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Base-15 Converter

Convert numbers into and out of pentadecimal (base 15) using digits 0-9 and A through E. Designed for software developers, electrical engineers, students, and computer architecture researchers requiring deterministic client-side accuracy.

Engine: Client-Side Verified (0ms Latency)

Allowed digits: 0-9 and A through E (10-14).

Calculated Output

Primary Representation
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Step-by-Step Mathematical Proof

Active Derivation
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Concept

What Is Base-15 Converter?

Pentadecimal (base 15) uses fifteen symbols: 0 through 9 and letters A, B, C, D, E.

Methodology

How Does It Work?

Expands digits with powers of 15 (1, 15, 225, 3375).

Formula & Rules

Mathematical Algorithm

N_{10} = \sum d_i 15^i
Worked Problem

Step-by-Step Example

Convert 1E4_{15} to decimal: (1 × 225) + (14 × 15) + (4 × 1) = 225 + 210 + 4 = 439_{10}.

Important Rules & Edge Cases

  • A=10, B=11, C=12, D=13, E=14.

Practical Applications in Engineering

  • Mathematical number theory.

Common Mistakes to Avoid

  • Caution: Entering F (F is 15, which is invalid in base 15).
FAQ

Frequently Asked Questions

Is F allowed in base 15?

No, base 15 only uses symbols up to E (14). F is value 15 and wraps to 10 in base 15.