1. What is Base Conversion?

Base conversion is the process of changing a number from one base (or radix) to another. In digital systems, 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 formula:

Where:

• \( Number \) — The original number (base 10)
• \( Base \) — The target base (2-36)
• \( Position \) — The digit position (1 being the least significant digit)
• \( \lfloor \rfloor \) — Floor function (round down)
• \( \mod \) — Modulo operation (remainder after division)

Explanation: The formula calculates the value of a specific digit in a number when represented in a different base.

3. Importance of Base Conversion

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

4. Using the Calculator

Tips: Enter a non-negative integer for the number, a base between 2 and 36, and a positive integer for the position. The calculator will show the digit at that position when the number is represented in the specified base.

5. Frequently Asked Questions (FAQ)

Q1: What is the range of bases supported?
A: The calculator supports bases from 2 to 36. Base 36 uses digits 0-9 and letters A-Z.

Q2: How is position counted?
A: Position 1 is the least significant digit (rightmost), position 2 is the next digit to the left, and so on.

Q3: What if the position is larger than needed?
A: The calculator will return 0 for positions beyond what's needed to represent the number in the given base.

Q4: Can I convert fractional numbers?
A: This calculator only works with integer numbers. For fractional numbers, a different approach is needed.

Q5: What are common uses of base conversion?
A: Common uses include computer programming (binary/hex), networking (IP addresses), and data encoding (Base64).