Before going ahead with decimal to binary conversion, we need to know about decimal and binary number. I think most of you know about this two number systems.
Decimal is the most common and naturally used number system where we use the digits 0 to 9 to write any number. Where binary is the 2 based number where we can only use 0 and 1 to write any number.
Binary number is well known to the machine and hardly known to human before calculation. But decimal number is very well known to everyone. Because we use decimal number in all our calculations.
Now, lets come to the point. In this post, I am going to teach you everything about decimal to binary conversion. How we can convert a number from decimal to binary will be discussed here.
As like as other conversion we have to know two rules for decimal to binary conversion. One is for integer and other is for fraction number. Now, let’s go ahead with some examples of converting.
Rules for converting integer:
- Divide the decimal number by the base of binary number (2) and write the reminder.
- Divide the result again by 2 and write the reminder and continue this process until you get 0 at the result.
- Now write down the remainder in opposite order which will be the binary equivalent of given decimal number.
Example : Conversion of (27)10 to equivalent binary number.
As like as the given two figure bellow, we have to divide the given 27 by the base of binary number which is 2. Then we have to store the reminder.
In the given figure, we have got 13 as the result and 1 as reminder. Then again divide 13 by the base of binary number.
Then we have got 6 as the result and 1 as reminder. Continue this process until get 0 at the result.
At last, we have to write all the reminder at the given direction followed by the arrow in both cases.
Here, we can use any one of this two method. Direction of arrow indicates the order of binary digits.
You can convert any integer decimal number to its equivalent binary number by this rule. Now, it is your time to do some practice of conversion. Now, let’s go to the next one which is for fraction numbers.
Rules for fraction number :
However, there are some different rules for converting a fraction number from decimal to binary. Let’s go through the rules first then we will see some example.
- Multiply the fraction part by 2 and write the integer portion if you get any. Otherwise write zero.
- Again, multiply the resultant fraction part which you have got from the first process and write down the integer part and continue this process until you get zero at the fraction part (minimum 4 to 5 times if it repeats).
- Now write down the integers or zeros you have got at the same order you have got them.
Now, see the method of converting at the example bellow. This will give you a clear concept to convert a fraction number from decimal to binary.
Example : Conversion of (0.45)10 to equivalent binary number.
For this conversion, we have to multiply the given number 0.45 by the base of binary number which is 2. Then we have to store the integer part which can be 0 or 1.
Here in this figure bellow, we have multiplied 0.45 by 2.
Then we have got 0.90 where the integer portion is 0 and fraction portion is .90
Then again multiply .90 by 2.
Now we have got 1.80 where the integer part is 1 and fraction is .80
Continue the process until you get 0 at the result. If it does not give zero at the result, then determine 4 to 5 times or as the given direction.
Here, direction of arrow indicates the order of priority of taking binary digits. Now, try yourself to do the same thing for some different fraction numbers.
See the following example conversion to learn more if you have any doubt still now. In this example we will convert a number from decimal to binary. It will really help you to understand this conversion.
Example : Conversion of (127.375)10 to equivalent binary number.
We will convert separately its integer and fraction part for converting the number from decimal to binary. At first we will convert the integer part and then fraction part.
Now, lets see the conversion of its integer part first. The rule for this conversion is same as we have discussed above.
So, the binary equivalence of 127 is 1111111 which we have got from the above two figure. However, you can use any one method from the above two methods.
Now, we will see the conversion of its fraction part to the equivalent binary number. Let’s try to understand by the given figure.
Here, we have got the binary equivalence of given fraction part is 0.011. We will combine this two part to get the full number of equivalence of the decimal number to binary number.
So, the total binary equivalent of this decimal number will be (1111111.011)10 . However, you can convert any decimal number to its equivalent binary number following this rules.
Now, it is your time to become expert to convert a number from decimal to binary. See our rules again if you have still any doubt.
I think, you have got a very clear idea about how we can convert a decimal number to its equivalent binary number. I have tried my best to make this topics very easy for you.
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