%ex1.1

\begin{enumerate}[label=(\alph*)]
	\item
	Assumed sector size: 4kB \\
	Average Rotational Delay \\
	$ AvgRotDelay = 0.5 * rotations * rotationalSpeed $ \\
	$ 1000 rotations = 60000 ms $ \\
	$ 1 rotation = 6 ms $ \\
	Transfer Time \\
	$ TimeToRead = 8192 kB / 133120 kB * 1000 ms $ \\
	$ AvgSeekTime = 4 ms $ \\
	$ TransferTime = AvgSeekTime + AvgRotDelay + TimeToRead $ \\
	$ TransferTime = 4 ms + 3 ms + 0.06 ms $ \\
	$ TransferTime = 7.06 ms $
	\item Random Blocks: \\
	$ TotalTransferTime = 20 * TransferTime $ \\
	$ TotalTransferTime = 20 * 7.06 ms $ \\
	$ TotalTransferTime = 141.2 ms $ \\
	Consecutive Blocks: \\
	$ BytesToRead = 20 * 8 kB $ \\
	$ BytesToRead = 160 kB => 1 Track $ \\
	$ TotalTransferTime = 1 * TrackSeekTime + 1 * AvgRotDelay + 20 * TransferTime $ \\
	$ TotalTransferTime = 4 ms + 3 ms + 20 * 0.06 ms $ \\
	$ TotalTransferTime = 8.2 ms $
	\item Record size: \\
	$ RecordSize = 120 B + 8 B + 12 B + 4 B + 1 B = 145 B $
	\item Blocking Factor: \\
	$ MaximumRecordCountPerBlock = math.floor( 8192 kB / 8 kB ) $ \\
	$ MaximumRecordCountPerBlock = 56 $ \\
	$ NumberOfBlocks = math.ceil( NumRecords / MaximumRecordCountPerBlock ) $ \\
	$ NumberOfBlocks = 715 $ \\
	$ WastedBytesPerBlock = BlockSize - ( MaximumRecordCountPerBlock * RecordSize ) $
	\item Average Search Time: \\
	$ NumberOfTracks = math.ceil( NumberOfBlocks * BlockSize / AverageTrackSize ) $ \\
	$ NumberOfTracks = math.ceil( 11.17 ) $ \\
	$ NumberOfTracks = 12 $ \\
	$ SeqScanReadtime = (NumberOfBlocks * BlockSize) * 1000 ms / 133129 kB $ \\
	$ SeqScanReadtime = (715 * 8 kB) * 1000 ms / 133129 kB $ \\
	$ SeqScanReadtime = 5720 kB * 1000 ms / 133129 kB $ \\
	$ SeqScanReadtime = 42.969 ms $ \\
	$ AverageSearchTime = 1 * AvgSeekTime + 0.5 * ( NumberOfTracks * AvgRotDelay + (NumberOfTracks - 1) * TrackToTrackSeekTime + SeqScanReadTime ) $ \\
	$ AverageSearchTime = 4 ms + 0.5 * ( 12 * 3 ms + 11 * 0.2 ms + (715 * 8 kB) ) $ \\
	$ AverageSearchTime = 44.585 ms $ \\
	$ AverageNonContinuousSearchTime = NumberOfBlocks * TransferTime $ \\
	$ AverageNonContinuousSearchTime = 715 * 7.06 ms $ \\
	$ AverageNonContinuousSearchTime = 5047.9 ms $
	\item AverageNumberOfBlockAccess: \\
	$ AverageNumberOfBlockAccess = log(NumberOfBlocks) $ \\
	$ AverageNumberOfBlockAccess = log(715) $ \\
	$ AverageNumberOfBlockAccess = 6.572 $ \\
	Average Block Search Time: \\
	$ AverageBlockSearchTime = AverageNumberOfBlockAccess * 7.06 $ \\
	$ AverageBlockSearchTime = 46.40 ms $
\end{enumerate}
