Mixed radix ($n={\sum }_i{x}_i{\prod }_{j<i}{b}_j$)

A positional representation in which each digit has its own positive integer base. Least-significant-first digits satisfy $0\le x_i<b_i$, and digit $i$ has weight ${\prod }_{j<i}{b}_j$. For $k$ positions, assume $0\le n<{\prod }_{i=0}^{k-1}{b}_i$. Repeated Euclidean division by the successive bases converts that integer to digits; a backwards version of Horner's method converts the digits back.