Wrap up on computers and data

1
Session 4

• Wrap up on computers and data
• Working with the primitives in Dr. Java

2
Announcements

• Want to do at home what you did in lab yesterday?
• Your textbook CD contains all of the files you
  need to do this, OR
• You can also download everything off of the web
• Java version 1.5.X
• Dr. Java
• This weeks topics will begin to look at how to
  manipulate data in a computer.
• (A start to learning how to program a computer!)

3
Review Primitive Types
byte
short
int
long
boolean
4
Review Primitive Types
byte
short
int
long
boolean
5
Review Binary Addition

• To add two decimal numbers you add the digits and
  if the total is greater than ten you carry the
  one into the next column
• To add two binary numbers
• 0 0 0
• 0 1 and 1 0 1
• 1 1 0 with a carry of 1 into the next column
  to the left

• 00 10 111
• 01 01 001
• ---- --- ------
• 01 11 1000
• 00111001010
• 01010101101
• -------------------
• 10001110111

6
Review 2s Compliment Notation

• Computers actually only know how to add
• So, how do they handle subtraction?
• Computers subtract by adding a negative number
• How do you represent a negative number in memory?
• Positive numbers in 2s compliment are just the
  same as a binary number
• For negative numbers reverse 0s and 1s and then
  add 1
• All negative numbers have a one for the leftmost
  bit

7
Decimal Number Storage

• How do you think a computer stores 3205.406?
• It uses an IEEE 754 format
• Stored as binary numbers in scientific notation
  -52.202 is -.52202 x 102
• For example
• 6.5 in decimal
• 110.1 in binary
• .1101 x 23 in binary with scientific notation
• Stores 3 things
• A bit for the sign
• A number between 0 and 1 (the mantissa)
• The power of 2 (the exponent 8 bits)

8
Decimal Number Storage

• The problem with this structure
• Many numbers actually dont encode well
• Remember yesterday when I asked you to
• It uses an IEEE 754 format
• Stored as binary numbers in scientific notation
  -52.202 is -.52202 x 102
• For example
• 6.5 in decimal
• 110.1 in binary
• .1101 x 23 in binary with scientific notation
• Stores 3 things
• A bit for the sign
• A number between 0 and 1 (the mantissa)
• The power of 2 (the exponent 8 bits)

9
ASCII code

• A simple conversion of the common American
  characters and computer commands to numbers.
• A 65
• a 97
• 1 49
• \t 11
• See www.asciitable.com for more information

10
What is DrJava?

• DrJava is a free integrated development
  environment for doing Java programming
• From Rice University
• It is written in Java
• It has several window panes in it
• For creating programs (definitions pane)
• For trying out Java code (interactions pane)
• Listing of open files (files pane)

11
Number literals in Java

• By default, Java assumes that anything without a
  decimal is an int.
• 2
• 2
• -5
• -5
• By default, Java assumes that anything with a
  decimal is a double.
• 3.5
• 3.5
• -4.0
• -4.0

12
Number literals in Java

• Because of this, you have to be careful about
  size
• 123456789
• 123456789
• 12345678901234567890
• NumberFormatException For input string
  12345.
• Integer.MAX_VALUE
• 2147483647
• Integer.MIN_VALUE
• -2147483648
• Integer.MAX_VALUE 1
• -2147483648

13
Math Operators in Java ( / - )

• But on their own, number literals are boring.
• Java provides 5 binary mathematical operators
• Here, binary means two numbers
• Addition
• 3 4
• Multiplication
• 3 4
• Division
• 3 / 4
• Subtraction
• 3 4
• Modulo (Remainder)
• 10 2 and 11 2

14
Math Operators Exercise

• How would I perform each of the following in
  DrJava and what would be the answer?
• Subtract 7 from 9
• Add 7 to 3
• Divide 3 by 2
• Divide 4.6 by 2
• Multiply 5 by 10
• Find the remainder when you divide 10 by 3

15
Why is the result of 3 / 2 1?

• Java is a strongly typed language
• Each value has a type associated with it
• Tells the computer how to interpret the number
• It is an integer, floating point, letter, etc
• The compiler determines the type if it isnt
  specified (literals)
• 3 is an integer
• 3.0 is a floating point number (has a fractional
  part)
• The result of an operation is in the same type as
  the operands
• 3 and 2 are integers so the answer is an integer 1

16
Casting

• There are other ways to solve the problem of 3 /
  2 has a result of 1
• You can make one of the values floating point by
  adding .0
• 3.0 / 2
• 3 / 2.0
• The result type will then be floating point
• Or you can cast one of the values to the
  primitive types float or double
• (double) 3 / 2
• 3 / (float) 2

17
Casting Exercise

• Use casting to get the values right for splitting
  up a bill for 3 people of 19 dollars.

18
Other Funny Math

• What is the result of
• 79.95 4 1.07
• Do it with a calculator and you get 342.186.
• BUT, the value we got in lab yesterday was
• 342.18600000000004
• Where does the extra stuff come from?
• Try 31.01 0.01

19
Other Funny Math

• Remember what we talked about in regards to
  encoding decimals
• 2n 2n-1 2n-2 22 21 20. 2-1 2-2 2-3
  2m-1 2m
• There are a limited number of places you can
  encode.
• Any leftovers get ignored which causes problems
  when you de-code

20
Operator Order

• The default evaluation order is
• Negation -
• Multiplication
• Division /
• Modulo (remainder)
• Addition
• Subtraction -
• The default order can be changed
• By using parenthesis
• (3 4) 2 versus 3 4 2