About

Quinary (Base-5) is a positional numeral system utilizing five digits: 0, 1, 2, 3, and 4. Unlike the ubiquitous Decimal (Base-10) or the machine-native Binary (Base-2), Quinary serves primarily as a pedagogical tool in number theory and historically in some linguistic counting systems (e.g., Gumatj). This tool not only performs the conversion but demonstrates the Euclidean division algorithm required to derive the result. For students, visualizing the modulus operations and remainders provides a deeper understanding of how value is assigned to position in any radix system.

Formulas

To convert from Decimal to Quinary, we repeatedly divide the integer by 5 and record the remainders:

q₀ = floor(n / 5)
r₀ = n mod 5

The Quinary representation is the sequence of remainders read from last to first.

To convert Quinary to Decimal:

n = k∑i=0 d_i × 5ⁱ

Reference Data

Decimal (10)	Quinary (5)	Binary (2)	Power of 5
1	1	1	5⁰ = 1
5	10	101	5¹ = 5
25	100	11001	5² = 25
125	1000	1111101	5³ = 125
625	10000	1001110001	5⁴ = 625

Frequently Asked Questions

Only digits 0, 1, 2, 3, and 4. If you see a "5" or higher, it is not a valid Quinary number.

While computers use binary, understanding arbitrary base conversion is critical for hashing algorithms, encoding schemes, and understanding floating-point precision errors. Base-5 is often used in coding interviews to test algorithmic thinking.

This tool currently handles integers. Fractional conversion requires multiplying the fractional part by the base (5) and taking the integer part iteratively.