104 LearnersLast updated on July 4th, 2025
Binary Division
Binary division uses only two symbols: 0 and 1, with a base of 2. The prefix ‘bi’ in the word refers to two, and division in this number system is one of the most important operations. Binary division is used in computer programming and data management. In this topic, we will explore the binary division method and its symbols in detail.
What is the Binary Division?
Binary division uses a long division method with only two digits, ‘0’ and ‘1’, to divide one number by another number. In this method, the dividend is divided by the divisor, and it results in a binary quotient and a remainder. In computers, this acts as a foundational system to store and represent information.
What are the Rules for Binary Division?
Binary division follows the same method as decimal division, but only uses 0s and 1s. This form of division follows certain rules that must be understood. It focuses on just two symbols, 0 and 1, and 2 is the base value of this technique. The four basic rules of binary division are:
| Binary Division Rules |
Explanation |
|
0 ÷ 0 = Undefined |
If zero is divided by zero, the result is undefined. |
|
0 ÷ 1 = 0 |
The result of dividing 0 by 1 is zero. |
|
1 ÷ 1 = 1 |
If 1 is divided by 1, the result is 1. |
|
1 ÷ 0 = Undefined |
No number multiplied by zero gives 1. |
How to Do Binary Division?
Using the long division method, we can easily divide binary numbers and find the result. We can perform binary division by following these steps:
Step 1: Before performing calculations, identify the dividend and the divisor. If the divisor is larger than the dividend, put 0 as the quotient and bring down the second bit of the dividend.
If the divisor is smaller than the dividend, multiply the divisor by 1, and the product becomes the subtrahend. After that, to get the remainder, subtract the subtrahend (the number we subtract) from the minuend (current part of the dividend we are working with).
Step 2: After bringing down the next bit from the dividend, repeat Step 1.
Step 3: Continue the same steps until the whole dividend has been processed, or the remainder becomes zero.
Let us take an example to understand the binary division in detail. For example, 110102 ÷ 1012
Here, the given binary numbers are 0110102 and 01012. The leading zeros of the given numbers do not change the value, so we can simplify the numbers to 110102 and 1012.
Dividend = 110102
Divisor = 1012
Step 1: Since the divisor is smaller than the dividend, we must multiply the divisor by 1. Hence, the product is 1012 (1012 × 1 = 1012).
The product (1102) becomes the subtrahend, then we can subtract the subtrahend from the minuend (1102).
1102 - 1012 = 0012
Here, the quotient starts with 1.
Step 2: Bring down the next bit (1) from the dividend, which makes the current portion of the dividend 00112. 1012 is greater than 00112, we can put 0 in the quotient and bring down the next bit (0), making it 01102.
Step 3: Multiply the divisor by 1, and 1012 × 1 = 1012
Step 4: Subtract 1012 from 1102.
1102 - 1012 = 0012
The quotient is 1012 and the remainder is 001 = 12.
Tips and Tricks of Binary Division
Here are some tips and tricks that should be kept in mind when performing binary division:
- Understand the four basic rules of binary division. They are:
0 ÷ 0 = Undefined
0 ÷ 1 = 0
1 ÷ 1 = 1
1 ÷ 0 = Undefined
- If the divisor is greater than the dividend, write 0 in the quotient. If the divisor is smaller than the dividend, multiply the divisor by 1.
- Bring down the next bit from the dividend after each subtraction.
- Remove the leading zeros from the dividend and divisor, as they will not change the value of the binary numbers.
- Use the long division method for binary division, as it is a simple and effective way to find the answer.
Common Mistakes and How to Avoid Them in Binary Division
The binary division uses only two digits 0 and 1, and 2 as a base. Sometimes, this method can be tricky for confusing students. Here are some common mistakes and helpful solutions to avoid these errors:
Mistake 1
Forgetting the Rules of Binary Division
Four rule of Binary Divisions are:
0 ÷ 0 = Undefined
0 ÷ 1 = 0
1 ÷ 1 = 1
1 ÷ 0 = Undefined
If students divide a binary number by 0, the result will be undefined or meaningless.
Mistake 2
Ignoring the Values of Dividend and Divisor
In binary division, students must remember to check the values of the divisor and dividend. If the divisor is greater than the dividend, they must write 0 in the quotient. If the divisor is smaller than the dividend, multiply the divisor by 1 and the result will be the subtrahend. If students forget these steps, they will get incorrect answers in binary division.
Mistake 3
Finding the Difference Between Binary Numbers Incorrectly
When performing the subtraction of binary numbers, keep in mind to correctly borrow values from the next higher bit. By mistake, students find the incorrect difference between binary numbers and end up with wrong subtraction values.
For example, subtract 1002 - 0112
1002 - 0112 = 0112
This is incorrect.
The correct answer is:
1002 - 0112 = 0012.
