1. What is a Binary Fraction?

A binary fraction is a representation of fractional numbers using the base-2 (binary) numeral system. It follows the same concept as decimal fractions but uses powers of 2 instead of powers of 10.

2. How Does the Calculator Work?

The calculator uses the binary fraction formula:

Where:

• \( b_1 \) — First bit after the binary point (value 0 or 1)
• \( b_2 \) — Second bit after the binary point (value 0 or 1)
• Each subsequent bit represents smaller negative powers of 2

Explanation: Each bit in the binary fraction represents a specific power of 2, starting from 2⁻¹ for the first bit after the point.

3. Importance of Binary Fractions

Details: Binary fractions are fundamental in computer science and digital systems where all data is represented in binary form. They are essential for representing fractional numbers in computers.

4. Using the Calculator

Tips: Select each bit (0 or 1) from the dropdown menus. The calculator will compute the equivalent decimal value of the binary fraction.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between binary and decimal fractions?
A: Binary fractions use base-2 (powers of 2) while decimal fractions use base-10 (powers of 10).

Q2: How accurate are binary fractions?
A: Binary fractions can represent many fractional values exactly, but some decimal fractions (like 0.1) cannot be represented exactly in binary.

Q3: Why are binary fractions important in computing?
A: Computers process all data in binary form, so binary fractions are essential for representing fractional numbers in digital systems.

Q4: Can this calculator handle more than 2 bits?
A: This basic version handles 2 bits, but the concept extends to any number of bits for more precise fractional representation.

Q5: How would 0.1011₂ convert to decimal?
A: It would be 1×2⁻¹ + 0×2⁻² + 1×2⁻³ + 1×2⁻⁴ = 0.5 + 0 + 0.125 + 0.0625 = 0.6875.