Bidirectional conversion between tetravigesimal (base 24) and decimal with detailed steps
Input Value
Result
Conversion Result
Step-by-Step Derivation
Base Conversion Principle
Tetravigesimal → Decimal: Place value expansion (each digit × 24ⁿ) and sum
Decimal → Tetravigesimal: Repeated division by 24 (reverse remainders)
Digits: 0-9, A=10, B=11, ..., N=23
Tetravigesimal (base 24) is a positional numeral system with twenty-four as its base. It aligns naturally with the 24-hour clock and has excellent divisibility properties with factors 2, 3, 4, 6, 8, and 12.
⚠Tetravigesimal numbers use digits 0-9 and letters A-N (uppercase). A=10, B=11, C=12, D=13, E=14, F=15, G=16, H=17, I=18, J=19, K=20, L=21, M=22, N=23. Any digit beyond N is invalid in base 24.
What Is Tetravigesimal (Base 24)?
Tetravigesimal is a base-24 number system. It uses twenty-four digits: 0-9 and A-N, where A=10, B=11, C=12, D=13, E=14, F=15, G=16, H=17, I=18, J=19, K=20, L=21, M=22, and N=23. Base 24 has special relevance to timekeeping with 24 hours in a day.
Time Alignment
Base 24 naturally matches the 24-hour clock. Each hour of the day could be represented as a single digit in base 24, making time calculations intuitive.
Place Value Expansion
Tetravigesimal to decimal: multiply each digit by 24^position. For example, 1A8₂₄ = 1×576+10×24+8×1 = 824₁₀.
Repeated Division by 24
Decimal to tetravigesimal: repeatedly divide by 24, collect remainders, and read in reverse. Remainders 10-23 become A-N.
Excellent Divisibility
24 has divisors 1, 2, 3, 4, 6, 8, 12, and 24. This makes many common fractions terminate in base 24, simplifying calculations.
💡 Teaching Example: Convert tetravigesimal 1A8₂₄ to decimal. Place value expansion: 1×24²+10×24¹+8×24⁰ = 1×576+10×24+8×1 = 576+240+8 = 824₁₀. Conversely, 824₁₀: 824÷24=34 r8, 34÷24=1 rA, 1÷24=0 r1 → 1A8₂₄.
Tetravigesimal is a base-24 number system using digits 0-9 and A-N (representing 10-23). It is useful for timekeeping (24 hours in a day) and can be divided evenly by 2, 3, 4, 6, 8, and 12.
How do you convert tetravigesimal to decimal?▼
Place value expansion: multiply each tetravigesimal digit by its power of 24, then sum. For example, 1A8₂₄ = 1×24²+10×24¹+8×24⁰ = 1×576+10×24+8×1 = 576+240+8 = 824₁₀.
How do you convert decimal to tetravigesimal?▼
Repeated division by 24: repeatedly divide by 24, collecting remainders. Remainders 10-23 become A-N. Read remainders in reverse. For example, 824÷24=34 r8, 34÷24=1 rA, 1÷24=0 r1 → 1A8₂₄.
What practical uses does base 24 have?▼
Base 24 is particularly relevant for time (24-hour clock), with natural alignment to hours in a day. It also has good divisibility by factors of 24, making it useful for scheduling, measurements, and any system naturally divided into 24 parts.
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