Iteration

1
Iteration Branching

• CSC 171 FALL 2001
• LECTURE 5

2
HistoryBoolean Logic

• 1854 - George Boole describes his system for
  symbolic and logical reasoning
• An Investigation into the Laws of thought
• Boolean logic later becomes the basis for
  computer design

3
Quote

• No matter how correct a mathematical theorem may
  appear to be, one ought never to be satisfied
  that there was not something imperfect about it
  until it also gives the impression of being
  beautiful.
• George Boole - Quoted in D MacHale, Comic
  Sections (Dublin 1993)

4
Boolean Logic

• Boolean expressions
• boolean expressions can take on one of two values
  (true or false)
• 3 lt 5
• true
• 3 gt 5
• false

5
Boolean Variables

• int x 5, y 3
• boolean test1, test2, test3, test4
• test1 x lt y
• test2 x gt y
• test3 test1 test2
• test4 test1 test 2

6
AND OPERATION
A B A B
False False False
False True False
True False False
True True True
7
OR OPERATION
A B A B
False False False
False True True
True False True
True True True
8
NOT OPERATION
A !A
FALSE TRUE
TRUE FALSE
9
The mathematical basis for computer design

• An open switch can represent
• Zero
• False
• A closed switch can represent
• One
• True
• A switch can control another switch
• A logic gate

10
Boolean Operations Circuits

• And
• Or
• Not

X
11
Branching Logic

• if (earnings lt 50000.00)
• tax income 0.35
• else
• tax income 0.45
• netpay earnings tax

12
While repetition

• int count 0
• while (count lt 10)
• sum count
• count

13
Design Technique

• State the problem
• Write a pseudocode algorithm
• Code around the comments

14
Example Decimal to binary

• Start with an integer value x and an empty
  string
• While the value of x is greater than zero
• If x is odd, prepend a 1 to the string
• If x is even, prepend a 0 to the string
• Divide the value of x by 2

15
Example Decimal to Binary

• int x 10 // Start with an integer value x
• String binstring // and an empty string
• while (x gt 0) // While x is greater than zero
• if ((x 2) 0) // If x is odd,
• binstring 1 binstring // prepend a 1
• else // If x is even
• binstring 0 binstring // prepend a 0
• x / 2 // Divide the value of x by 2

16
Trace at the top of the loop

• x10, binstring , (x2) 0
• x5, binstring 0, (x2)1
• x2, binstring 10, (x2)0
• x1, binstring 010, (x2)1
• x0, binstring 1010, (x2)0

17
In class example

• The user wants to know how much money he will
  have saved year by year for retirement.
• Questions to ask
• How old are you, now?
• How much can you save, each year?
• How old will you be when you retire?
• How much do you need, during retirement?
• How old will you be when you die?
• What interest rate should we invest at?

18
In class excercise

• You design the program (pair up)
• Use dialog boxes for input, console for output
• Identify the key variables needed
• Write a pseudocode program
• You have 10 minuites to do this