Binary numbers

one page computer Number Systems Homework 

Objectives

• Utilize the ASCII (American Standard Code for Information Exchange) coding scheme
• Demonstrate understanding of the binary and hexadecimal number systems
• Convert between binary and decimal numbers
• Convert between hexadecimal and decimal numbers
• Convert between hexadecimal and binary numbers

Assignment

Answer the questions listed below.
Write your answers on 8½ x 11 paper (lined or unlined) or print out this page and write your answers on it. When answering questions number the answer to match the question and state the answer in a complete sentence such that the reader will have a good idea of what the original question was.
Example:

    Question:
    1. What is an algorithm?

    Answer:
    1. An algorithm is a list of steps to solve a problem in a finite
       amount of time.

Section A: Complete the exercise below utilizing the ASCII (American Standard Code for Information Exchange) coding scheme handed out in class, . Write your answer in the space provided.

Exercise using ASCII Code - 10 points

Write a short sentence in English (4 or more words). Translate each letter of each word including spaces and punctuation into its binary representation using the ASCII chart you were given. Note that lower case and upper case letters have different codes! (Don't forget about spaces!) Example: At 10000011110100

 

Section B: Working with Binary and Hexadecimal Numbers - 100 points

For the following questions show your work, that is, how you arrived at your answers. Use additional sheets of paper as needed to show your work.

1. How many different symbols are used in the decimal (base 10) number system? (3 points total) ___________
    
2. How many different symbols are used in the binary (base 2) number system? Write your answer in decimal and binary: (2 points total)
    
   
   1. Decimal: ___________
       
   2. Binary: ___________
    
3. How many different symbols are used in the hexadecimal (base 16) number system? Write your answer in decimal and hexadecimal: (2 points total)
    
   
   1. Decimal: ___________
       
   2. Hexadecimal: ___________
    
4. Consider the decimal (base 10) number system: (3 points per question, 9 points total)
    
   
   1. How many different values can be represented in 3 decimal digits? ___________
       
   2. What is the lowest (starting) value? ___________
       
   3. What is the highest (ending) value? ___________
       
5. Consider the binary (base 2) number system: (3 points per question, 15 points total)
    
   
   1. How many different values can be represented in 6 binary digits (bits)? ___________
       
   2. What is the lowest (starting) value? ___________
      Write it as a binary number. ___________
       
   3. What is the highest (ending) value? ___________
      Write it as a binary number. ___________
       
6. Convert the decimal number 66 to binary and find the ASCII character represented by this number. (3 points per question, 6 points total)
    
   
   1. 66₁₀   >   binary: ___________
       
   2. 66₁₀ is the ASCII character code for: ___________
       
7. Convert the decimal number 98 to binary and find the ASCII character represented by this number. (3 points per question, 6 points total)
    
   
   1. 98₁₀   >   binary: ___________
       
   2. 98₁₀ is the ASCII character code for: ___________
       
8. Convert the following decimal numbers to binary.
   Show your work. (3 points per question, 15 points total)
    
   
   1. 10₁₀   >   binary: ___________
       
   2. 16₁₀   >   binary: ___________
       
   3. 57₁₀   >   binary: ___________
       
   4. 103₁₀   >   binary: ___________
       
   5. 255₁₀   >   binary: ___________
       
9. Convert the following binary numbers to decimal and hexadecimal.
   Show your work. (3 points per question, 18 total points)
    
   
   1. 01111010₂   >   decimal: ___________
       
   2. 01111010₂   >   hexadecimal: ___________
       
   3. 00011111₂   >   decimal: ___________
       
   4. 00011111₂   >   hexadecimal: ___________
       
   5. 10110101₂   >   decimal: ___________
       
   6. 10110101₂   >   hexadecimal: ___________
       
10. Convert the following hexadecimal numbers to decimal and binary.
    Show your work. (3 points per question, 24 points total)
     
    
    1. CA   >  decimal: ___________  binary:  ___________
        
    2. B0   >  decimal: ___________  binary:  ___________
        
    3. A1   >  decimal: ___________  binary:  ___________
        
    4. 49   >  decimal: ___________  binary:  ___________