How to Divide Binary Numbers

The binary division, similar to other binary arithmetic operations, is performed on binary numbers. The algorithm for binary division is 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 performed while performing binary division. The use of only '0' and '1' makes binary division quite simpler in comparison to decimal division. Other operations used while performing binary division are binary multiplication and binary subtraction.

Binary Division Rules

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:

1 ÷ 1 = 1

1 ÷ 0 = Undefined

0 ÷ 1 = 0

0 ÷ 0 = Undefined

Binary division questions can be resolved by using the long division method, which is one of the most efficient and easiest methods to divide binary numbers. Below are examples to understand the binary division method.

Steps to Solve:

The division process is performed like decimal division. The rules for binary division are:

◆ Start from the left of the dividend.

◆ Perform a series of subtraction in which the divisor is subtracted from the dividend.

◆If subtraction is possible, put a 1 in the quotient and subtract the divisor from the corresponding digits of the dividend.

◆ If subtraction is not possible (the divisor is greater than the remainder), record a 0 in the quotient.

◆ Bring down the next digit to add to the remaining digits. Proceed as before like long division.

Example: Divide 100001 by 110.

Step 1: Divisor greater than 100, so put 0 in the quotient.

Step 2: Add a digit from the dividend to the group used above.

Step 3: Subtraction is possible so put 1 in the quotient.

Step 4: Remainder from subtraction plus digit from dividend

Step 5: Divisor greater, so put 0 in the quotient.

Step 6: Add a digit from the dividend to the group.

Step 7: Subtraction is possible, so put 1 in the quotient.

Example: Divide (1111000)₂ by (100)₂.

Key Notes Regarding Binary Division

Some of the crucial points to keep in mind about the process of binary division are:

1- Binary division involves the application of two other arithmetic operations - multiplication and subtraction.

2- To perform a binary division, a student is expected to follow the same procedure with which we divide regular numbers. The only difference is, in the case of binary division, we need to decide if it's 1 or 0 as a placeholder in the quotient, This makes calculation very easy.

3- Mathematical problems in binary division are simplified with the help of the long division method, which is easy and one of the most efficient ways to solve binary division.

Today, this method finds its application in the field of computer technology.

Important Point: Binary division is a process also known as the long division method, It is used to find the resultant easily. Hence it is used in place of other division methods (e.g. double division method)

Let us take another example with "Logic Kit" app this app is very easy and so good in these subjects of number systems. Download This app from the app store for iOS devices click here.

1- Open the app

2- Choose More Arithmetic

3- Select the base 2

4- write your equation you need to solve

5- You see the solution then click on show steps