
They go into the computer as input .
Information
The output of processing of input .
Is printed in the form of reports.
17
Data
Data
Processed
into Information
Report
Balance
Sheet
Calculates the
Balance
Checks
Deposits
Bank Charge
Input Output
Processing Data – How a computer
Balances a Checkbook
Data Types 18
Data can come with different type :(Most common types)
Numeric
Character
Logical
Computer should know the data type of each variable or constant .
Most languages include other data types
Date
User-defined
Numeric Types 19
Include all types of numbers.
The only data type that can be used in numeric calculation.
Integers
3, 5, -5, 0, -1 and 32,767
Real numbers (floating point numbers)
Are whole numbers plus decimal parts (3.1459, -5745)
Scientific Notation
2.3E5 or 5.4E-3, where E stands for the Power of 10
Can be Positive or Negative.
Numeric data are used for value ( salary , rate of pay)
Data Types & Data Sets 20
Each data type has a data set
A data set is the set of value that are allowed in a
particular data type.
Data Types & Data Sets
Data Type Data Set Examples
Numeric :Integer All whole numbers 3456
-43
Numeric :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
21
Character Types 22
Alphanumeric data set
Consists of
all single-digit numbers,
letters, and
special characters available to the computer
contained within quotation marks
An upper case letter is considered a different
character from a lower case letter .
Table of ASCII Characters 23
Dec Char Dec Char
97 a 65 A
98 b 66 B
99 c 67 C
100 d 68 D
101 e 69 E
...... ...... ...... ......
…... …... …... …...
String Data Type 24
Made up of one or more characters.
Contained within quotation marks
Cannot be used within calculations
Items that would not have mathematical
computations performed on them should be
designed string data type .
some languages do not differentiate between
characters and strings .
Strings - Caution 25
“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
Comparing Characters & Strings
The computer’s particular coding scheme (ASCII,
Unicode, or EBCDIC) converts the character to its
associated ordinal number
The computer gives each character a number.
The number representation is necessary because the computer work only with numbers. example:
A 65
a 97
26
Note: Uppercase letters have a smaller ordinal values than
lowercase letters
“A” = 65 whereas “a” = 97 (ASCII 8-bit)
Once converted, each character, one at a time, can
be compared.
Example:
Banana is larger than Apple because B has larger
number representing it than A
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Comparing Characters & Strings
Comparing Characters & Strings
Concatenation could be used to join a first name with
a last name or to join pieces of data together.
Characters and String data can be compared and
arranged in alphabetical order (as ascending order).
28
Concatenation 29
Joins character data or string data together with the
+ operator .
Example :
“James” + “ ” + “T.” + “ ” + “Kirk” = “James T. Kirk”
“100” + “3” = “1003” not “ 103 “
Logical (Boolean) Data Type 30
Consists of two value in the data set :
True and False
Some languages accept yes, T, and Y for true .
no, F, and N c for False .
Example :
Check someone’s credit record ; true means credit is ok.
False means it’s not ok.
For example, the variable Warm might be declared as a
logical data type to describe if temperature values are
warm or not.
Other Data Types 31
date data type and user defined data type
Date data type is a number for the date that is the number of days from a certain date .
Is a numeric data type because you can perform mathematical calculation on any date .
User-Defined Data Types 32
User-defined Data types
Defined by the user as a new data type
Example( kind of cars )
Car_Type
GMC
Ford
Toyota
End
Rules for Data Types
Programmer chooses the data type during the
programming process .
The data that define the value of a variable or a constant
will be one of three data type : numeric , character or
logical .
Data types can not be mixed, Once a constant or a
variable has been given a data type it cannot change.
All data to be used in calculations must be declared as a
numeric data type.
33
Rules for Data Types
Each data type uses a data set or domain
Numeric – uses the set of all base 10 numbers, the plus sign(+), and the negative sign(-) .
Characters – all characters included in the computer.
Logical – the words “true” and “false”
34
Examples of Data
Types
Data Type Data
Numeric
Real
The price of item
4.25
String Account number
“1234567”
Numeric
Integer
Room numbers
112
String Name of company
“Apple Macintosh”
Logical Check status
Pass/Fail
True or False
Date or
String
Date
12/3/2011
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COP1006
How the Computer Stores Data
Data Storage
Each variable name is given a memory location
Each memory location can hold one and only one
value at a time.
This memories are temporary storage, when a user
enters a new value the old one is destroyed
Example:
Functions 37
Small sets of instructions that perform specific tasks
and return values.
FunctionName(data)
Are used as parts of instructions in a solution .
Two types:
Pre-defined
each language has a set of functions within it .
User-defined
Programmers write their own functions.
Functions 38
The name of function may vary from language to
language
Benefits
Reduces the amount of code that needs to be written,
thus reducing errors of repetition.
Function Parameters 39
the data which is listed as part of the function and
are called parameters .
In Sqrt(n), the n represents the parameter, in this case a
number
In Value(s), the s represents a string
Not all function need parameters
In Random , no data are needed
Parameter can be a constant , a variable , or an
expression
Function Types 40
1. Mathematical
Used in science and business , Calculate such things as square root, absolute value
2. String
Manipulate string variable
3. Conversion
Convert data from one data type to another
4. Statistical
5. Utility
Important in business programming
Mathematical Functions 41
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
String Functions 42
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
Conversion Functions 43
Function Form Example Result
Valued ConversionValue(s) Value("-12.34") -12.34
String Conversion String(n) String(-12.34) "-12.34"
For example, since character string can not be used
in calculations, one of these functions would convert
a string value to a numeric value
Statistical Functions 44
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
Utility Functions
45 Result Exampl
e
Definition Functio
n
09/15/08 Date Returns the current date from the
system. The date may be in various
forms:
mm/dd/yy, day only, month only, year
only, or Julian calendar
Date
9:22:34 Time Returns the current time from the
system. The time may be in various
forms:
hh:mm:ss, seconds from midnight, or
minutes from midnight
Time
Returns control to the program when a
systems error occurs.
