A few things about Lab1

1
A few things about Lab1

• Worth 10 points
• There is a two letter grade code in green. Use
  this to look up your grades online.
• Read everything
• Follow directions
• Answer everything

2
Your turn 1

• What unsigned decimal numbers are represented by
  the following binary numbers?
• Example 00000101 5
• 00000100
• 00001101
• 00110011
• Answers 4, 13, 51

3
Your turn 2

• How would you write the following numbers in
  binary?
• Example 14 8 4 2 -gt 00001110
• 3
• 21
• 43
• Answers 00000011, 00010101, 00101011

4
Binary Addition

• To add two decimal numbers you add the digits and
  if the total is greater than ten you carry the
  leading digit (with two number, always a 1) into
  the next column
• To add two binary numbers
• 0 0 0
• 0 1 and 1 0 1
• 1 1 10
• Write down the zero and carry the 1 into the next
  column to the left

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

5
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

6
2s Compliment Example

• To subtract 3 from 7
• First represent both as a binary number
• 7 is 0000 0111 (1 2 4)
• 3 is 0000 0011 (1 2)
• Reverse the 0s and 1s and then add 1 to get -3
• 0000 0011 reversed is 1111 1100
• add 1 0000 0001
• The result is 1111 1101

7
Add the Negative Number

• To subtract 3 from 7
• Add -3 to 7
• 7 is 0000 0111
• -3 is 1111 1101
• The result is 1 0000 0100
• Through away the leftmost 1
• The answer is 0000 0100 which is 4

8
Basic Data Types

• Most languages start with a basic 4 types of data
  at the primitive level.
• Integers (numbers without fractional parts)
• Floating point numbers (numbers with fractional
  parts)
• A single character
• Booleans (True and false values)

9
As an example - Java Primitive Types
Data stored as 2s complement
10
As an example - Java Primitive Types
Data stored in IEEE 754
11
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)

12
Decimal Number Storage

• The problem with this structure
• Many numbers actually dont encode well
• How would you encode 32.01??

13
As an example - Java Primitive Types
Data stored in ASCII
14
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