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\textbf{CSE248 Fall 2023 Exercise 1: Floorplanning Topologies} \\
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\noindent{\textbf{Due Time : 11:50pm, Wednesday 10/11, 2023}}
\textbf{Submit to Gradescope \\ Gradescope: \url{https://gradescope.com/} }\\
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A. Read IEEE IRDS International Roadmap Executive Summary, and write a summary ($<$30 words) of the potential progress of Moore's Law in the next five years.\\
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B. Read slide Chapter 1 from the book of LT Wang to get an overview of the VLSI design process. Try to write your prediction ($<$30 words) on what process can facilitate the progress of Moore's law in the next five years.\\
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C. In this exercise, we investigate floorplanning topologies using the On-Line Encyclopedia of Integer Sequences (OEIS) for 2D and 3D layouts.
For 2D layout, we are given a 2D rectangular box. We divide the box into $n$ rectangles with no dead-space.
For 3D layout, the box is a three-dimensional rectangular
cube.
The dimensions of the rectangles (cubes) are flexible but strictly positive.
Each division configuration is mapped to a topology.
Two topologies are viewed as identical if we can adjust the lengths
of the rectangles (cubes) and the bounding box to make the configuration (plot) the same.\\
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1. Enumerate the number of topologies for 2D floorplanning as a function $f_2(n)$ of rectangles $n$. \\
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2. Validate that the sequence $f_2(n)$ is equal to the sequence number
of twin binary trees.\\
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3. Assume that the floorplan is symmetric by rotation. Repeat item 1. Check the OEIS result.\\
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4. Assume that the floorplan is symmetric by flipping. Repeat item 1. Check the OEIS result.\\
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5. Assume that the floorplan is symmetric by rotation and/or flipping.
Repeat item 1. Check the OEIS results.\\
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6. Enumerate the number of topologies for 3D floorplanning as a function $f_3(n)$ of rectangles $n$. Check the OEIS result.\\
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7. Assume that the floorplan is symmetric by rotation. Repeat item 6. Check the OEIS result.\\
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8. Assume that the floorplan is symmetric by flipping. Repeat item 6. Check the OEIS result.\\
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9. Assume that the floorplan is symmetric by rotation and/or flipping.
Repeat item 6. Check the OEIS results.\\
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