You have heard that computers use 0's and 1's to represent characters and data. You will research why the binary number system is used instead of decimal number system. You will then convert numbers from base 2 to base 10 and vice versa. You will also convert numbers from base 16 to base 10 and vice versa.

You will use the Internet to find the reason why the computer uses the binary number system (or the so called "on-off" state ). Then using the following web sites as resources, learn about positional value of our numeration system. The learn how to convert numbers between base 2 and 10, base 16 and 10, and base 2 and base 16. Step by step explanation will help you accomplish this task.

 IMPORTANT: AFTER VISITING A SITE, TO RETURN TO THIS PAGE, CLICK THE BACK BUTTON ON THE UPPER LEFT CORNER OF THAT SITE.

The Development of Computer  - discusses the development of computers and the significance of binary numbers

 Binary  - gives a brief history if the binary numbers and its relationship to decimal numbers

 E. Chu's Notes  - gives a step by step explanation of how to convert numbers in base 2 and 16 to base 10 and vice versa.

 Understanding Hexadecimal and Binary Number Bases  - more explanations of  the hexadecimal and binary 
                                                                                         number bases
 

2. Visit either the Binary or  E. Chu's Notes  sites to learn how to convert a number in base 2 to 
    base 10.  Answer the following questions.
     a) How many digits are there in the decimal number system? What are they?
     b) How many digits are there in the binary number system? What are they?
     c) Write the decimal number 325 in the expanded notation.
     d) Write the binary number 1011 in expanded notation.
     e) Convert 1011₂  to base 10. Show all the steps.
     f) What is the place value of the digit that is underlined in 101001₂ ?
     g) Write the next 4 numbers after 1011₂ .

3. Using the same two sites to learn how to convert a number in base 10 to base 2. Answer the following 
     questions. 
     a) Convert 58 in base 10 to base 2. How many digits are there? Show all your work.
     b) Convert 128 in base 10 to base 2. How many digits are there? Show all the steps you use.

4. Converting from base 16 to base 10. Again, go the the two sites and learn how to convert numbers in 
     base 16 to base 10 and vice versa. Answer the following questions.
     a) What is the place value of the underlined digit in the number 1E2A₁₆ ?
     b) Convert 2A₁₆  to base 10.
     c) Convert 58 in base 10 to base 16. Show all your work.
     d) Write the next four numbers after 3D₁₆.

5. Now that you know how to convert a number in base 2 to base 10 and base 16 to base 10. Can you 
    figure out a way to convert a number in base 2 to base 16 and vice versa without converting to base 10
    first?

6.  Now, visit the site where there is a  Base Converter .
     Choose your own numbers in base 2 or base 16 or base 10. Place each of them in their proper box and
     press enter to see what the conversions in the other two bases are. There are more than three bases in 
     the converters. In fact, these converters can be programmed to convert a given number in any base to 
     any base. However, for our activity, we concentrate on the binary, decimal and hexadecimal.

7. For each entry you make in number 6, check the conversions by actually performing the conversions 
   using the methods that you learned in steps 1 through 5.

Remember that in any given base, the number of different digits that any one position can hold is the same as the base. However, the the position cannot have the base as one of the digits. For example, in base 10, there are 10 different digits that any one position can have. The digits that you can have are 0,1-9, a total of 10 digits. In base 2, you can have only 0 and 1. In base 16, you can have up 16 different digits. However, we know only 10 numeral digits , 0-9. For the six other digits , we have to use letters A-F. So in base 16, the digits are 0-9, A-F.

After you have completed this web quest, you should have an understanding of what a binary number is and why it is used in computers. You should also have learned how to perform base conversions using paper and pencil through understanding its basic concept. Now, you are ready to perform operations in different bases.