Binary division is a mathematical operation that involves dividing two binary numbers, which are numbers composed of only 0’s and 1’s. Binary division is similar to decimal division, except that the base of the number system is 2 instead of 10.
In this article, we will learn about Binary Numbers, Binary Division, and Rules to perform Binary Division, accompanied by solved examples, practice problems, and answers to frequently asked questions.
What is Binary Division?
Binary division is a mathematical operation performed on binary numbers, which are composed of only the digits 0 and 1. We use 0 to 9 in the case of decimal division, whereas 0’s (zeros) and 1’s (ones) are used in binary division.
- Similar to decimal division, binary division involves dividing one binary number (the dividend) by another (the divisor) to obtain a quotient and a remainder.
- Binary division is fundamental in computer science and digital systems, as binary is the foundational numeral system for representing information in computers.
Learn, Division
Before learning more about Binary Divisions, let’s first learn about Binary Numbers
What are Binary Numbers?
Binary Number is a number that is used to represent various numbers using only two symbols “0” and “1”.
- The binary numbers are expressed in the base-2 numeral system.
- Each digit in this system is called a bit.
Example of Binary Number
Binary of equivalent of 6 = (110)2
Learn More, Binary Number System
Binary Division Rules
Binary Division is performed in the same manner as decimal numbers are divided. However, there are some specific rules regarding the division among the binary digits 0 and 1 which we need to follow while performing division of Binary Division. The Binary Division rules is shown in the Binary Division Table below:
Binary Division Table
The rules for Binary Division is tabulated below:
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Table of Binary Division Rule
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Rules for Binary Division
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Meaning
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0 / 0 = ∞
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If 0 (zero) is divided by another 0 (zero), then the result is meaningless.
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0 / 1 = 0
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if 0 (zero) is divided by 1 (one), then the result will be 0 (zero).
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1 / 0 = ∞
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If 1 (one) is divided by 0 (zero), then the result is meaningless.
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1 / 1 = 1
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If 1 (one) is divided by another 1 (one), then the result will be 1 (one).
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Binary Multiplication Table
Since, while performing division we need to write numbers below dividend by multiplying quotient and divisor. Hence we should also have the recap of the binary multiplication rule which is tabulated below:
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Table for Binary Multiplication Rule
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Rules for Multiplication
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Meaning
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0 × 0 = 0
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If 0 (zero) is multiplied to another 0 (zero), then the result is 0 (zero).
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0 × 1 = 0
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If 0 (zero) is multiplied to 1 (one), then the result is 0 (zero).
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1 × 0 = 0
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If 1 (one) is multiplied to 0 (zero), then the result is 0 (zero).
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1 × 1 = 1
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If 1 (one) is multiplied to another 1 (one), then the result is 1 (one).
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Binary Subtraction Table
Since, in division we continuously subtract the product of quotient and divisor from dividend we need to have a recap of binary subtraction rule which is tabulated below:
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Table of Binary Subtraction Rule
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Rules for Subtraction
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Meaning
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0 – 0 = 0
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If 0 (zero) is subtracted from another 0 (zero), then the result is 0 (zero).
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0 – 1 = 1
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If 1 (one) is subtracted from 0 (zero), then the result is 1 (one) with a borrow from next higher significant digit.
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1 – 0 = 1
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If 0 (zero) is subtracted from 1 (one) then the result is 1 (one).
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1 – 1 = 0
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If 1 (one) is subtracted from another 1 (one), then the result is 0 (zero).
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How to do Binary Division
Just like decimal division, in long division method there are four key steps involved. Now we have learnt the Binary Division Rule let’s learn the steps to do binary division
Step 1: Divide the bits of the dividend and record the quotient.
Step 2: Multiply the divisor by the quotient and write the product.
Step 3: Subtract the product from the dividend and write the difference.
Step 4: Bring down the next digit and repeat.
Binary Division Examples
Here are some solved examples on Binary Divison based on above Binary Divison Rules and steps
Example 1: (11011)2 ÷ (11)2
Solution:
We start by taking the first two digits of the dividend (11)2 which is equal to the divisor.
Step 1: Write 1 as the first digit of the quotient. Then, subtract the divisor from the first part of the dividend and write down the remainder.
Step 2: Bring down the next digit of the dividend (0). Now we have (0)2 which is less than the divisor (11)2. So, write 0 in the quotient.
Step 3: Next bring down the next digit of the dividend (1). Now we have (1)2 which is less than the divisor (11)2. So, write 0 in the quotient. We subtract the divisor from the current part of the dividend and write down the remainder.
Step 4: Finally, bring down the last digit of the dividend (1). Now we have (11)2 which is equal to the divisor (11)2. So, write 1 in the quotient and 0 as the remainder.
Binary Division Example 1
So, the quotient of (11011)2 ÷ (11)2 is (1001)2 and the remainder is (0)2
Example 2: (101101)2 ÷ (110)2
Solution:
We start by taking the first four digits of the dividend (1011)2 which is greater than the divisor (110)2.
Step 1: rite 1 as the first digit of the quotient. Then, we subtract the divisor from the first part of the dividend and write down the remainder.
Step 2: Next, we bring down the next digit of the dividend (0). Now we have (1010)2 which is greater than the divisor (110)2. So, we write 1 in the quotient. We subtract the divisor from the current part of the dividend and write down the remainder.
Step 3: Finally, we bring down the last digit of the dividend (1). Now we have (1001)2 which is greater than the divisor (110)2. So, we write 1 in the quotient. We subtract the divisor from the current part of the dividend and write down the remainder.
