Understanding VB Math Operations: Precedence, Parentheses, and Functions

1. Topics • Five Fundamental Math Operations • Precedence of Math Operations • Using Parentheses to override precedence • Writing and Interpreting VB Calculation Statements • Mathematical Functions “A computer lets you make more mistakes faster than any invention in human history—with the possible exceptions of handguns and tequila” Mitch Ratcliffe

2. Numeric Operations in Computer Code • Computers were invented to process large quantities of numeric data • Computers perform arithmetic operations on numeric values incredibly rapidly • All computer operations can be performed using the basic operations of addition, subtraction, multiplication, and division. • Most computer languages also provide for exponentiation • Most also provide built in functions for more complex operations

3. Objectives • Understand the five fundamental arithmetic operations in VB • Understand how to write and interpret mathematical calculations in VB • Understand the precedence of mathematical operations in computers and how parenthetical grouping affects calculation order • Understand the use of predefined mathematical functions available in VB

4. Five Fundamental Arithmetic Operations • VB supports five built-in arithmetic operations: OperationConventional NotationComputer Symbol • Addition 3 + 4 3 + 4 • Subtraction 3 - 4 3 - 4 • Multiplication 3 x 4 3 * 4 • Division 3  3 / 4 • Exponentiation 34 3 ^ 4

5. The Assignment Operation • Many times the results of a calculation or other operation are assigned to a variable, property, or other value holder intSum = intFirstValue + intSecondValue intSum = Val(txtFirst.Text) + Val(txtSecond.Text) MainMenu.Top = (Screen.Height - MainMenu.Height) / 3 • The calculation on the right of the equal sign is performed first and assigned to the location on the left • The Equal Sign is an assignment operator

6. Legal statements x = 4 y = 2 z = x + 5 t = x * 2 txtPrice.Text = x + y Const Pi = 3.14 dblDiameter = Pi * sglRadius dSqrt = x ^ .5 Illegal statements 4 x + y z% = x% + txtInput.Text sglPrice = $1,456.98 Using Numeric Calculations

7. Precedence of Numeric Calculations • Q: What is the result of 3 + 5 * 2?A: • Numeric operations have a defined hierarchy or precedence of calculation 1. Exponentiation 2. Multiplication and division 3. Addition and subtraction 4. Left to right within categories • Because multiplication precedes addition 5 is multiplied by two giving 10 first after which the three is added to give 13

8. x + y / 2 y ^ 3 / 4 x + 2 * y - 2 * x 8 + x * y / 3 -8 + y ^ -2 16 ^ (1 / 4) Precedence Exercises What are the results of the following calculations if x = 12 and y = 4?

9. Using Parentheses to Group Calculations • Operations grouped in parentheses are performed first, regardless of the natural order of calculation3 + 5 * 2 = 13(3 + 5) * 2 = 16 • Parentheses may be nested((3 + 5) * 8) / (2 * 4) = ? • Parentheses may be used to visually format mathematical expressions even if no change to the calculation order is needed Inner parentheses are evaluated first

10. More Precedence Exercises Write computer expressions for each mathematical expression

11. Numeric Functions • VB (and most other programming languages) provide predefined numeric calculations in the form of functions • Functions often operate on a value and return some transformation of the value • E.g. in x = 25 y = Sqrt(x)Sqr( ) is a predefined function which returns the square root of its argument (x in this case)

12. Functions and Expressions as Arguments • Functions may be nested E.g., in Math.Sqr(Math.Abs(x)) the absolute value of x is determined first and then becomes the argument of the square root function • A calculation may be performed inside the argument of a function E.g., in Math.Sqr(x ^ 2) the value of x is first squared and then the square root of the result is taken • Functions are always calculated from the inside out

13. Empty Variables in Mathematical Operations • Variables which have never been assigned a value are said to be ‘empty’ • If a mathematical operation is performed on an empty variable the variable behaves as if its value is zero • Be very careful as division by zero results in a runtime error which will crash the program. • NB: Variables loaded from databases may sometimes contain a null value which is different from empty.

14. Converting Data Types Introduces inefficiency • VB will automatically convert many numeric data types before performing calculations • Single precision values can be multiplied by integers, assigned to currency variables etc. • Some conversions cannot take place • String values cannot be assigned to explicitly declared numeric variables (non variants) • Commonly arises when using text boxes, list boxes, grid controls, etc.

15. The Val( ) Function • Val( ) returns the numeric value of its argument • Argument is typically a string but may be a number • Val converts strings to numbers • A common use of Val is to convert values which must be treated as text into numbersintQty = Val(txtQty.Text)intCourse = Val(cboCourseNumber.Text)sglPrice = Val(InputForm.Tag) • Or use the Convert method Some properties always contain characters

16. The Val ( ) Function: Examples • Val (“123.54”) 123.54 • Val (““) 0 • Val(“123A45”) 123 • Val(“A123”) 0 • Val(“ 123 456”) 123456

17. Methods of the Math Class

18. Methods of the Math Class (cont.)