Unravelling the Mystery of Binary Fractions - Convert 0000.1010 to Decimal!

Binary numbers are a crucial part of the digital world. They are the building blocks of computers, smartphones, and the Internet. Binary numbers are a representation of numbers using the base-2 number system, which is composed of only two digits: 0 and 1. Binary fractions are a subset of binary numbers which represent decimal fractions. If you are interested in understanding how to convert the fractional binary number 0000.1010 to decimal, this blog post is for you!

What are Binary Fractions?

Binary fractions are numbers between 0 and 1 written in the binary number system. In binary fractions, the binary point is used instead of the decimal point. The binary point separates the whole numbers from the fractional part of the number. It is important to note that, unlike in decimal fractions, the binary point is always assumed to be at the extreme right of the number. For example, the binary number 0000.1010 can be written as 00001010.2.

How to Convert Binary Fractions to Decimal?

Converting a binary fraction to decimal is quite straightforward. All you need to do is multiply each bit in the fractional part of the binary number by the corresponding power of two and add the result to get the decimal equivalent. The bit at the extreme right has a weight of 2^-1 (2 to the power -1), the bit to the left of it has a weight of 2^-2, and so on.

For example, to convert the fractional binary number 0000.1010 to decimal, we need to multiply each bit by the corresponding power of two and add the result. The binary number 0000.1010 can be rewritten as 00001010.2. The bits from the extreme right to the left are 0, 1, 0, 1, 0, 0, 0. These bits correspond to the weights 2^-1, 2^-2, 2^-3, 2^-4, 2^-5, 2^-6, and 2^-7 respectively. Now, we multiply each bit by the corresponding power of two and add the result.

Therefore, the decimal equivalent of 0000.1010 is 0 + 0 + 0 + 1 x 2^-4 + 0 + 1 x 2^-2 + 0 x 2^-1 = 0.625.

Conclusion

In this blog post, we discussed how to convert the fractional binary number 0000.1010 to decimal. We started by introducing binary fractions and discussing how different they are from decimal fractions. Then, we went on to discuss how to convert a binary fraction to decimal. We saw that the process is quite straightforward and involves multiplying each bit by the corresponding power of two and adding the result. Finally, we saw that the decimal equivalent of

Dated : 01-Feb-2023

Category : Education

Tags : Mathematics