1. What is Decimal Fraction to Binary Conversion?

Decimal fraction to binary conversion is the process of converting fractional decimal numbers (values between 0 and 1) to their binary representation. This is essential in computer science and digital systems where fractional values need to be represented in binary form.

2. How Does the Conversion Work?

The conversion uses the following method:

Example: Convert 0.625 to binary

• 0.625 × 2 = 1.25 → record 1, keep 0.25
• 0.25 × 2 = 0.5 → record 0, keep 0.5
• 0.5 × 2 = 1.0 → record 1, keep 0.0
• Result: 0.101

3. Importance of Binary Conversion

Details: Binary representation of fractions is crucial in computer systems for floating-point arithmetic, digital signal processing, and scientific computing where precise fractional values are needed.

4. Using the Calculator

Tips: Enter a decimal fraction between 0 (inclusive) and 1 (exclusive). Set the desired precision (number of bits). The calculator will show the binary representation with a leading "0.".

5. Frequently Asked Questions (FAQ)

Q1: Why does some fractions produce infinite binary representations?
A: Similar to how 1/3 = 0.333... in decimal, some fractions that terminate in decimal may repeat infinitely in binary (e.g., 0.1 in decimal is 0.0001100110011... in binary).

Q2: What's the maximum precision I should use?
A: For most practical purposes, 8-16 bits is sufficient. The calculator limits to 32 bits which is common in single-precision floating point.

Q3: How accurate is the conversion?
A: The accuracy depends on the precision (number of bits) specified. More bits mean more accurate representation but may include more trailing zeros.

Q4: Can I convert binary fractions back to decimal?
A: Yes, by summing each bit multiplied by 2^-position (e.g., 0.101 = 1×2^-1 + 0×2^-2 + 1×2^-3 = 0.625).

Q5: What about negative fractions?
A: This calculator handles positive fractions only. For negative numbers, convert the absolute value first, then apply the sign.