Mistake 4
Forgetting to Bring Down the Next Bit
Remember to bring down the next bit from the dividend at each step of the division. Sometimes, students forget to bring down the next bit and stop the subtraction too early. By bringing down the next bit, they can prevent errors and get the correct answer.
Mistake 5
Not Removing Leading Zeros
While performing binary division, students can remove the unnecessary zeros from the dividend and quotient. Since leading zeros do not change the value, they may be disregarded. It will help them to perform calculations easily and give accurate answers. For example, if the given binary numbers are 0110102 and 01012, removing the leading zeros simplifies them to 110102 and 1012.
Solved Examples of Binary Division
Problem 1
Evaluate 10102 ÷ 102 using the long-division method.
Quotient = 1012
Remainder = 02
Explanation
Here, we are dividing 10102 by 102.
Dividend = 10102
Divisor = 102
The divisor (102) is two digits, so start by looking at the first two digits of the dividend.
Step 1: To begin with, we can start with the first two digits of the dividend.
The divisor is 102, and the first two digits of the dividend are also 102.
We can divide:
102 ÷ 102 = 12
Step 2: Now write the first digit of the quotient as 1.
Then subtract 102 - 102 = 02.
Step 3: Next, we can bring down the next digit from the dividend.
So, we have 012, which is smaller than 102.
So, the next digit of the quotient is 0.
Step 4: Bring down the next digit from the dividend.
Now we have 102, which is equal to the divisor.
Hence, the next digit of the quotient is 1.
Subtract 102 - 102 = 02
So, the quotient = 1012
Remainder = 02
Problem 2
Evaluate 11102 ÷ 102 using the long-division method.
Quotient = 1112
Remainder = 02
Explanation
Dividend = 11102
Divisor = 102
Step 1: We can start with the first two digits of the dividend.
112 is the first two digits, which is greater than the divisor 102.
We can divide:
112 ÷ 102 = 12
Step 2: The first digit of the quotient is 1.
Subtract 112 - 102 = 012
Step 3: Bring down the next digit of the dividend.
Now we have 0112.
The first two digits 112 are greater than the divisor 102.
So, the second digit of the quotient is 1.
Subtract 112 - 102 = 012
Step 4: Bring down the last digit of the dividend.
Now we have 102, which is equal to the divisor.
So, the quotient is 1.
Subtract 102 - 102 = 02
Thus, 11102 ÷ 102
Quotient = 1112
Remainder = 02
Problem 3
Evaluate 11002 ÷ 112 using the long-division method.
Quotient = 1002
Remainder = 02
Explanation
Dividend = 11002
Divisor = 112
Step 1: Start with the first two digits of the dividend.
The first two digits are 112, which is equal to the divisor 112.
Step 2: 112 ÷ 112
Hence, the first digit of the quotient is 1.
Subtract 112 - 112 = 02
Step 3: Bring down the next digit of the dividend.
Now we have 02, which is smaller than 112.
So, the quotient is 0.
Step 4: Bring down the next digit of the dividend.
Now we have 002, which is smaller than 112.
Hence, the quotient is 0.
Thus, 1100 ÷ 112
Quotient = 1002
Remainder = 02
Problem 4
Evaluate 101002 ÷ 1002 using the long-division method.
Quotient = 1012
Remainder = 02
Explanation
Dividend = 101002
Divisor = 1002
Step 1: Start with the first three digits of the dividend.
1012 is the first three digits, which is greater than the divisor 1002.
Step 2: 1012 ÷ 1002
1 = Quotient and
1 = Remainder.
Thus, the first digit of the quotient is 1.
Subtract 1012 - 1002 = 0012
Step 3: We can bring down the next digit of the dividend.
Now we have 0102, which is smaller than 1002.
Hence, the quotient is 0.
Step 4: Now we can bring down the last digit of the dividend.
It is 1002, which is equal to the divisor.
Hence, the quotient is 1.
Next, we can subtract 1002 - 1002 = 02
Thus, 101002 ÷ 1002
Quotient = 1012
Remainder = 02
Problem 5
Evaluate 10012 ÷ 12.
Quotient = 10012
Remainder = 02
Explanation
Here, we divide the binary number (1001)2 by 1, the result will be the same as the dividend.
Thus, 10012 ÷ 12
Quotient = 10012
Remainder = 02
FAQs of Binary Division
1.Differentiate decimal numbers and binary numbers.
2.List the rules of binary division.
3.What is the significance of leading zeros in binary division?
4.When will the quotient become 0?
5.What will be the result of dividing a binary number by 0?
6.How can children in Indonesia use numbers in everyday life to understand Binary Division?
7.What are some fun ways kids in Indonesia can practice Binary Division with numbers?
8.What role do numbers and Binary Division play in helping children in Indonesia develop problem-solving skills?
9.How can families in Indonesia create number-rich environments to improve Binary Division skills?
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Hiralee Lalitkumar Makwana
About the Author
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
Fun Fact
: She loves to read number jokes and games.
