| Title: | Mathematics at DEC |
| Moderator: | RUSURE::EDP |
| Created: | Mon Feb 03 1986 |
| Last Modified: | Fri Jun 06 1997 |
| Last Successful Update: | Fri Jun 06 1997 |
| Number of topics: | 2083 |
| Total number of notes: | 14613 |
Proposed by Frederick Stern, San Jose State University, San Jose,
California.
Let a < b be positive integers, and let
2^a-1
t = -----.
2^b-1
What is the relative frequency of 1's (versus 0's) in the binary
expansion of t?
| T.R | Title | User | Personal Name | Date | Lines |
|---|---|---|---|---|---|
| 1979.1 | a/(b-a) | FLOYD::YODER | MFY | Mon Jun 19 1995 09:21 | 7 |
The binary expansion has period b, because b b a 2 t = (2 - 1)t + t = (2 - 1) + t so the expansion is an infinite repetition of (b-a) zeros followed by a ones. Thus the answer is a/(b-a). | |||||