Decimal to binary conversion method :
It is known as the repetitive division method, which is normally used in decimal to binary conversion method. There are other methods also available which can also be used in decimal to binary conversion. But repetitive division method is one of the easiest and best ways to convert a decimal number to its equivalent binary form.
In this article, we will learn how to convert decimal to binary using this repetitive division method.
As we studied in our binary number system section, that the base of the binary number system is always 2. So, here we divide the given decimal number repetitively by 2 until we get a 0 as the answer at the bottom.
Look at the example below :
Decimal to binary conversion steps:
- We divided 10 (a decimal number) by 2 (base of binary number system) and got the answer 5, and 0 as our remainder.
- We again divided 5 by 2. So, here we got 2 as the answer and 1 as our remainder.
- So here we again divided 2 and got answer 1 and remainder 0.
- By dividing 1 by 2, we got 0 and remainder 1.
- Since we got 0 at the bottom so we stop this division process and we write the remainders in upward direction i.e. 1010, which is the equivalent binary form of the decimal number (10)10. And we write it as (1010)2.
Using above mentioned steps we can easily convert any decimal number to its equivalent binary form. Below is another example of decimal to binary conversion of a decimal number (125)10 to its equivalent binary form (111101)2.
Till now, we have learned the conversion of decimal integer to binary. Now we will move to the conversion of decimal fraction to binary.
Now, let’s take an example of decimal fraction (15.65)10. So, how would we convert that to its binary equivalent?
Here we can divide (15.65)10 into two parts.
- Integer part i.e. (15)10.
- Fraction part i.e. (0.65)10.
For the integer (15)10, we do the conversion as usual and we get (1111)2 which is the binary equivalent of (15)10.
Now we will convert the fraction part i.e. (0.65)10 using the following method.
Decimal fraction to binary conversion method:
Here we take the fraction part and multiply it with the destination base. We repeat this process that when we get a fraction part, we will multiply it by 2. We will keep doing this process until we get 0 as a fraction.
If we can’t find 0 in fraction we will stop this repetitive multiplication process after we get sufficient digits in the fraction.
Conversion of decimal fraction to binary steps :
- We take 0.65 and multiply it by 2. It gives us answer 1.3, where 0.3 is again fraction part, we note the integer part i.e. 1.
- Now, we multiplied 0.3 with 2 and we got 0.6. Here we got 0.6 as a fraction, we note the integer part. Here it is 0.
- Now, 0.6 is multiplied by 2 and we got 1.2. Here 1 is the integer and 0.2 is fraction part.
- We multiplied 0.2 with 2 and got 0.4. We got integer 0 and fraction 0.4.
- Again we multiplied 0.4 with 2 and again we got integer 0 and fraction 0.8.
- We notice that if we multiply 0.8 with 2 again we will get a fraction part and this process will continue. So we stop this repetitive multiplication process here.
- Write down the integer part downward as 10100. Which is the binary equivalent of the decimal fraction (0.65)10.
Now we can combine both integer and fraction part as (1111.10100)2. Which is the binary equivalent of the given decimal number (15.65)10.