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]:=

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]:=

bases = MixedRadix[{10, 6, 10, 8}];

Number of soldiers in a contubernia, using this number system.

In[3]:=

FromDigits[{1, 0}, bases]

Out[3]=

Number of soldiers in a century.

In[4]:=

FromDigits[{1, 0, 0}, bases]

Out[4]=

Number of soldiers in a cohort.

In[5]:=

FromDigits[{1, 0, 0, 0}, bases]

Out[5]=

Number of soldiers in a legion.

In[6]:=

FromDigits[{1, 0, 0, 0, 0}, bases]

Out[6]=

Vice versa, decompose the number of soldiers in these tactical units.

In[7]:=

IntegerDigits[16894, bases]

Out[7]=

In[8]:=

IntegerDigits[16894, bases]; Thread[units -> %]

Out[8]=