1. Algorithms computer as the tool process – algorithm
Arithmetic: addition,subtraction,multiplication,division
Save information for future use
Receive and put out information - i/o
Comparison
Repeat any group of operations
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2. Assignment operator = Value assigning differs from equality
x = 3 vs if x = 3
 variable = expression
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3. variable = expression variable -physical location in computer memory
constant
x = 10;
x = PI;
another variable to which a value has previously been assigned
y = x;
a formula to be evaluated
y = a* x /2 + 3;
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4. assignment
Processor evaluates the right member of an assignment statement to get a single value
it places this value in the memory location (variable name) given as the left member.
Not a mathematical equation, can't be switched
stamp = is a valid assignment statement
14 = stamp is not
 The left member of an assignment statement must always be the name of a computer memory location (variable name). It cannot be a constant or formula.
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5. Invalid assignment
14 = x; a + x = 2 + y; Why?
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6. Given the declarations:
int stuff; string name; int widget; int numWidgets;
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7. the value 10 is placed in the memory location numWidgets
Assignment Statement
What happens in memory
numWidgets = 10;
the value 10 is placed in the memory location numWidgets
numWidgets = numWidgets + 1;
numWidget is evaluated. Contains a 10, one is added to 10, 11 is stored at the memory location numWidgets
name = "toby"
the four characters t-o-b-y are stored in the memory location name
(note: The single quotes are used as delimiters and are not stored in memory.)
stuff = numWidgets;
Assuming the value 11 in the memory location numWidgets, this assignment statement places the value 11 in answer
(note: Now both stuff and numWidgets have the same value.)
widget = numWidgets * 2
the ALU evaluates the expression on the right and places the value 30 in the memory location widget
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8. Arithmetic Operators Op Operation + Addition - Subtraction *
Multiplication /
Division
pow
Exponentiation %
Modulus
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9. Addition +
int x; x = x + 1; // this is an increment float item1Price; float item2Price; float total; total = item1Price + item2Price;
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10. Subtraction -
int x; x = x - 1; // this is a decrement float grossPay; float tax; float netPay; netPay = grossPay - tax;
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11. Multiplication *
int x; x = x * 2; float bill; float tip; float totalBill; tip = bill * .20; // could use constant here totalBill = bill + tip;
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12. Division /
Can’t divide by zero integer division yields integer result 5/10 => 0 10/3 => 3 5/10.0 => .5 (float) num1/num2 => float result
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13. Modulus % Remainder Useful for determining even or odd numbers
10 % 5 => 0
23 % 5 => 3
7 % 2 => 1
58 % 10 => 8
Useful for determining even or odd numbers
if (num1 % 2 == 0)
cout << “even”;
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14. Precedence Order of Operations
exponentiation
multiplication and division
addition and subtraction
left to right
 Z * X * Y => (Z * X ) * Y
 evaluate parentheses first
innermost first
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15. Example 1:Problem Definition
Read three numbers, add them together and print the total.
Step 1: define input and output
Step 2: define list of actions. Hint: Use verbs, these steps
usually involve the input and output defined in step 1
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16. Example 1: Solution Algorithm
int main() {
int num1;
int num2;
int num3;
int sum;
cout << "Input three numbers“;
cin >> num1 >> num2 >> num3;
sum = num1+num2+num3;
cout << "Sum is " << sum; }
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17. Why is this better? int main() { int num1; int num2; int num3;
int sum;
cout << "Input three numbers“;
cin >> num1 >> num2 >> num3;
sum = num1+num2+num3;
cout << num1 << " + " << num2 << " + " << num3
<< " = " << sum; }
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18. Relation op operation < Less than <= Less than or equal to >
Greater than
>=
Greater than or equal to ==
Equal to !=
Not equal to
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19. true only if both are true
AND
&&
exp1 && exp2
true only if both are true OR ||
exp1 || exp2
true if either or both are true
NOT !
! exp1
true if exp1 is false
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20. x y
x && y
TRUE
FALSE
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21. x y
x || y
TRUE
FALSE
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22. x !x
TRUE
FALSE
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23. Assignment Statement What happens in memory cup = 2; saucer = cup;
Assume that: cup, saucer, and plate are integer variables name1 and name2 are string variables hival, lowval, and midval are boolean variables Explain what the processor will do with each of the following assignment statements. Assume the assignment statements are in sequence. (Helpful hint: First, evaluate the expression given the right member and then place that value in the memory location specified as the left member of the assignment statement.)
Assignment Statement What happens in memory
 cup = 2;
 saucer = cup;
 plate = 15 * cup – saucer;
 cup = cup + cup;
 saucer = cup * (plate - saucer);
 name1 = “jefferson”;
 name2 = name1;
 hival = TRUE;
 lowval = FALSE ;
midval = hival && lowval;
 lowval = !(hival || lowval);
 hival = !hival;

24. Trace Trace - simulate the algorithm using known results (desk check)
 Most major logic errors occur during the development of the algorithm
 test data- simple input
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25. list variables across the top of the page Include column for output
Step through code one line at a time (pretend to be the computer)
Fill in variables as they change
Fill in output column if appropriate
Do for 3 sets of data
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26. Sample trace (shown one line at a time)
num1
num2
num3
sum
Output
Enter three numbers 1 2 3 6
Sum = 6
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27. Sample of 3 traces num1 num2 num3 sum Output 1 2 3 6
Enter three numbers
Sum = 6
Sum = 0 -3 -2 -1 -6
Sum = -6
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