Error
Operators 46
The data connectors within expressions and
equations.
thy tell the computer how to process the data .
They also tell the computer what type of the
processing( mathematical, logical, or …..) needs to
done.
The operand are the data that the operator
connect and processes ( constants or variable).
The data type of the operands of an operator must
be the same.
The resultant is the answer that results when the
operation is completed .
The data type of operands and the resultant
depends on the operator .
Ex : 5 + 7
Operator Types 48
1. Mathematical
The data types of operands and resultants of mathematical operators are always numeric
+, -, *, /
\, Mod ( used in business )
^
functions
Two Special Math Operators 49
Integer Division (\)
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.
Mathematical Operators
Resultant Operation Compute
r Symbol
Operator
8.2 3.0 + 5.2 + Addition
3.5 7.5 – 4.0 - Subtraction
40.0 8.0 * 5.0 * Multiplication
2.25 9.0/4.0 / Division
2 9\4 \ Integer division
1 9 MOD 4 MOD Modulo division
9 3^2 ^ Power
Relational Operators
Relational operators
Perform comparisons
the use of relational operators is the only way for the computer to make decisions .
The resultant of relational operation is logical data type .
The operand s can be numeric or character
51
Relational operatores
Resultant Operation Computer
Symbol
Operator
False 5 = 7 = Equal to
True 5 < 7 < Less than
False 5 > 7 > Greater than
True 5 < = 7 < = Less than or equal to
False 5 > = 7 > = Greater than or equal to
True 5 < > 7 < > Not
Logical Operators
53
AND, OR, NOT
used to connect relational expressions .
a = b AND c < d
Perform operations on logical data.
They are defined by using Truth Tables…
Logical opeartores
Resultant Operation Compute
r Symbol
Operator
False NOT True NOT Not
True True AND True AND And
True True OR False OR Or
The AND Operator 55
Significance: The only time the result is True is if both A and B are True.
A B A AND B
True True True
True False False
False True False
False False False
The OR Operator 56
Significance: The only time the result is False is if both A and B are False.
A B A OR B
True True True
True False True
False True True
False False False
The NOT Operator 57
Also called the “logical complement” or
“logical negation”
Significance: Whatever the value of A is, NOT A will be the opposite.
A NOT A
True False
False True
Hierarchy of Operations 58
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.
The processing of the operands always starts with
”functions” then the innermost parentheses and
works outward, and processes from left to right
Note: Whenever you want to clarify an equation, use
the parentheses!
The Order of Precedence 59
Resultant Data Type Operand Data Type Order of Operations
( ) reorders the hierarchy; all operations are completed within the
parentheses using the same hierarchy
Numeric Numeric Power ^
Numeric Numeric \, MOD
Numeric Numeric *, /
Numeric Numeric +, _
Logical Numeric or string or
character
=, <, >, < =, > =, < >
Logical Logical NOT
Logical Logical AND
Logical Logical OR
Example 60
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…
61
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
Expressions & Equations 62
Expressions
Process the data and the operands, through the use
of the operators
Does not store the resultant (answer)
Examples :
to find the number of square feet in a room :
Length * Width
Equations 63
Same as an expression, except the equation stores the resultant (answer) in a memory location
“takes on the value of” not equals
Examples
Area = Length * Width
Often called Assignment Statements
Expressions Equations
A+B
A and B are numeric.
The resultant is numeric and is not stored
C= A + B
C ,A and B are numeric.
The resultant is stored in C .
A < B
A and B are numeric , character, or string.
The resultant is logical and is not stored .
C = A < B
A and B are numeric , character, or string .
The resultant is stored in C ;
C is logical.
A OR B
A and B are logical .
The resultant is logical and is not stored
C = A OR B
C ,A and B are logical .
The resultant is stored in C .
Example : evaluating a mathematical
expression .
5 * ( X + Y ) – 4 * Y / ( Z + 6 )
uses the following values to evaluate the expression :
X = 2 Y = 3 Z = 6
Operation resultant
1. X + Y 5
2. Z + 6 12
3. 5 * resultant of 1 25
4. 4 * Y 12
5. Resultant of 4 / resultant of 2 1
6. Resultant of 3 – resultant of 5 24
Example : evaluating a relational expression .
A – 2 B
uses the following values to evaluate the expression :
A = 6 b= 8
Operation resultant
1. A – 2 4
2. Resultant of 1 B false
Example : evaluating a logical expression .
A AND B OR C AND A
uses the following values to evaluate the expression :
A = true B = false C = true
Operation resultant
1. A AND B false
2. C AND A true
3. Resultant of 1 OR resultant of 2 true
68
Straight-Line Form
Algebraic Expressions cannot be represented in the
computer.
They must be converted to a form the computer will
recognize.
Thus, Straight Line Form
2
2
)(
)(
)(
YX
YX
YXY
= (X – Y) / ( (X + Y)^2 / (X – Y )^2 )
straight line form
Attachment: ASCII Coding
McManus COP1006
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