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Base-3 Converter

Convert numbers into and out of ternary (base 3) using digits 0, 1, and 2 with powers of 3. Designed for software developers, electrical engineers, students, and computer architecture researchers requiring deterministic client-side accuracy.

Engine: Client-Side Verified (0ms Latency)

Enter valid base-3 digits (0, 1, 2).

Calculated Output

Primary Representation
Calculating...

Step-by-Step Mathematical Proof

Active Derivation
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Concept

What Is Base-3 Converter?

Ternary (base 3) is a numeral system that uses three symbols: 0, 1, and 2. Each column represents an increasing power of three (1, 3, 9, 27, 81, 243).

Methodology

How Does It Work?

Converts base-3 strings by multiplying each digit by 3^i and summing the terms.

Formula & Rules

Mathematical Algorithm

N_{10} = \sum_{i=0}^{n-1} d_i 3^i \quad (d_i \in \{0, 1, 2\})
Worked Problem

Step-by-Step Example

Convert 2102_3 to decimal: (2 × 3^3) + (1 × 3^2) + (0 × 3^1) + (2 × 3^0) = 54 + 9 + 0 + 2 = 65_{10}.

Important Rules & Edge Cases

  • Only digits 0, 1, and 2 are allowed.
  • Powers of 3 triple at each step to the left.

Practical Applications in Engineering

  • Ternary optical computing and three-valued logic circuits.
  • Ternary tree data structures in computer science.

Common Mistakes to Avoid

  • Caution: Entering digits 3 or higher.
FAQ

Frequently Asked Questions

What is balanced ternary?

Balanced ternary is a variation using digits -1, 0, and +1, allowing negative numbers without a sign bit.