Unlock the mysteries of digital representation with our Binary Fraction Converter. Easily convert decimal fractions to binary and binary fractions to decimal. Perfect for students, developers, and anyone working with numerical systems. Get instant, accurate results for your fractional conversions!
Formula:
The conversion of fractions between decimal and binary systems involves different processes:
Decimal to Binary Fraction:
To convert a decimal fraction (e.g., 0.625) to binary, multiply the fractional part by 2. The integer part of the result is the next binary digit. Repeat the process with the new fractional part until the fractional part becomes zero or the desired precision is reached.
Example for 0.625:
- 0.625 × 2 = 1.25 (Binary digit: 1)
- 0.25 × 2 = 0.5 (Binary digit: 0)
- 0.5 × 2 = 1.0 (Binary digit: 1)
Result: 0.1012
Binary to Decimal Fraction:
To convert a binary fraction (e.g., 0.101) to decimal, sum the products of each binary digit and powers of 2 (2-1, 2-2, etc.) corresponding to its position after the binary point.
Formula: \( \text{Decimal} = d_{-1} \cdot 2^{-1} + d_{-2} \cdot 2^{-2} + d_{-3} \cdot 2^{-3} + \dots \)
Where d represents the binary digit at that position.
Example for 0.1012:
- 1 × 2-1 = 1 × 0.5 = 0.5
- 0 × 2-2 = 0 × 0.25 = 0.0
- 1 × 2-3 = 1 × 0.125 = 0.125
Result: 0.5 + 0.0 + 0.125 = 0.625