Convert between mixed radix (variable base per digit) and decimal
Bases (right to left, separated by spaces)
Digits (left to right, separated by spaces or colons)
Result
Conversion Result
Step-by-Step Derivation
Conversion Principle
Mixed Radix → Decimal: digit × weight and sum
Weights: right to left, cumulative product
Decimal → Mixed Radix: repeated division with remainders
Mixed radix notation uses different bases for different digit positions. Each digit position has its own base. Examples: time, feet+inches, old currency, degrees/minutes/seconds.
⚠Specify bases from RIGHT TO LEFT. For time HH:MM:SS, bases are 24 60 60. Digits must be < their base, from 0 to base-1.
What Is Mixed Radix Notation?
Mixed radix notation uses different bases for different digit positions. The rightmost digit has its own base, the next digit to the left has another base, and so on.
Real-World Examples
Time (24, 60, 60), feet+inches (..., 3, 12), degrees/minutes/seconds (..., 60, 60) are common mixed radix systems.
Weight Calculation
Weights: rightmost weight = 1, next = 1 × rightmost base, next = previous × next base, etc.
Repeated Division
Decimal to mixed radix: start with rightmost base, divide, remainder is digit, quotient continues left.
Factoradic System
Factorial number system: bases 2,3,4,..., digits 0,0-1,0-2,... Used in permutations.
Mixed radix notation uses different bases for different digit positions. For example, time (hours, minutes, seconds) is mixed radix: seconds base 60, minutes base 60, hours base 24.
How do you convert mixed radix to decimal?▼
Compute weights: rightmost digit weight = 1, next weight = previous weight × rightmost base, etc. Then: each digit × weight, sum all. For time: 1:30:45 = 1×3600+30×60+45 = 5445.
How do you convert decimal to mixed radix?▼
Repeated division: start with rightmost base, divide, remainder is digit, quotient continues with next base to the left. Stop when quotient 0.
What are examples of mixed radix in real life?▼
Time (HH:MM:SS), feet+inches, days+hours+minutes, old currency (pounds/shillings/pence), degrees/minutes/seconds, factoradic/factorial number system.
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