1. What is Base Conversion?

Base conversion is the process of changing a number from one base (radix) to another. Common bases include binary (base 2), octal (base 8), decimal (base 10), and hexadecimal (base 16).

2. How Does the Calculator Work?

The calculator uses the base conversion formula:

Where:

• \( \text{digit\_i} \) — Digits in original base (unitless)
• \( \text{base} \) — Radix (unitless)
• \( \text{i} \) — Position (unitless)

Explanation: The equation converts the number to base 10 first by summing each digit multiplied by the base raised to its position, then converts from base 10 to the target base.

3. Importance of Base Conversion

Details: Base conversion is essential in computer science, digital electronics, and mathematics. Different bases are used for different purposes - binary for computer operations, hexadecimal for memory addressing, etc.

4. Using the Calculator

Tips: Enter the number to convert, its original base (2-36), and the target base (2-36). The calculator supports bases from 2 to 36 (digits 0-9 and letters A-Z).

5. Frequently Asked Questions (FAQ)

Q1: What is the maximum base supported?
A: The calculator supports bases from 2 to 36 (using digits 0-9 and letters A-Z).

Q2: How are letters handled in bases > 10?
A: Letters A-Z represent values 10-35 (case insensitive).

Q3: Can I convert fractional numbers?
A: This calculator currently only handles integer conversions.

Q4: What happens if I enter invalid digits for a base?
A: The conversion will fail. Ensure all digits are valid for the given base.

Q5: Why is base conversion important in computing?
A: Computers use binary (base 2) internally, but hexadecimal (base 16) is often used for more compact representation of binary data.