1. What is Decimal to Binary Conversion?

Decimal to binary conversion is the process of transforming a base-10 (decimal) number into its equivalent base-2 (binary) representation. Binary numbers consist only of 0s and 1s and are fundamental in computer science and digital electronics.

2. How Does the Calculator Work?

The calculator uses PHP's built-in decbin() function to perform the conversion:

Where:

• \( decimal \) — A non-negative integer in base-10
• \( binary \) — The equivalent binary string representation

Explanation: The conversion involves repeatedly dividing the decimal number by 2 and recording the remainders.

3. Importance of Binary Conversion

Details: Binary representation is essential in computing as it's the fundamental language of computers. Understanding binary conversion helps in programming, digital circuit design, and computer architecture.

4. Using the Calculator

Tips: Enter any non-negative integer (0 or greater) and click "Convert" to see its binary equivalent. The calculator handles numbers up to 64-bit integers.

5. Frequently Asked Questions (FAQ)

Q1: What is the maximum number this calculator can convert?
A: On 64-bit systems, it can handle numbers up to 2^63-1 (9,223,372,036,854,775,807).

Q2: How are negative numbers handled?
A: This calculator only accepts non-negative integers. Negative numbers would require two's complement representation.

Q3: What about fractional/decimal numbers?
A: This calculator converts only integer parts. For fractional numbers, a different method involving multiplication by 2 would be needed.

Q4: Why is binary important in computing?
A: Binary is used because computer hardware uses transistors that have only two states (on/off), making base-2 the most natural representation.

Q5: How can I convert binary back to decimal?
A: You can use the bindec() function in PHP or sum the powers of 2 for each '1' in the binary string.