  An m-extracting procedure produces unbiased random bits from a loaded dice
with m faces. A binarization takes inputs from an m-faced dice and produce bit
sequences to be fed into a (binary) extracting procedure to obtain random bits.
Thus, binary extracting procedures give rise to an m-extracting procedure via a
binarization. An entropy- preserving binarization is to be called complete, and
such a procedure has been proposed by Zhou and Bruck. We show that there exist
complete binarizations in abundance as naturally arising from binary trees with
m leaves. The well-known leaf entropy theorem and a closely related structure
lemma play important roles in the arguments.
