In this article we will learn to convert a number from binary to decimal through some example. We have to learn two rules for converting a number from binary to its equivalent decimal. First rule is for integer number where the second is for fraction number. Now, let’s go ahead with these two rule.
Rules for integer number
- Determine the positional value of every digit of binary number. Multiply every digit by 2^{0} 2^{1} 2^{2} 2^{3} 2^{4} and so one from right to left.
- Add all these values which will be the equivalent decimal number.
Example : Conversion of 1011010_{2} to the equivalent decimal number
Solution :
= 1 × 2^{6} + 0 × 2^{5} + 1 × 2^{4} + 1 × 2^{3} + 0 × 2^{2} + 1 × 2^{1} + 0 × 2^{0}
= 64 + 0 + 16 + 8 + 0 + 2 + 0
= 90
We can apply another method to convert this number from binary to decimal. See the method bellow.
That means , we have got the decimal equivalence of this number is 90. Now, let’s see the rules for converting the fraction number.
Rules for fraction number
- Determine the positional value of every digit of binary fraction number multiplying every digit by 2^{-1} 2^{-2} 2^{-3} 2^{-4} and so one from left to right.
- Add all these values which will give the equivalent value of fractional binary number to decimal number.
Example : Convert 0.1101_{2} to its equivalent decimal number
Solution :
= 1 × 2^{-1} + 1 × 2^{-2} + 0 × 2^{-3} + 1 × 2^{-4}
= 0.5 + 0.25 + 0 + 0.0625
= 0.8125
So, the result after converting of this binary fraction number to decimal is 0.8125
See the following full example if you have successfully completed all the rules which we have given here in this article. This will clear all of your doubt about convert a number from binary to decimal.
Example : Conversion of 1111111.0101_{2} to equivalent decimal number.
Solution :
To convert this binary number to its equivalent decimal number we have to convert separately its integer part and fraction part. You can use our given rules for this purpose.
Lets see the conversion of its integer part first.
= 1 × 2^{6} + 1 × 2^{5} + 1 × 2^{4} + 1 × 2^{3} + 1 × 2^{2} + 1 × 2^{1} + 1 × 2^{0}
= 64 + 32 + 16 + 8 + 4 + 2 + 1
= 90
The another method for this conversion is as follows;
We will now convert its fraction part from binary to decimal number. Let’s see the figure bellow.
= 0 × 2^{-1} + 1 × 2^{-2} + 0 × 2^{-3} + 1 × 2^{-4}
= 0 + 0.25 + 0 + 0.0625
= 0.3125
So, the total decimal equivalence of this binary number will be (127.3125)_{10} . These rules are applicable for any other number to convert them as well. You can convert any binary number to its equivalent decimal number by this rules.
If you have any doubt still now, let us tell in the comment box bellow. We will try our best to help you about this. However, we are very font of haring from you.
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