1. What is Decimal to Binary Conversion?

Decimal to binary conversion is the process of converting fractional decimal numbers (numbers less than 1) to their binary (base-2) representation. This is particularly important in computer science and digital systems.

2. How Does the Calculator Work?

The calculator uses the multiplication-by-2 method:

Example for 0.270:

• 0.270 × 2 = 0.540 → 0
• 0.540 × 2 = 1.080 → 1
• 0.080 × 2 = 0.160 → 0
• 0.160 × 2 = 0.320 → 0
• 0.320 × 2 = 0.640 → 0
• Result: 0.01000...

3. Importance of Binary Conversion

Details: Understanding fractional binary representation is crucial for working with floating-point numbers in computers, digital signal processing, and computer graphics.

4. Using the Calculator

Tips: Enter a decimal fraction between 0 and 0.999. The calculator will show the binary equivalent with up to 10 bits of precision.

5. Frequently Asked Questions (FAQ)

Q1: Why does some decimal fractions have infinite binary representation?
A: Just like 1/3 = 0.333... in decimal, some fractions have repeating patterns in binary that may be infinite.

Q2: How accurate is this conversion?
A: The calculator shows up to 10 bits of precision. More bits can be calculated by continuing the process.

Q3: What's the maximum decimal value I can convert?
A: This calculator handles values from 0 up to (but not including) 1.000.

Q4: Can I convert whole numbers with this?
A: This calculator is designed for fractional parts only. Whole numbers require a different conversion method.

Q5: Why is binary important in computing?
A: Computers use binary because it's easy to represent with two physical states (on/off, high/low voltage).