In this tutorial we will learn binary to decimal conversion for a number with fractional part.

Before we dive into the main topic lets talk a little about Decimal and Binary Number System that we are going to work with in this tutorial.

A decimal number system consists of 10 digits: 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. So, any number that we use in our daily life is actually in decimal number system.

A binary number system consists of only 2 digits: 0 and 1. And it is most commmonly used in computers.

How to convert a binary number with fractional part into decimal number?

To convert a binary number having fractional part into decimal form we have to multiply the tenths position by 2^{-1} hundredths position by 2^{-2} and so on…

Convert binary number 0.001_{(base 2)} into decimal form

The following table shows the places, binary number and the multipliers for the corresponding places.

So, the required decimal number is 0.001_{(base 2)} = 0.125_{(base 10)} Alternatively, (0.001)_{2} = (0.125)_{10} Where, (base 10) means the number is in decimal number system and (base 2) means the number is in binary number system.

Convert binary number 1010.00101_{(base 2)} into decimal form

To convert a binary number having integer and fractional part into decimal form we have to multiply the integer part ones place with 2^{0} tens place with 2^{1} hundreds place with 2^{2} ans so on... and the fractional part tenths position by 2^{-1} hundredths position by 2^{-2} and so on...

The following table shows the places, binary number and the multipliers for the corresponding places.

So, the required decimal number is 1010.00101_{(base 2)} = 10.15625_{(base 10)} Alternatively, (1010.00101)_{2} = (10.15625)_{10} or, (1010.00101)_{2} = (10.16)_{10} (approx. value) Where, (base 10) means the number is in decimal number system and (base 2) means the number is in binary number system.