So, the quotient of (101101)2 ÷ (110)2 is (111)2 and the remainder is (11)2
Example 3: (1011011)2 ÷ (101)2
Solution:
We start by taking the first three digits of the dividend (101)2 which is equal to the divisor.
Step 1: Write 1 as the first digit of the quotient. Then, we subtract the divisor from the first part of the dividend and write down the remainder.
Step 2: Next, we bring down the next digit of the dividend (1). Now we have (1)2 which is less than the divisor (101)2. So, we write 0 in the quotient.
Step 3: Next, we bring down the next digit of the dividend (0). Now we have (10)2 which is less than the divisor (101)2. So, we write 0 in the quotient.
Step 4: Next, we bring down the next digit of the dividend (1). Now we have (101)2 which is equal to the divisor (101)2. So, we write 1 in the quotient. We subtract the divisor from the current part of the dividend and write down the remainder.
Step 5: Finally, we bring down the last digit of the dividend (1). Now we have (1)2 which is less than the divisor (101)2. So, we write 0 in the quotient and 1 as the remainder.
So, the quotient of (1011011)2 ÷ (101)2 is (10010)2 and the remainder is (1)2
Example 4: (1010011.1010)2 ÷ (100)2
Solution:
We start by taking the first three digits of the dividend (101)2 which is greater than the divisor (100)2.
Step 1: Write 1 as the first digit of the quotient. Then, we subtract the divisor from the first part of the dividend and write down the remainder.
Step 2: Next, we bring down the next digit of the dividend (0). Now we have (10)2 which is less than the divisor (100)2. So, we write 0 in the quotient.
Step 3: Next, we bring down the next digit of the dividend (0). Now we have (100)2 which is equal to the divisor (100)2. So, we write 1 in the quotient. We subtract the divisor from the current part of the dividend and write down the remainder.
Step 4: Next, we bring down the next digit of the dividend (1). Now we have (1)2 which is less than the divisor (100)2. So, we write 0 in the quotient.
Step 5: Next, we bring down the next digit of the dividend (1). Now we have (11)2 which is less than the divisor (100)2. So, we write 0 in the quotient.
Step 6: Next, we bring down the next digit of the dividend (.). This indicates that we are now moving into the fractional part of the division. We continue the process as before.
Step 7: Next, we bring down the next digit of the dividend (1). Now we have (111)2 which is greater than the divisor (100)2. So, we write 1 in the quotient. We subtract the divisor from the current part of the dividend and write down the remainder.
Step 8: Next, we bring down the next digit of the dividend (0). Now we have (110)2 which is greater than the divisor (100)2. So, we write 1 in the quotient. We subtract the divisor from the current part of the dividend and write down the remainder.
Step 9: Next, we bring down the next digit of the dividend (1). Now we have (101)2 which is equal to the divisor (100)2. So, we write 1 in the quotient. We subtract the divisor from the current part of the dividend and write down the remainder.
Step 10: Finally, we bring down the last two digits of the dividend (0). Now we have (10)2 which is less than the divisor (100)2. So, we write it as the remainder.
So, the quotient of (1010011.1010)2 ÷ (100)2 is (10100.1110)2 and the remainder is (10)2
Example 5: (10011001)2 ÷ (1001)2
Solution:
We start by taking the first four digits of the dividend (1001)2 which is equal to the divisor.
Step 1: Write 1 as the first digit of the quotient. Then, we subtract the divisor from the first part of the dividend and write down the remainder.
Step 2: Bring down the next digit of the dividend (1). Now we have (1)2 which is less than the divisor (1001)2. So, we write 0 in the quotient.
Step 3: Bring down the next digit of the dividend (0). Now we have (10)2 which is less than the divisor (1001)2. So, we write 0 in the quotient.
Step 4: Bring down the next digit of the dividend (0). Now we have (10)2 which is less than the divisor (1001)2. So, we write 0 in the quotient.
Step 5: Finally, bring down the last digit of the dividend (1). Now we have (1001)2 which is equal to the divisor (1001)2. So, we write 1 in the quotient and 0 as the remainder.
So, the quotient of (10011001)2 ÷ (1001)2 is (10001)2 and the remainder is (0)2
Also, Check
Binary Division – Practice Questions
Since, we have learnt how to divide Binary Numbers, here are some questions of Binary Division to Practice
Q1. Divide (10110)2 by (10)2
Q2. Is (10010101)2 is a multiple of (11)2?
Q3. Divide (11001110)2 by (1001)2
Q4. Divide (11110010)2 by (1010)2
Q5. Divide (11010)2 by (101)2
Binary Division – FAQs
1. Define Binary Numbers.
Binary Numbers are defined as the numbers expressed in the form of 0 and 1 only
2. What is a Bit?
A bit in Binary Number System is defined as a individual digits that holds the value ‘0’ or ‘1’.
3. What are Types of Number Systems?
There are various types of number systems and some of them are,
- Binary Number System
- Octal Number System
- Decimal Number System
- Hexadecimal Number System
3. Is Binary Division same as Decimal Division?
Yes, We use 0 (zero) to 9 in case of decimal division, whereas 0’s (zero) and 1’s (ones) are used in binary division.
4. Can we divide by 0 (zero) in Binary Division?
No, dividing by 0 (zero) leads to an undefined value.
5. What are Rules of Binary Division?
The rules of Binary Division are mentioned below:
- 1 ÷ 1 = 1
- 1 ÷ 0 = Meaningless
- 0 ÷ 0 = Meaningless
- 0 ÷ 1 = 0
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