Introduction
by Eunice M. Dimacuta
The purpose of this WebQuest is to help the students understand Binary Arithmetic (Binary Addition | Subtraction | Multiplication | Division) and to help them learn how to solve it.
Introduction
All digital computers represent data as a collection of bits. A bit is the smallest possible unit of information. It can be in one of two states - off or on, 0 or 1. The meaning of the bit, which can represent almost anything, is unimportant at this point. The thing to remember is that all computer data - a text file on disk, a program in memory, a packet on a network - is ultimately a collection of bits.
Task
Task
The goal of this study is for each student to gain knowledge about Binary Arithmetic and you’ll have the opportunity to practice Binary addition, subtraction, multiplication and division problems. There are several sites given to help you gain further more knowledge in Binary Arithmetic.
The student will be expected to be familiarized to the rules in Binary Arithmetic, to be able to master it. A set of problems will be given to each student to solve.
Process
Process
To be able to understand and learn on how to solve this, you must gain knowledge on Binary Arithmetic. There are several sites given below provide for you:
http://www.tutorialspoint.com/computer_logical_organization/binary_arithmetic.htm
http://bscshortnote.blogspot.com/2013/05/binary-addition-subtraction.html
http://en.wikipedia.org/wiki/Binary_number
Rules for solving for Binary Addition
0 + 0 = 0
0 + 1 = 1
1 + 0 = 1
1 + 1 = 0, and carry 1
Examples
|
Binary Addition. Example 1. |
Problem: 11 + 1 =?
Answer: 11 + 1 = 100
Explanation:
1 1
+ 1
1 0 0
|
Binary Addition. Example 2. |
Problem: 1010 + 11 =?
Answer: 1010 + 11 = 1101
Explanation:
1 0 1 0
+ 1 1
1 1 0 1
|
Binary Addition. Example 3. |
Problem: 100101 + 10101 =?
Answer: 100101 + 10101 = 111010
Explanation:
1 0 0 1 0 1
+ 1 0 1 0 1
1 1 1 0 1 0
Rules for solving for Binary Subtraction
0 - 0 = 0
0 - 1 = 1, and borrow 1 from the next
1 - 0 = 1
1 - 1 = 0
Examples
|
Binary Subtraction. Example 1. |
Problem: 101101 - 100111 =?
Answer: 101101 - 100111 = 110
Explanation:
1 0 1 1 0 1
+ 1 0 0 1 1 1
1 1 0
|
Binary Subtraction. Example 2. |
Problem: 1110110 - 1010111 =?
Answer: 1110110 - 1010111 = 11111
Explanation:
1 1 1 0 1 1 0
- 1 0 1 0 1 1 1
1 1 1 1 1
|
Binary Subtraction. Example 3. |
Problem: 1000101 - 101100 =?
Answer: 1000101 - 101100 = 11001
Explanation:
1 0 0 0 1 0 1
- 1 0 1 1 0 0
1 1 0 0 1
Rules for solving for Binary Multiplication
0 * 0 = 0
0 * 1 = 1
1 * 0 = 1
1 * 1 = 1
Examples
|
Binary Multiplication. Example 1. |
Problem: 1011 * 1001 =?
Answer: 1011 * 1001 = 1100011
Explanation:
1 0 1 1
* 1 0 0 1
1 0 1 1
0 0 0 0
0 0 0 0
1 0 1 1
1 0 0 0 1 1
|
Binary Multiplication. Example 2. |
Problem: 111 * 11 =?
Answer: 111 * 11 = 10101
Explanation:
1 1 1
* 1 1
1 1 1
1 1 1
1 0 1 0 1
|
Binary Multiplication. Example 3. |
Problem: 10101 * 1101 =?
Answer: 10101 * 1101 = 100010001
Explanation:
1 0 1 0 1
* 1 1 0 1
1 0 1 0 1
0 0 0 0 0
1 0 1 0 1
1 0 1 0 1
1 0 0 0 1 0 0 0 1
Rules for solving for Binary Division
Example
|
Binary Division. Example 1. |
Problem: 111011 / 11 =?
Answer: 111011 / 11 = 10011
Explanation:
Please answer the set of problems in this site: http://www.binarymath.info/practice-exercises.php
to be able to test your Binary Arithmetic skills.
Evaluation
Evaluation
Conclusion
Conclusion
Congratulations!! Wow ... Well done now you have finally mastered Binary Arithmetic.