How to convert decimal fraction to binary ?
Are you looking to learn how to convert a decimal fraction to binary? If so, then you've come to the right place.
In this blog article, we will explore the process of converting a decimal fraction to binary.
We will break down the steps involved in converting a decimal fraction to binary, providing clear explanations and examples along the way.
By the end of this article, you'll have a better understanding of how to convert a decimal fraction to binary.
So, let's get started!
What are decimal fraction ?
Decimal fractions are numbers that contain a decimal point, such as 0.5, 0.25, and 0.75. They are used to represent a fraction of a whole number or represent a fractional part of a whole number.
What are Binary numbers ?
Binary numbers are numbers that are expressed in base-2, meaning that they only contain two digits: 0 and 1. Binary numbers are used to represent data in computers, including digital images, sound, and text.
How to convert decimal fraction to binary ?
Converting a decimal fraction into a binary number involves the following steps:
First identify the decimal number that needs to be converted to binary.
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Separate the whole number and fractional part:
Start by separating the given decimal fraction into its whole number and fractional part.
For example, if the decimal fraction is 5.75, the whole number is 5 and the fractional part is 0.75.
Convert the whole number to binary:
To convert the whole number part into binary, divide it continuously by 2 and note down the remainder at each step.
The binary representation will be the sequence of remainders read in reverse order.
For example, converting 5 to binary would give us the remainder sequence 1, 0, 1, which translates to 101 in binary.
Convert the fractional part to binary:
To convert the fractional part into binary, multiply it continuously by 2 and note down the integral part (before the decimal point) at each step.
The binary representation will be the sequence of integral parts read in order.
You can easily understand by the help of below example
Explanation of above problem
To convert a decimal fraction 25.75 into a binary number, we have to follow these steps:
Convert the integer part of the decimal fraction into binary. In this case, the integer part is 25.
To convert 25 into binary, divide it successively by 2 and write down the remainders.
The remainders, read from bottom to top, give the binary equivalent of 25, which is 11001.
Convert the fractional part of the decimal fraction into binary.
In this case, the fractional part is 0.75. Multiply the fractional part by 2 and write down the whole number part of the result.
Repeat this process until the fractional part becomes 0 or the desired precision is achieved. The whole number parts, read from top to bottom, give the binary equivalent of 0.75, which is 11.
Combine the binary representation of the integer part and the fractional part. Place a binary point between
By following those above steps, you can easily convert any decimal number to its binary equivalent.
Conclusion
In conclusion, converting a decimal fraction to a binary number is relatively simple if you follow the steps laid out in this article.
The process involves first converting the fractional part of the decimal number to its binary equivalent, then combining the integer part and fractional part to get the final binary number.
Although the process may seem complicated at first, it is an important skill to learn in order to effectively work with binary numbers. With just a little practice, you should be able to quickly and confidently convert a decimal fraction into a binary number.
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