Duodecimal (Base 12) — Definition, Formula & Examples
Duodecimal (base 12) is a number system that uses twelve digits instead of the ten digits we normally use. The digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A (representing 10), and B (representing 11).
The duodecimal system is a positional numeral system with radix 12, in which each digit position represents a successive power of 12. It requires twelve distinct symbols: the standard digits 0–9 plus two additional symbols (conventionally A and B) for the values ten and eleven.
How It Works
In base 12, each place value is a power of 12, just as each place value in base 10 is a power of 10. The rightmost digit represents , the next digit left represents , then , and so on. To find the base-10 value of a duodecimal number, multiply each digit by its place value and add the results. When a position needs to represent ten or eleven, you use the letters A or B instead of two-digit numbers.
Worked Example
Problem: Convert the duodecimal number 2A3₁₂ to base 10.
Identify place values: The digits from right to left are 3, A (which equals 10), and 2. Their place values are 12⁰, 12¹, and 12².
Multiply each digit by its place value: Multiply each digit's value by the corresponding power of 12.
Add the results: Sum all the products to get the base-10 equivalent.
Answer: 2A3₁₂ = 411 in base 10.
Why It Matters
Base 12 appears naturally in everyday life — there are 12 inches in a foot, 12 months in a year, and 12 hours on a clock face. Understanding duodecimal helps build intuition for how positional number systems work, which is essential when you study binary (base 2) and hexadecimal (base 16) in computer science.
Common Mistakes
Mistake: Treating A and B as the letters rather than as digits worth 10 and 11.
Correction: In base 12, A always stands for the value 10 and B for 11. When converting to base 10, substitute these numerical values before multiplying by place values.