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LSP 121 -- 11/2/10

Review Questions

Definition:   A bit is a single base 2 digit (0 or 1).

1. Match the culture to the number system base:
   

   Yoruba	2
   Babylonian	3
   Arabic	4
   Yuki	5
   Dozenal	8
   Luo	10
   Islamic Prayers	12
   Electronic Computers	60
   DNA	64
   Arabic

   Ans: Yoruba: 5, Babylonian 60, Arabic 10, Yuki 5, Dozenal 12, Luo 8, Islamic Prayers 3, Electronic Computers 2, DNA 4.

2. Give the base of the positional number system for each of the following:
   Binary    Decimal    Hexadecimal

3. Convert the following numbers to base 10:
   5473₈   3EX₁₂   110110₂

   Ans:
   5 × 8^3 + 4 × 8^2 + 7 × 8^1 + 3 × 8^0 = 2560 + 256 + 56 + 3 = 2875

   3 × 12^2 + 11 × 12^1 + 10 × 12^0 = 432 + 132 + 10 = 574

   1 × 2^5 + 1 × 2^4 + 0 × 2^3 + 1 × 2^2 + 1 × 2^1 + 0 × 2^0 = 32 + 16 + 4 + 2 = 54

4. Convert the following base 10 numbers to base 2 using this Powers of Two Table:
   19₁₀   61₁₀   107₁₀

   Ans:

   19 - 16 = 3; 3 - 2 = 1; 1 - 1 = 0
   19 = 16 + 2 + 1 = 10011₂

   61 - 32 = 29; 29 - 16 = 13; 13 - 8 = 5; 5 - 4 = 1; 1 - 1 = 0.
   61 = 32 + 16 + 8 + 4 + 1 = 111101₂

   107 - 64 = 43; 43 - 32 = 11; 11 - 8 = 3; 3 - 2 = 1; 1 - 1 = 0.
   107 = 64 + 32 + 8 + 2 + 1 = 1101011₂

5. Convert the following base 16 numbers to base 2 by translating each hex digit to four bits according to this Hex Digits Table:
   4ED7₁₆   3AE8₁₆   BE31₁₆

   Ans:

   01001110 11010111    00111010 11101000     10101110 00110001
   

6. Convert the following base 2 numbers to base 16 by translating each group of four bits to one hex digit according to this Hex Digits Table:
   01101101₂   00100111₂   11011010₂

   Ans: 6D₁₆    27₁₆    DA₁₆

7. Use this ASCII table to convert this word in to hex (base 16) ASCII characters and then digit by digit into binary:
   Halloween

   ASCII means American Standard Code for Information Interchange.

   Ans: 48 61 6C 6C 6F 77 65 65 6E
   01001000 01100001 01101100 01101100 01101111 01110111 01100101 01100101 01100001

8. Use this ASCII table to convert this word into hex (base 16) and then to ASCII:

   01000111 01101000 01101111 01110011 01110100 01100010 
   01110101 01110011 01110100 01100101 01110010 01110011
   

   Ans: Ghostbusters

Positional Number Systems

• Positional Number Systems Tutorial

Alice

• To download Alice for your home PC:
  1. Go to www.alice.org >> Downloads >> Get Alice 2.0 >> Download Alice 2.0 for Windows (250 MB) into the folder C:\Alice. This may take some time.

  2. Using Microsoft Explorer, go to the folder where Alice2.0.zip was downloaded. Right click on Alice2.0.zip >> Extract All. Follow the directions of the Extraction Wizard. Place the extracted files into the folder C:\Alice

  3. Navigate to the folder C:\Alice using the Windows Explorer. Right click on Alice.exe >> Create Shortcut. Cut this shortcut (Shortcut to Alick.exe), paste it onto the desktop.

• Invoke Alice. View these Alice tutorials: Tutorial1 (Skater) and Tutorial2 (Defending Naptime).

• Note the locations of these Alice windows:
  World Window   Object Tree   Details Area   Editor Area   Events Area

• New Terms:

  Object   An item in the Alice World, whose position can be changed, that can perform actions, and that can respond to events.

  Method   An action that a method can perform. A method is also called a procedure.

  Property   Aspects or pieces of information about an object than can be changed.

  Event   Something that happens to an object that can cause methods (called event handlers) to be executed.