1. What Is Base 7 Conversion?

Base 7 (septenary) is a numeral system with seven as its base. It uses digits 0-6. This calculator converts base 7 numbers to their decimal (base 10) equivalent using the formula: Decimal = Σ (Digit × 7^Position).

2. How The Calculator Works

The calculator uses the base conversion formula:

Where:

• Digit — A single digit from the base 7 number (0-6)
• Position — The position of the digit, starting from 0 at the rightmost digit
• 7 — The base value

Explanation: Each digit in the base 7 number is multiplied by 7 raised to the power of its position, with all results summed to get the decimal equivalent.

3. Base 7 Number System

Details: The base 7 system is a positional numeral system that uses seven distinct digits. Unlike the common decimal system (base 10), each digit's value depends on its position relative to the septenary point.

4. Using The Calculator

Tips: Enter a valid base 7 number using only digits 0-6. The calculator will automatically compute and display the decimal equivalent.

5. Frequently Asked Questions (FAQ)

Q1: What digits are valid in base 7?
A: Base 7 uses digits 0 through 6 only. Any digit 7 or higher is invalid in the base 7 system.

Q2: Can this calculator handle fractional base 7 numbers?
A: No, this calculator only converts whole base 7 numbers to decimal. It doesn't handle fractional values.

Q3: What is the largest base 7 number this calculator can handle?
A: The calculator can handle numbers up to PHP's integer limit, which is typically 2⁶³-1 on 64-bit systems.

Q4: Are negative base 7 numbers supported?
A: No, this calculator only converts positive base 7 numbers to their decimal equivalents.

Q5: How is positional value determined in the conversion?
A: Positions start at 0 from the rightmost digit. Each position to the left increases the exponent by 1.