How to convert Binary Fraction to Decimal ?

Converting a binary fraction to the decimal number system can seem complex at first, but with a step-by-step approach, it becomes much simpler.

In this blog article, we will explore the process of converting binary fractions to their decimal equivalents. By understanding the principles and following a systematic method, you will be able to confidently convert binary fractions to decimal numbers in no time.

So let's get started!

What are binary fraction ?

Binary fractions are a representation of numbers in the binary number system, which uses only two digits: 0 and 1. Binary fractions are commonly used in computing and computer science because it is easy to represent numbers in binary form.

To write a binary fraction, we use a decimal point and continue the pattern of powers of 2 in the fractional part.

For example, the binary fraction 0.101 represents the decimal value 1/2 + 0/4 + 1/8 = 0.625.

What is a Decimal number system ?

A decimal number system is a base 10 number system, which means that it uses 10 distinct symbols (0,1,2,3,4,5,6,7,8 and 9) to represent different values.

There are two terms which are used to describe the ordering of bits in a binary number:

• LSB (Least Significant Bit)

  LSB stands for Least Significant Bit and is the bit located at the right most position in a byte or word. It is the lowest order bit and its value is usually 0 or 1.

  For example in the byte

  11010100, the LSB is 0

• MSB (Most Significant Bit

  MSB stands for Most Significant Bit and is the bit located at the left most position in a byte or word. It is the highest order bit and its value is usually 0 or 1.

  For example in the byte

  11010100, the MSB is 1

How to convert Binary fraction to Decimal ?

1. To convert a binary fraction to its decimal number, we have to follow these steps:

2. Convert the whole number part to a decimal number.

3. Convert the fractional part to a decimal number.

4. Convert the fractional part of binary to decimal equivalent

5. Add the two decimal numbers together to get the final decimal number.

You can easily understand by the help of below example

Explanation of above problem

To convert a binary fraction 110.101 into a decimal number, we have to follow these steps:

1. To convert a binary fraction (110.101) to its decimal number, we have to follow these steps:

2. Multiply each digit separately from left side of radix point till the first digit by 2^0, 2^1, 2^2 respectively.

3. Add all the result coming from step 1.

4. Convert the fractional part of binary to decimal equivalent

5. Divide each digit from right side of radix point till the end by 2^1, 2^2, 2^3 respectively.

6. Add all the result coming from step 1.

7. Add both integral and fractional part of decimal number.

By following those above steps, you can easily convert any decimal to its hexadecimal equivalent.

Conclusion

In conclusion, converting a binary fraction number to decimal is a relatively simple process. All you need to do is identify the fractional portion of the binary number, convert each digit to its decimal value, and then add these decimal values together. Following these steps can help you quickly and accurately convert binary fractions into decimal numbers.