- Binary Division Definition: Binary division is defined as an arithmetic operation involving the division of binary numbers.
- Initial Step: The first step in binary division is to consider the left-most digits of the dividend and multiply the divisor by 1.
- Binary Subtraction: Subtract the divisor from the selected digits of the dividend to proceed to the next step.
- Updating Quotient: Insert 0 into the quotient if the multiplication result exceeds the minuend and bring down the next bit.
- Final Result: Complete the division process to find the quotient and remainder.
How to Divide Binary Numbers
Binary division is an essential yet 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 binary arithmetic.
Binary division isn’t too difficult, but it can be harder to understand at first compared to other binary operations.
This is because all the other binary operations share similarities with each other, whereas binary division is a bit of an outlier.
For example, all of the other binary operations had four basic steps which made them a bit easier to understand.
But the process of binary division does not have any specific rules to follow—although it is quite similar to decimal division.
To make this a bit clearer, let’s look at a binary division example problem.
Let us take A = 11010 and B = 101, where we want to divide A by B.
The structure of binary division is similar to decimal division. Let’s break down the steps to understand it better.
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. we get:
In this step 101 is subtracted from 110 (see the binary subtraction for help with that)
Now going into the next step:
According to division rules, bring down the next least significant bit. If multiplying the divisor by 1 results in a value larger than the minuend, insert 0 into the quotient and move 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 by 1 and the result is written, the result is similar to the first one because all the numbers are the 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.
All done!
Please leave a comment below if you’d like to see more binary division example problems (with solutions, of course!).
