Mixed-Radix Computations
MixedRadix allows working with numerical systems in which different digits of a number correspond to different bases.
These are names of several units of soldiers in a Roman army.
In[1]:=
![Click for copyable input](assets.en/mixed-radix-computations/In_20.png)
units = {"legion", "cohort", "century", "contubernia", "soldier"};
A legion was made of 10 cohorts, a cohort of 6 centuries, a century of 10 contuberniae, and a contubernia of 8 soldiers.
In[2]:=
![Click for copyable input](assets.en/mixed-radix-computations/In_21.png)
bases = MixedRadix[{10, 6, 10, 8}];
Number of soldiers in a contubernia, using this number system.
In[3]:=
![Click for copyable input](assets.en/mixed-radix-computations/In_22.png)
FromDigits[{1, 0}, bases]
Out[3]=
![](assets.en/mixed-radix-computations/O_19.png)
Number of soldiers in a century.
In[4]:=
![Click for copyable input](assets.en/mixed-radix-computations/In_23.png)
FromDigits[{1, 0, 0}, bases]
Out[4]=
![](assets.en/mixed-radix-computations/O_20.png)
Number of soldiers in a cohort.
In[5]:=
![Click for copyable input](assets.en/mixed-radix-computations/In_24.png)
FromDigits[{1, 0, 0, 0}, bases]
Out[5]=
![](assets.en/mixed-radix-computations/O_21.png)
Number of soldiers in a legion.
In[6]:=
![Click for copyable input](assets.en/mixed-radix-computations/In_25.png)
FromDigits[{1, 0, 0, 0, 0}, bases]
Out[6]=
![](assets.en/mixed-radix-computations/O_22.png)
Vice versa, decompose the number of soldiers in these tactical units.
In[7]:=
![Click for copyable input](assets.en/mixed-radix-computations/In_26.png)
IntegerDigits[16894, bases]
Out[7]=
![](assets.en/mixed-radix-computations/O_23.png)
In[8]:=
![Click for copyable input](assets.en/mixed-radix-computations/In_27.png)
IntegerDigits[16894, bases];
Thread[units -> %]
Out[8]=
![](assets.en/mixed-radix-computations/O_24.png)