Conversion
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.
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…
The following table shows the places, binary number and the multipliers for the corresponding places.
= 0x20 + 0x2-1 + 0x2-2 + 1x2-3 = 0 + 0 + 0 + 0.125 = 0.125
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.
To convert a binary number having integer and fractional part into decimal form we have to multiply the integer part ones place with 20 tens place with 21 hundreds place with 22 ans so on... and the fractional part tenths position by 2-1 hundredths position by 2-2 and so on...
= 1x23 + 0x22 + 1x21 + 0x20 + 0x2-1 + 0x2-2 + 1x2-3 + 0x2-4 + 1x2-5 = 8 + 0 + 2 + 0 + 0 + 0 + 0.125 + 0 + 0.03125 = 10.15625
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.