They had number words for 1 to 10, and then for 10 multiplied by several powers of 2. The word takau (which Bender and Beller denote as K) means 10; paua (P) means 20; tataua (T) is 40; and varu (V) stands for 80. In this notation, for example, 70 is TPK and 57 is TK7.
To my non-mathematically trained ears this doesn't sound like a binary system at all, but more like the highly inefficient Roman system. Am I missing something?
It's not at all like a Roman system except for the use of letters. You can separate a natural number n into two parts:
n = 10 * q + k, where 0 <= k < 10 and q in N
q = 1 * K? + 2 * P? + 4 * T? + 8 * V?
where K?, P?, T?, and V? are 0 if the letter is absent and 1 if the letter is present. n is a textbook base 10 decomposition, and q is a sparse binary representation.
Roman numerals didn't use quotient/remainder or a geometric expansion at all. Since the 'base' seems to switch between 2 and 5 each time, you can't cleanly decompose it. And there was that weird subtractive case.
To my non-mathematically trained ears this doesn't sound like a binary system at all, but more like the highly inefficient Roman system. Am I missing something?