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Base16 To Base12 Converter

Convert hexadecimal (base16) to duodecimal/dozenal (base12) with detailed step-by-step derivation

Hexadecimal Number

Hex To Base12 Conversion Principle

① Hex → Decimal: expand by 16^n place values
② Decimal → Base12: divide by 12, collect remainders
③ Remainders: 0-9, A=10, B=11

Base12 (dozenal) is a fascinating alternative base with more divisors than decimal, making many fractions terminate neatly.

This converter uses A=10 and B=11 for base12. Some systems use X=10 and E=11 instead.

What Is Base12 (Dozenal)?

Base12 (dozenal/duodecimal) is a positional numeral system with base 12, praised for its mathematical properties due to 12 having many divisors.

Divisors of 12

1, 2, 3, 4, 6, 12. More than 10 (which has 1,2,5,10). Great for fractions!

Terminating Fractions

1/2=0.6, 1/3=0.4, 1/4=0.3, 1/6=0.2, 1/12=0.1 all terminate in base12!

Digits Used

0-9 for 0-9, A for 10, B for 11. Total of 12 distinct digits needed.

Historical Use

12 inches in foot, 12 months, 2×12 hours, 12 dozen in gross. Dozenal has cultural roots!

💡 Teaching Example: Hex FF = 255 decimal. 255 ÷ 12 = 21 rem 3, 21 ÷ 12 = 1 rem 9, 1 ÷ 12 = 0 rem 1. Read remainders: 1 9 3 → 193 base12.

Applications

Mathematics Number Theory Recreational Math Education Dozenal Advocacy

Frequently Asked Questions

What is base12 (duodecimal/dozenal)?
Base12 is a positional numeral system with twelve as its base. It uses digits 0-9 plus two additional symbols, typically A and B (or X and E) for ten and eleven.
Why is base12 interesting?
12 has more divisors (1,2,3,4,6,12) than 10 (1,2,5,10), making fractions simpler. 1/3 = 0.4, 1/4 = 0.3, 1/2 = 0.6 in base12 instead of repeating decimals!
How to convert hex to base12?
First convert hexadecimal to decimal by expanding place values, then convert decimal to base12 using repeated division by 12, collecting remainders.
What digits are used in base12?
0,1,2,3,4,5,6,7,8,9 for values 0-9, plus A (or X) for 10, and B (or E) for 11. This converter uses A=10, B=11.

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