12:23 mixed radix 🧮

Conversion between mixed radix representations

10 = 16 = 10:2:3 = 10:3:2 = 6 = 2 = 3
 
 

First /6 combinations …2:…3 with : figures

Some explanations

Something as this 47528 is a representation in radix (base) 8 of the number 2×1 + 5×8 + 7×82 + 4×83 = 2538 (represented in radix 10).

Mixed radices as 3610:2045:023 is a representation of the number 2×1 + 0×3 + (4×1 + 0×5 + 2×52)×32 + (6×1 + 3×10)×32×53 = 40988 (in radix 10).

Each radix must be a number between 2 and 36. Figures in radix 36 are 036, 136, 236, …, 936, a36, b36, c36, …, z36 . You can also use upper cases.

Set a number in one input box (in the silver frame above) in the corresponding radix and all representations will be updated.
  • … represent the number, always in radix 10.
  • …16 represent the number in a given radix.
  • …10:…2:…3 represent the number split in 3 parts: remain:second part:first part
  • …10:…3:…2 represent the number split in 3 parts, with first and second parts swapped.
  • …6 represent the number in a radix computed from a combination of radices used by first and second parts. If one of these radices is divisible by the other then get the product of them, else get the least common multiple of them. In both cases with a maximum of 36.
  • …2 represent the number in radix used by second part.
  • …3 represent the number in radix used by first part.
  • In the largest input box you can enter general mixed radix representation. (All not valid characters are ignored or deleted, then all not valid parts are also ignored or deleted.) For example 2p_30:42_6:41:44_5:0101_2 is a representation 2p30:426:4110:445:01012 of 123456789 (in radix 10).

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