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Step By Step Binary Fractional To Decimal Converter

Convert Fractional Binary to Decimal number

Steps to convert binary fractional number to decimal

Binary number system is the fundamentals for the internal storage and processing of data used by electronic computers. In daily life we use decimal number system that has base or radix 10. It means in this number system there are TEN digits from 0 to 9. But storage data is managed by computers in the form of binary digits. To understand how these digits are formed by electronic machines. Here we provide a step by step conversion of binary numbers to the decimal numbers.

For conversion of binary to decimal here we have a series of steps that followed to find the equivalent decimal number.

  1. First of all we have to provide a valid binary number.
  2. In second step we will write the weights or powers of each digit in particular number.
  3. Power/weight is obtained from the position of each digit starting from right to left of integer part.
  4. The first digit of integer part from right hand side will have weight 0
  5. Subsequently the weight of digits will be incremented by 1 to left hand side.
  6. Each position of the digit is raised to the power of given number system base.
  7. In this example this will raise to the power of 2. (As of given number system is binary).
  8. The equivalent decimal of binary 0 and 1 is same as 0 and 1.


binary to decimal conversion
How to convert fractional Binary number into Decimal

How to convert fractional Binary into Decimal

for conversion of binary numbers having fractional part we assign negative weights to the fractional part digits and the calculate the required number. Each digit has negative power from its base. It's mean that the first digit will have power -1 second will have -2 and so Nth digit will have power -n.

Binary to Decimal Conversion Examples

The basic to advance questions for practice conversion of binary to decimal are as.

These examples will help to learn more about How to convert binary to decimal

  • Convert 10011.11100 to decimal number system.
  • How to convert 111011.10101 into decimal number?
  • What will be the decimal equivalent of binary number 11.010101?
  • Write down stepwise procedure for finding decimal of 110100.11.
  • Calculate decimal of binary number 11010.11110
  • Find the decimal number of given binary number 10101.010
  • Calculate decimal equivalent of 11111

Binary to Decimal Formula

Here is mathematical formula that can be used to calculate equivalent decimal number. This formula represent calculation mathematically. Both integer and fractional part will be calculated independently.

Decimal Number (Integer Part) = i=1 n n th bit * 2 n-1

Fractional Part

Decimal Number (Fractional Part) = i=1 n n th bit * 2 1/n