Digit readers: the real place

A reader that sees a number through its digits, a few at a time, and must act before the digits end. How many digits it reads beyond the ones it writes is its lookahead. These pages cover numerations read digit by digit: positional bases read from either end; continued fractions; the Ostrowski numeration, which writes each integer as a sum of multiples of the denominators of an irrational's continued-fraction convergents, read on the circle, and the maps linear in its digits; redundant outputs; and signed-digit streams. Each page says how much lookahead its maps cost (on continued fractions, a lag in quotients and a deficit in scale), or that no lookahead reads them, and the first page asks which place pays for a Lipschitz map that no lookahead reads.

• READING — what a digit-by-digit reader computes
• RATES — what a reader pays where a digit's scale varies
• OSTROWSKI — the circle a trailing numeration reads
• FLUSH — what a redundant reader of the circle computes
• SHIFTS — a digit shift is a change of numeration
• DUAL — the leading end of base b, read against the trailing end
• REDUNDANT — what a signed-digit reader of integers computes