Binary numbers
one page computer Number Systems Homework
Print out this assignment and do your work on it.
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!)

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.
 How many different symbols are used in the decimal (base 10) number system? (3 points total) ___________
 How many different symbols are used in the binary (base 2) number system? Write your answer in decimal and binary: (2 points total)
 Decimal: ___________
 Binary: ___________
 Decimal: ___________
 How many different symbols are used in the hexadecimal (base 16) number system? Write your answer in decimal and hexadecimal: (2 points total)
 Decimal: ___________
 Hexadecimal: ___________
 Decimal: ___________
 Consider the decimal (base 10) number system: (3 points per question, 9 points total)
 How many different values can be represented in 3 decimal digits? ___________
 What is the lowest (starting) value? ___________
 What is the highest (ending) value? ___________
 How many different values can be represented in 3 decimal digits? ___________
 Consider the binary (base 2) number system: (3 points per question, 15 points total)
 How many different values can be represented in 6 binary digits (bits)? ___________
 What is the lowest (starting) value? ___________
Write it as a binary number. ___________
 What is the highest (ending) value? ___________
Write it as a binary number. ___________
 How many different values can be represented in 6 binary digits (bits)? ___________
 Convert the decimal number 66 to binary and find the ASCII character represented by this number. (3 points per question, 6 points total)
 66_{10} > binary: ___________
 66_{10} is the ASCII character code for: ___________
 66_{10} > binary: ___________
 Convert the decimal number 98 to binary and find the ASCII character represented by this number. (3 points per question, 6 points total)
 98_{10} > binary: ___________
 98_{10} is the ASCII character code for: ___________
 98_{10} > binary: ___________
 Convert the following decimal numbers to binary.
Show your work. (3 points per question, 15 points total)
 10_{10} > binary: ___________
 16_{10} > binary: ___________
 57_{10} > binary: ___________
 103_{10} > binary: ___________
 255_{10} > binary: ___________
 10_{10} > binary: ___________
 Convert the following binary numbers to decimal and hexadecimal.
Show your work. (3 points per question, 18 total points)
 01111010_{2} > decimal: ___________
 01111010_{2} > hexadecimal: ___________
 00011111_{2} > decimal: ___________
 00011111_{2} > hexadecimal: ___________
 10110101_{2} > decimal: ___________
 10110101_{2} > hexadecimal: ___________
 01111010_{2} > decimal: ___________
 Convert the following hexadecimal numbers to decimal and binary.
Show your work. (3 points per question, 24 points total)
 CA > decimal: ___________ binary: ___________
 B0 > decimal: ___________ binary: ___________
 A1 > decimal: ___________ binary: ___________
 49 > decimal: ___________ binary: ___________
 CA > decimal: ___________ binary: ___________