89 lines
2.0 KiB
TeX
Executable File
89 lines
2.0 KiB
TeX
Executable File
\documentclass[
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solutions,
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hidewarning,
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singlenumbering,
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nopagenumber
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]{../../resources/ormc_handout}
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\usepackage{../../resources/macros}
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\usepackage{tikz}
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\title{The Sysadmin's Warm-Up}
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\uptitler{\smallurl{}}
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\subtitle{Prepared by Mark on \today}
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\begin{document}
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\maketitle
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Most of you have seen a hard drive. Many have touched one, and a lucky few have poked around inside one. These devices have two interesting properties:
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\begin{enumerate}
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\item They hold valuable data
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\item They eventually fail
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\end{enumerate}
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Needless to say, this is a problem. \par
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We need to design a system that allows hard drives to fail without data loss.
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\definition{}
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You can think of a hard drive as a long string of bits. \par
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Assume all hard drives can store 1 TiB of data.
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\begin{center}
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\begin{tikzpicture}
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\node[above] at (1/2, 0) {Drive A};
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\draw (0cm, 0cm) -- (0cm, -3cm);
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\draw (1cm, 0cm) -- (1cm, -3cm);
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\foreach \i in {0,...,-6} {
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\draw (0cm,\i cm / 2) -- (1cm ,\i cm / 2);
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}
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\node at (1/2, - 1 / 4) {1};
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\node at (1/2, - 3 / 4) {1};
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\node at (1/2, - 5 / 4) {0};
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\node at (1/2, - 7 / 4) {...};
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\node at (1/2, - 9 / 4) {1};
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\node at (1/2, -11 / 4) {0};
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\node[above] at (5/2, 0) {Drive B};
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\draw (2cm, 0cm) -- (2cm, -3cm);
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\draw (3cm, 0cm) -- (3cm, -3cm);
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\foreach \i in {0,...,-6} {
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\draw (2cm,\i cm / 2) -- (3cm ,\i cm / 2);
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}
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\node at (5/2, - 1 / 4) {0};
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\node at (5/2, - 3 / 4) {1};
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\node at (5/2, - 5 / 4) {0};
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\node at (5/2, - 7 / 4) {...};
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\node at (5/2, - 9 / 4) {0};
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\node at (5/2, -11 / 4) {1};
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\end{tikzpicture}
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\end{center}
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\problem{}
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Suppose we have two hard drives. How can we arrange our data so that...
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\begin{enumerate}
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\item We get 1 TiB of usable storage
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\item We lose no data if any one drive fails
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\end{enumerate}
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\vfill
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\problem{}
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Suppose we have three hard drives. How can we arrange our data so that...
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\begin{enumerate}
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\item We get 2 TiB of usable storage
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\item We lose no data if any one drive fails
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\end{enumerate}
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\vfill
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\end{document} |