Binary Division (How To Guide With Rules And Examples)

How to Divide Binary Numbers

Binary division is an important but often overlooked part of binary arithmetic.

Binary addition, binary subtraction, binary multiplication and binary division are the four types of arithmetic operations that occur in the binary arithmetic.

Though binary division not too difficult, it can initially be a bit harder to understand than the other binary operations as they shared similarities. For example, they all had four basic steps which made all the processes quite easy to understand.

But the process of binary division does not have any specific rules to follow. Though this process is quite similar to the decimal division. The process will not be clear until we look at an example

Let us take A = 11010 and B = 101, where we want to divide A by B.

The structure of the operation of binary division is similar to that of decimal division, now we will look into the operation step by step to make it understanding as much as possible.

In the first step the left most digits of dividend i.e. A are considered and depending upon the value the divisor is multiplied with 1 and the result which is the result of multiplication of 101 and 1 are written. As we already know that 1 × 1 = 1, 1 × 0 = 0 and 1 × 1 = 1 that is exactly what is written.

In this step 101 is subtracted from 110. This step is also very easy to understand as we already know binary subtraction method. Now going into the next step.

As of the rules of division the next least significant bit comes down and we try to multiply 1 with divider i.e. B but the result is bigger than the minuend so this step cannot be completed and we have to go to the next step.

0 is inserted into the quotient and the least significant bit comes down now we can proceed to the next step.

Now again the divisor is multiplied with 1 and the result is written, the result is similar to the first one because all the numbers are same. Now we are going into the final step.

In the final step binary subtraction is done and we get the remainder and the operation of binary division is completed and we get the following result.
Quotient = 101 and remainder = 1.

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