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.
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
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Binary Division
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.
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