1. What is Fractional Binary?

Fractional binary represents numbers less than 1 in binary form, where each digit represents a negative power of 2 (1/2, 1/4, 1/8, etc.). It's the binary equivalent of decimal fractions.

2. How Does the Conversion Work?

The conversion uses the formula:

Where:

• \( b_1 \) — First binary digit after the point (1/2 place)
• \( b_2 \) — Second binary digit (1/4 place)
• \( b_3 \) — Third binary digit (1/8 place)
• And so on for each subsequent digit

Example: Binary "101" converts to:
1×(1/2) + 0×(1/4) + 1×(1/8) = 0.5 + 0 + 0.125 = 0.625

3. Importance of Binary Conversion

Details: Understanding binary fractions is essential in computer science, digital systems, and floating-point number representation. It's fundamental for accurate numerical computations in computing.

4. Using the Calculator

Tips: Enter a sequence of 0s and 1s representing the fractional binary number. The calculator will convert it to its decimal equivalent.

5. Frequently Asked Questions (FAQ)

Q1: What's the maximum precision I can get?
A: The precision depends on the number of bits you enter. Each additional bit doubles the precision.

Q2: How do I represent 0.1 in binary?
A: 0.1 in decimal is a repeating binary fraction: 0.0001100110011...

Q3: Why can't some decimal fractions be represented exactly in binary?
A: Just like 1/3 can't be represented exactly in decimal (0.333...), some fractions don't have exact binary representations.

Q4: What's the relationship between bits and decimal places?
A: Each binary digit provides about 0.3 decimal digits of precision (log₁₀2 ≈ 0.3010).

Q5: How is this used in computers?
A: Computers use binary fractions to represent all non-integer numbers, with floating-point being the most common representation.