1 BEGINNING PROBLEM-SOLVING CONCEPTS FOR THE COMPUTER Chapter 2
2 3 Types of Problems that can be solved on computers : 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, +, -, /
5 Constants 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 8 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.
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).
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. Variable Names PayRate Rate HoursWorked Amount Tempreature StudentName Constant Name PI KCONATANT MULTIPLIER
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 Processing Data How a computer Balances a Checkbook Data Input Data Processed into Information Output Report Checks Deposits Bank Charge Calculates the Balance Balance Sheet
18 Data Types 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 Char Dec Char Dec A 65 a 97 B 66 b 98 C 67 c 99 D 68 d 100 E 69 e 101........................
24 String Data Type 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 26 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
Comparing Characters & Strings 27 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 COP1006 McManus
Comparing Characters & Strings 28 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).
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.
32 User-Defined Data Types User-defined Data types Defined by the user as a new data type Example( kind of cars ) Car_Type End GMC Ford Toyota
Rules for Data Types 33 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.
Rules for Data Types 34 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
Examples of Data Types Data The price of item 4.25 Account number 1234567 Room numbers 112 Name of company Apple Macintosh Check status Pass/Fail True or False Date 12/3/2011 Data Type Numeric Real String Numeric Integer String Logical Date or String
36 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: COP1006 McManus
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 2. String Used in science and business, Calculate such things as square root, absolute value 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(S) where S Length String Length(s) = "Thomas" 6
Conversion Functions 43 Function Form Example Result Valued Conversion Value(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 Functio Definition Exampl Result n e Date Time Error 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 Returns the current time from the system. The time may be in various forms: hh:mm:ss, seconds from midnight, or minutes from midnight Returns control to the program when a systems error occurs. Date Time 09/15/08 9:22:34
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 Operator Compute r Symbol Operation Resultant Addition + 3.0 + 5.2 8.2 Subtraction - 7.5 4.0 3.5 Multiplication * 8.0 * 5.0 40.0 Division / 9.0/4.0 2.25 Integer division \ 9\4 2 Modulo division MOD 9 MOD 4 1 Power ^ 3^2 9
51 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
Relational operatores Operator Computer Symbol Operation Resultant Equal to = 5 = 7 False Less than < 5 < 7 True Greater than > 5 > 7 False Less than or equal to < = 5 < = 7 True Greater than or equal to > = 5 > = 7 False Not < > 5 < > 7 True
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 Operator Compute r Symbol Operation Resultant Not NOT NOT True False And AND True AND True True Or OR True OR False True
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
57 The NOT Operator 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
58 Hierarchy of Operations 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 Order of Operations Operand Data Type Resultant Data Type ( ) reorders the hierarchy; all operations are completed within the parentheses using the same hierarchy Power ^ \, MOD *, / +, _ =, <, >, < =, > =, < > NOT AND OR Numeric Numeric Numeric Numeric Numeric or string or character Logical Logical Logical Numeric Numeric Numeric Numeric Logical Logical Logical Logical
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) True False False True False False False True True
62 Expressions & Equations 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 A+B A and B are numeric. The resultant is numeric and is not stored A < B A and B are numeric, character, or string. The resultant is logical and is not stored. A OR B A and B are logical. The resultant is logical and is not stored Equations C= A + B C,A and B are numeric. The resultant is stored in C. C = A < B A and B are numeric, character, or string. The resultant is stored in C ; C is logical. 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
Straight-Line Form 68 Algebraic Expressions cannot be represented in the computer. They must be converted to a form the computer will recognize. Thus, Straight Line Form Y ( X ( X ( X Y ) = (X Y) / ( (X + Y)^2 / (X Y )^2 ) Y ) Y ) 2 2 straight line form
Attachment: ASCII Coding 69 COP1006 McManus