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\textbf{CS 141} \\ Advanced Topics in Algorithms \\ Spring 2004 \\
Problem Set 7a \\ Due Wednesday, March 3 in class
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  \item \textbf{[30 Points]  Tally Circuits!} A tally circuit has $n$
binary inputs and 
  $\lceil \log_2 (n+1) \rceil$ outputs.  Interpreted as a binary number,
  the outputs give the number of 1's in the input.  For example,
  if the input is $1101111$ then the output is $110$, indicating that
there are six 1's in the input.  Describe a tally circuit with
depth $O(\log n)$ and size $O(n)$.  Show your analyses.
(Careful here -- achieving the depth and size requirements will require
some care.)

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