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.
 

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:

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.

 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.