1. Beginning Problem-Solving Concepts for the Computer Lesson 2 McManusCOP10001

2. 3 Types of Problems 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. McManusCOP10002

3. Fundamental Concepts The building blocks of equations and expressions –Constants –Variables –Operators –Functions (predefined—more about user- defined functions later) McManusCOP10003

4. Constants 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 McManusCOP10004

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 –Note: no spaces allowed within names –Examples SALES_TAX_RATE = 6 COMMISSION_RATE = 6 McManusCOP10005 Constant name are usually in ALL CAPS

6. Variables The name references the memory or storage location where the value is stored –May change during processing –May be of any data type –A name is assigned to each variable used in a solution. Examples –Age, LastName, Address, PayRate McManusCOP10006

7. Rules for Naming Variables Use mnemonic terms-- the name is meaningful –Use PayRate not Z Do not use spaces Do not use special symbols, except the underscore –Examples PayRate, Pay_Rate, PAYRATE, or PAY_RATE Use appropriate naming convention Be consistent! –Some languages are case sensitive –Either combine terms (PayRate) or include an underscore to separate (Pay_Rate) McManusCOP10007

8. So, what do we store? Data or Information? McManusCOP10008

9. Data Vs. Information Data –The raw, organized facts Information –The meaningful output McManusCOP10009

10. Data Types Most common types –Numeric –Character –Logical Most languages include other data types –Date –Currency –User-defined –Strings McManusCOP100010

11. Rules for Data Types –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 - -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” –Data types cannot be mixed Called data typing –Programmer designates the data type McManusCOP100011

12. Data Types & Data Sets Data TypeData SetExamples IntegerAll whole numbers3456 -43 RealAll real numbers (whole + decimal) 3456.78 -123.45 0.000123 Character (uses quotation marks) All letters, numbers, and special symbols “A”, “a”, “1”, “+”, “%” String (uses quotation marks) Combinations of more than one character “Mulder” “123-45-6789” LogicalTrue or FalseTrue False McManusCOP100012

13. Numeric Types Includes all types of numbers –Natural Numbers - The set of positive (counting) numbers Ex. {1,2,3,4,5,…} –Integers - The set of real numbers consisting of the natural numbers, their additive inverses, and zero Ex.3, 5, -5, 0, -1 and 32,767 –Real numbers (floating point numbers) Ex. 3.1459, 1.618039887, -5745 & Scientific Notation McManusCOP100013

14. Can I Confuse You? Which is larger? The set of Integers or the set of Real Numbers? Well, actually… There are several different levels of infinity! Confused? McManusCOP100014

15. Levels of Infinity Complex Numbers Real Numbers Irrationals Rationals Integers Naturals McManusCOP100015

16. Character Types Alphanumeric data set –Consists of all single-digit numbers, letters, and special characters available to the computer –contained within quotation marks McManusCOP100016

17. Coding Systems –EBCDIC Extended Binary Coded Decimal Information Code –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 McManusCOP100017 See Appendix B or online

18. String Data Type Made up of one or more characters. Contained within quotation marks Cannot be used within calculations –There is some debate about using strings… The new consensus is that if the value will be used in a mathematical calculation, make it a number, otherwise make it a string. The alternative view (older view) is to look at the amount of storage that is needed for the value. A number generally takes up less memory space than a string. McManusCOP100018

19. Strings - Caution “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 McManusCOP100019

20. Comparing Characters & Strings –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 McManusCOP100020

21. Concatenation Joins character or string data together –Operators: + and & Dependent on programming language & can mix data types + cannot mix data types (also known as Join in databbases) 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. McManusCOP100021

22. Logical (Boolean) Data Type 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 McManusCOP100022

23. Other Pre-defined Data Types Dependent on programming language, numerous other pre-defined data types are available. –Examples Dates01/01/1900 January 1, 1900 Times03:35:05 PM15:35:05 Currency3000.00 –Note: This is how the data will be stored, not how it is formatted. McManusCOP100023

24. User-Defined Data Types User-defined Data types –Defined by the user as a new data type Example –Record McManusCOP100024 Employee_Record Fname Lname SSN BirthDate HireDate TerminationDate PayRate End

25. Functions Small sets of instructions that perform specific tasks and return values. Two types: –Pre-defined Built into a computer language or application –User-defined More about these later McManusCOP100025

26. Functions Benefits –Reduces the amount of code that needs to be written, thus reducing errors of repetition –Shortens the development time –Improves readability McManusCOP100026

27. Function Parameters 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 McManusCOP100027

28. Function Types Mathematical String Conversion Statistical Utility Specific to each programming language…a partial list follows McManusCOP100028

29. Mathematical Functions McManusCOP100029 Random is a random number selected between 0 and 1

30. String Functions McManusCOP100030

31. Conversion Functions McManusCOP100031

32. Statistical Functions McManusCOP100032

33. Utility Functions McManusCOP100033 Error is a special function that appears in most languages and upon execution return control to the program when (not if) system errors occur. Such as Disk Errors…

34. Operands, Resultants & Operators Operands –The data that the operator connects and processes Resultant –The answer that results when the operation is executed Operators –The data connectors within expressions and equations. –Two types of operations Unary – Negation Binary – Addition, Subtraction, Multiplication, Floating Point Division and Integer Division McManusCOP100034

35. Operator Types Mathematical –+, -, *, / –\, Mod {Integer Division & Modulo} –^, {Exponentiation} and –functions Relational –, =, =, <> Logical –And, Or, Not, XOR, EQV McManusCOP100035

36. Two Special Math Operators 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. McManusCOP100036

37. The Boolean Data Type 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 McManusCOP100037

38. Relational Operators 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 McManusCOP100038

39. Logical (Boolean) Operators And, Or, Not, XOR, 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! McManusCOP100039 Hint! These are on the Test!

40. The AND Operator Significance: The only time the result is True is if both A and B are True. McManusCOP100040

41. The OR Operator Significance: The only time the result is False is if both A and B are False. McManusCOP100041

42. The NOT Operator Also called the “logical complement” or “logical negation” Significance: Whatever the value of A is, NOT A will be the opposite. McManusCOP100042

43. The XOR (Exclusive Or) Operator 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. McManusCOP100043

44. The EQV (Equivalent) Operator 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. McManusCOP100044

45. 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. –Note: Different programming languages use different Order of Precedence… –Note: Whenever you want to clarify an equation, use the parentheses! McManusCOP100045

46. The Order of Precedence McManusCOP100046

47. Example Evaluate the following: A = True, B = False, C = True, D = False To do this, we create what’s called an Evaluation Tree… McManusCOP100047 A or B or C and D and A and B and (not C) or (not D)

48. The Evaluation Tree McManusCOP100048 A or B or C and D and A and B and (not C) or (not D) False True False True 1 2 4 3 6 5 7 8

49. Expressions & Equations 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 Height * Width McManusCOP100049

50. Equations Same as an expression, except the equation stores the resultant (answer) in a memory location (must be on the left side of Assignment Operator) “takes on the value of” not “equals” –Examples –SalesTax is the memory location where the answer will be stored, the resultant Often called Assignment Statements McManusCOP100050 SalesTax = Price * SalesTaxRate OvertimePay = (Hours – 40) * Wage * 1.5 Area = Height * Width

51. More about Equations 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. McManusCOP100051 SalesTax = = Price ** SalesTaxRate D R-I ND R-I ND R-I Ahh..but what about this one? Count = Count + 1

52. 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 McManusCOP100052 = ( 2 *(X – Y ) ) / ( ( ( 2 * X + Y )^2 ) / ( ( X – Y )^2 ) ) straight line form

53. Next? McManusCOP100053