Bidirectional conversion between duodecimal (base 12) and decimal with detailed steps
Input Value
Result
Conversion Result
Step-by-Step Derivation
Base Conversion Principle
Duodecimal → Decimal: Place value expansion (each digit × 12ⁿ) and sum
Decimal → Duodecimal: Repeated division by 12 (reverse remainders)
Digits: 0-9, A=10, B=11
Duodecimal (base 12) is a positional numeral system with twelve as its base. It is convenient for divisibility by 2, 3, 4, and 6, making fractions simpler.
⚠Duodecimal numbers use digits 0-9 and letters A-B (uppercase). A=10, B=11. Any digit beyond B is invalid in base 12.
What Is Duodecimal (Base 12)?
Duodecimal (also called dozenal) is a base-12 number system. It uses twelve digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, and B, where A=10 and B=11. Base 12 has more divisors than base 10, making it more practical for many calculations.
Divisibility Advantage
12 is divisible by 1, 2, 3, 4, 6, and 12. This makes fractions like 1/2, 1/3, 1/4, and 1/6 terminating in base 12, whereas 1/3 is repeating in base 10.
Place Value Expansion
Duodecimal to decimal: multiply each digit by 12^position. For example, 1A8₁₂ = 1×144+10×12+8×1 = 272₁₀.
Repeated Division by 12
Decimal to duodecimal: repeatedly divide by 12, collect remainders, and read in reverse. Remainders 10→A, 11→B.
Practical Applications
Base 12 appears in timekeeping (12 months, 12 hours), measurements (12 inches in a foot), and traditional counting systems (dozen, gross).
💡 Teaching Example: Convert duodecimal 1A8₁₂ to decimal. Place value expansion: 1×12²+10×12¹+8×12⁰ = 1×144+10×12+8×1 = 144+120+8 = 272₁₀. Conversely, 272₁₀: 272÷12=22 r8, 22÷12=1 rA, 1÷12=0 r1 → 1A8₁₂.
Duodecimal (or dozenal) is a base-12 number system using digits 0-9 and A-B (representing 10 and 11). It is convenient for timekeeping (12 months, 12 hours), measurements (12 inches), and fractions (1/2, 1/3, 1/4, 1/6 are terminating in base 12).
How do you convert duodecimal to decimal?▼
Place value expansion: multiply each duodecimal digit by its power of 12, then sum. For example, 1A8₁₂ = 1×12²+10×12¹+8×12⁰ = 1×144+10×12+8×1 = 144+120+8 = 272₁₀.
How do you convert decimal to duodecimal?▼
Repeated division by 12: repeatedly divide by 12, collecting remainders. Remainders 10 and 11 become A and B. Read remainders in reverse. For example, 272÷12=22 r8, 22÷12=1 rA, 1÷12=0 r1 → 1A8₁₂.
Why is base 12 considered better than base 10?▼
Base 12 has more divisors (1, 2, 3, 4, 6, 12) than base 10 (1, 2, 5, 10), making fractions simpler. 1/3 is 0.4 in base 12 vs. 0.333... in base 10. Dozenalists advocate base 12 for practical calculations.
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