Binary Division
The binary division is one of the important operations of binary arithmetic. A binary number system or basetwo is a counting technique that uses two digits: 0 and 1, and represents the number with the base 2. Here, the prefix 'bi' means 'two.' It is called binary as it has a base of 2 and it uses only two digits 0 and 1. Binary number systems are most commonly used in computer technology. All computers use a binary number system in their programming languages, that relies upon just two symbols, 0 and 1. With the rapid technological advancements across the globe, it is essential for one to understand the binary number system well.
In this article, we will learn the stepbystep method to make binary division easy to understand.
1.  Binary Division 
2.  Binary Division Rules 
3.  How To Do Binary Division? 
4.  Solved Examples 
5.  Practice Questions 
6.  FAQs on Binary Division 
Binary Division
Binary division, similar to other binary arithmetic operations, is performed on binary numbers. The algorithm for binary division is somewhat similar to decimal division, the only difference here lies in the rules followed using the digits '0' and '1'. Binary multiplication and binary subtraction are the two binary arithmetic operations that are performed while performing binary division. The use of only '0' and '1' makes binary division quite simpler in comparison to decimal division. Other operations that are used while performing binary division are binary multiplication and binary subtraction.
Binary Division Rules
We can perform all arithmetic operations such as addition, subtraction, multiplication, and division on binary numbers, in the same way as we perform arithmetic operations on the decimal number system. Binary subtraction, binary multiplication, binary addition, and binary division are the four types of arithmetic operations that are performed here. We just need to follow some rules while dividing two binary numbers. There are four rules to be followed while performing binary division. Similar to the decimal system (or in any other number system), division by 0 is meaningless in Binary division. The binary division rules are as follows:
The four rules given above are all the possible conditions for the division of binary numbers as binary numbers include only two digits 0 and 1.
How To Do Binary Division?
Binary division problems can be solved by using the long division method, which is one of the most efficient and easiest ways to divide binary numbers. These are the steps to be followed in a binary division operation:
 Step 1: Compare the divisor with the dividend. If the divisor is larger, place 0 as the quotient, then bring the second bit of the dividend down. If the divisor is smaller, multiply it with 1 and the result becomes the subtrahend. Then, subtract the subtrahend from the minuend to get the remainder.
 Step 2: Then bring down the next number bit from the dividend portion and perform step 1 again.
 Step 3: Repeat the same process until the remainder becomes zero or the whole dividend is divided.
Let us understand binary division operation better using the following example:
Example: Consider two binary numbers, B = \(011010_{2}\) and C = \(0101_{2}\) where we want to divide B by C.
Given: Dividend, \(011010_{2}\) and the divisor,C = \(0101_{2}\).
Step1: Since the zero in the most significant bit position doesn't change the value of the number, let's remove it from both the dividend and divisor. So the dividend becomes \(11010_{2}\), and the divisor becomes \(101_{2}\).
Step 2: Let us use the longdivision method. In this step, compare the divisor \(101_{2}\) with the first digit in the dividend \(11010_{2}\), since the divisor is smaller, it will be multiplied with 1 and the result will be the subtrahend.As per the binary multiplication rules:
 1 × 1 = 1
 1 × 0 = 0
 0 × 1 = 0
 0 × 0 = 0
So, 101 × 1 = \(101_{2}\), and this result is written below.
Step 3: Subtract the subtrahend \(101_{2}\) from the minuend \(110_{2}\).
As per the binary subtraction rules,
 0  1 = 1, we need to borrow 1 from the next more significant bit.
 0  0 = 0
 1  1 = 0
 1  0 = 0
When we apply the above rules, this is how the calculation is done:
 For the first digit on the right, we have to subtract (0  1). So, we borrow a 1 from the digit on the left or the next higher order digit. Therefore, the result is 1.
 Then, (0  0 = 0) since the number in the next higher order digit becomes 0 after borrowing.
 1  1 = 0 in the second next higher order digit.
 So, \(110_{2}\)  \(101_{2}\) = \(001_{2}\), and this result is written below.
Step 4: As per the rules of division, the next least significant bit comes down, and the divisor is multiplied by 1. Since the result, \(101_{2}\) is bigger than the minuend \(0011_{2}\), this step cannot be completed. Then, we have to go to the next step
Step 5: We write 0 as the next bit of the quotient and then, the least significant bit 0 comes down.
Step 6: Again the divisor is multiplied by 1 and the result is written as 101 × 1 = \(101_{2}\).
Step 7: Now we are at the final step. As per the binary subtraction, we subtract \(101_{2}\) from \(110_{2}\). We get, \(110_{2}\)  \(101_{2}\) = \(001_{2}\). The remainder is similar to Step 3, as all the numbers are the same.
The binary division operation is completed now and we get the following result. Quotient = \(101_{2}\)
 Remainder = 001 = 1
Related Topics
Check out these interesting articles to learn more about binary division and its related topics.
 Binary Calculator
 Binary Subtraction
 12 in Binary
 15 In Binary
 100 In Binary
 32 in Binary
 Decimals and Fractions
Important Notes
Here are some of the important points to be kept in mind regarding binary division.
 Binary division involves two other binary arithmetic operations  multiplication and subtraction.
 In order to perform a binary division, we follow the same process which we follow for dividing regular numbers. But, in this case, we only need to decide if it's going to be a 1 or a 0 and this makes calculation far easier.
 Binary division problems can be solved by using the long division method, which is one of the most efficient and easiest ways to solve binary division.
 The most common application of the binary number system can be found in computer technology.
Solved Examples

Example 1: Evaluate \(1001011_{2}\) ÷ \(11_{2}\) using the longdivision method.
Solution:
Here, Dividend = \(1001011_{2}\), Divisor = \(11_{2}\). Let us use the longdivision method as follows:
Answer: Quotient = \(11001_{2}\), Remainder = 0. 
Example 2: Evaluate \(10010_{2}\) ÷ \(11_{2}\) using the longdivision method.
Solution:
Here, Dividend = \(10010_{2}\), Divisor = \(11_{2}\). Let us use the longdivision method to solve this:
Answer: Quotient = \(110_{2}\), Remainder = 0
FAQs on Binary Division
What is the Main Difference Between Decimal Numbers and Binary Numbers?
The main difference between binary and decimal systems is the number of digits that are used to represent any given number. The decimal number system uses 10 digits ranging from 0 to 9 (0,1,2,3,4,5,6,7,8,9) to represent any decimal number integer or fraction; whereas, the binary system uses only 2 digits (0 and 1) to represent binary numbers.
What are the Rules of Binary Division?
The rules of binary division are: 1 ÷ 1 = 1, 1 ÷ 0 = Meaningless, 0 ÷ 1 = 0, 0 ÷ 0 = Meaningless.
Define Binary Number System
A binary number system or basetwo is a counting technique that uses two digits: 0 and 1, and represents the number with the base 2. Here, the prefix 'bi' means 'two.' It is called binary as it has a base of 2 and it uses only two digits 0 and 1.
What are the Rules of Binary Subtraction?
The rules of binary division are: 0 – 0 = 0, 0 – 1 = 1 (we need to borrow 1 from the next more significant bit), 1 – 0 = 1, and 1 – 1 = 0.
Is it Possible to Perform Arithmetic Operations on Binary Numbers?
Yes, we can perform all arithmetic operations such as addition, subtraction, multiplication, and division on binary numbers in the same way as we perform arithmetic operations in the decimal number system.
Which Division Method Is Used to Perform Binary Division?
Binary division problems can be solved by using the long division method, which is one of the most efficient and easiest ways to solve binary division.
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